{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Description \n", "\n", "Smoothing Example Notebook\n", "\n", "This notebook provides example code based on the lecture material.\n", "\n", "If you wish to run or edit the notebook, we recommend downloading it and running it either on your local machine or on JupyterHub." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "import statsmodels.formula.api as sm\n", "\n", "%matplotlib inline " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "# Variables are\n", "# subject: subject ID number\n", "# age: age diagnosed with diabetes\n", "# acidity: a measure of acidity called base deficit\n", "# y: natural log of serum C-peptide concentration\n", "# Original source is Sockett et al. (1987)\n", "# mentioned in Hastie and Tibshirani's book \n", "# \"Generalized Additive Models\".\n", "\n" ] }, { "data": { "text/html": [ "
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" ], "text/plain": [ " subject age acidity y\n", "0 1 5.2 -8.1 4.8\n", "1 2 8.8 -16.1 4.1\n", "2 3 10.5 -0.9 5.2\n", "3 4 10.6 -7.8 5.5\n", "4 5 10.4 -29.0 5.0" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diab = pd.read_csv(\"data/diabetes.csv\")\n", "print(\"\"\"\n", "# Variables are\n", "# subject: subject ID number\n", "# age: age diagnosed with diabetes\n", "# acidity: a measure of acidity called base deficit\n", "# y: natural log of serum C-peptide concentration\n", "# Original source is Sockett et al. (1987)\n", "# mentioned in Hastie and Tibshirani's book \n", "# \"Generalized Additive Models\".\n", "\"\"\"\n", ")\n", "diab.head()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "diab.plot.scatter(x='age',y='y',c='Red',title=\"Diabetes data\")\n", "plt.xlabel(\"Age at Diagnosis\")\n", "plt.ylabel(\"Log C-Peptide Concentration\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear Regression\n", "After a lot of time with SKLearn, we're moving back to Statsmodels because of its fuller implementation of statistical tools, like confidence intervals.\n", "\n", "We'll also be using statsmodels' powerful formula interface. It lets one write complex models succinctly and without building complex design matrices by hand. Below, we write `'y~age'` to mean \"the y column is approximately $\\beta_1$ times the age column (plus a constant $\\beta_0$\". We could include more columns, or transformations of the age column, e.g. '`y ~ age + age**2 + acidity'`." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "fit1_lm = sm.ols('y~age',data=diab).fit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We create a very dense set of values to predict on. Remember: the _point_ of a model is to provide outputs for a wide variety of inputs. No need to only predict on the training or test values-- the model can predict on anything you ask it to!\n", "\n", "Further, it's *important when working with statsmodels that we make a named data frame*- if we only use a numpy array statsmodels won't know it's the 'age' variable." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "xpred = pd.DataFrame({\"age\":np.arange(0,16.1,0.1)})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the prediction line and confidence intervals" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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meanmean_semean_ci_lowermean_ci_upperobs_ci_lowerobs_ci_upper
03.9960310.2445903.5020714.4899912.6008285.391235
14.0043400.2423243.5149574.4937232.6107505.397929
24.0126480.2400623.5278344.4974632.6206565.404640
34.0209570.2378043.5407034.5012112.6305475.411367
44.0292660.2355503.5535624.5049692.6404215.418111
\n", "
" ], "text/plain": [ " mean mean_se mean_ci_lower mean_ci_upper obs_ci_lower \\\n", "0 3.996031 0.244590 3.502071 4.489991 2.600828 \n", "1 4.004340 0.242324 3.514957 4.493723 2.610750 \n", "2 4.012648 0.240062 3.527834 4.497463 2.620656 \n", "3 4.020957 0.237804 3.540703 4.501211 2.630547 \n", "4 4.029266 0.235550 3.553562 4.504969 2.640421 \n", "\n", " obs_ci_upper \n", "0 5.391235 \n", "1 5.397929 \n", "2 5.404640 \n", "3 5.411367 \n", "4 5.418111 " ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pred1 = fit1_lm.predict(xpred)\n", "prediction_output = fit1_lm.get_prediction(xpred).summary_frame()\n", "prediction_output.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Above, we use `fitted_model.get_prediction().summary_frame()` to get predictions _and_ confidence intervals." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax1 = diab.plot.scatter(x='age',y='y',c='Red',title=\"Diabetes data with least-squares linear fit\")\n", "ax1.set_xlabel(\"Age at Diagnosis\")\n", "ax1.set_ylabel(\"Log C-Peptide Concentration\")\n", "\n", "ax1.plot(xpred.age, prediction_output['mean'],color=\"green\")\n", "\n", "# CI for the predection at each x value, i.e. the line itself\n", "ax1.plot(xpred.age, prediction_output['mean_ci_lower'], color=\"blue\",linestyle=\"dashed\")\n", "ax1.plot(xpred.age, prediction_output['mean_ci_upper'], color=\"blue\",linestyle=\"dashed\");\n", "\n", "# CIs for where future data will fall\n", "#ax1.plot(xpred.age, prediction_output['obs_ci_lower'], color=\"skyblue\",linestyle=\"dashed\")\n", "#ax1.plot(xpred.age, prediction_output['obs_ci_upper'], color=\"skyblue\",linestyle=\"dashed\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Polynomial Regression\n", "In sklearn we would use polynomial_features. Here we use `vander` to build the matrix of transformed inputs. In particular, `vander` is a numpy function and therefore usable directly in the formula- it saves us from writing out `y ~ age + age**2 + age**3 + ...` and so on.\n", "\n", "`vander` is for Vandermonde. It's a matrix where the first column is $x^0$, the second is $x^1$, the third is $x^2$ and so on.\n", "\n", "` np.vander([6,3,5], 4, increasing=True) = \n", " array([[ 1, 6, 36, 216], \n", " [ 1, 3, 9, 27], \n", " [ 1, 5, 25, 125]])\n", "` \n", "\n", "Since we have a constant column in the matrix, we put a -1 in the formula to drop the additional constant term statsmodels would otherwise insert\n", "\n", "Note that this is **not** an _orthogonal_ polynomial basis. Our estimated coefficients will be more sensitive to the data than they need to be." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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meanmean_semean_ci_lowermean_ci_upperobs_ci_lowerobs_ci_upper
02.7404810.5081971.7125563.7684061.1562384.324724
12.8063260.4860911.8231153.7895381.2507244.361929
22.8709020.4647641.9308273.8109771.3421984.399606
32.9342190.4442192.0357023.8327371.4307144.437725
42.9962910.4244562.1377473.8548351.5163274.476255
.....................
1565.0205750.3624814.2873875.7537633.6096326.431518
1575.0317050.3794994.2640955.7993153.6025726.460837
1585.0434140.3971954.2400115.8468173.5947426.492087
1595.0557160.4155724.2151425.8962903.5861046.525328
1605.0686210.4346334.1894945.9477493.5766226.560620
\n", "

161 rows × 6 columns

\n", "
" ], "text/plain": [ " mean mean_se mean_ci_lower mean_ci_upper obs_ci_lower \\\n", "0 2.740481 0.508197 1.712556 3.768406 1.156238 \n", "1 2.806326 0.486091 1.823115 3.789538 1.250724 \n", "2 2.870902 0.464764 1.930827 3.810977 1.342198 \n", "3 2.934219 0.444219 2.035702 3.832737 1.430714 \n", "4 2.996291 0.424456 2.137747 3.854835 1.516327 \n", ".. ... ... ... ... ... \n", "156 5.020575 0.362481 4.287387 5.753763 3.609632 \n", "157 5.031705 0.379499 4.264095 5.799315 3.602572 \n", "158 5.043414 0.397195 4.240011 5.846817 3.594742 \n", "159 5.055716 0.415572 4.215142 5.896290 3.586104 \n", "160 5.068621 0.434633 4.189494 5.947749 3.576622 \n", "\n", " obs_ci_upper \n", "0 4.324724 \n", "1 4.361929 \n", "2 4.399606 \n", "3 4.437725 \n", "4 4.476255 \n", ".. ... \n", "156 6.431518 \n", "157 6.460837 \n", "158 6.492087 \n", "159 6.525328 \n", "160 6.560620 \n", "\n", "[161 rows x 6 columns]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# *cubic* polynomial (vander's input is one more than the degree)\n", "fit2_lm = sm.ols(formula=\"y ~ np.vander(age, 4, increasing=True) -1\",data=diab).fit()\n", "# the same model written out explicitly\n", "fit2_lm_long = sm.ols(formula=\"y ~ age + np.power(age, 2) + np.power(age, 3)\",data=diab).fit()\n", "\n", "poly_predictions = fit2_lm.get_prediction(xpred).summary_frame()\n", "poly_predictions" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax2 = diab.plot.scatter(x='age',y='y',c='Red',title=\"Diabetes data with least-squares cubic fit\")\n", "ax2.set_xlabel(\"Age at Diagnosis\")\n", "ax2.set_ylabel(\"Log C-Peptide Concentration\")\n", "\n", "# CI for the predection at each x value, i.e. the curve itself\n", "ax2.plot(xpred.age, poly_predictions['mean'],color=\"green\")\n", "ax2.plot(xpred.age, poly_predictions['mean_ci_lower'], color=\"blue\",linestyle=\"dashed\")\n", "ax2.plot(xpred.age, poly_predictions['mean_ci_upper'], color=\"blue\",linestyle=\"dashed\");\n", "\n", "# CIs for where future data will fall\n", "#ax2.plot(xpred.age, poly_predictions['obs_ci_lower'], color=\"skyblue\",linestyle=\"dashed\")\n", "#ax2.plot(xpred.age, poly_predictions['obs_ci_upper'], color=\"skyblue\",linestyle=\"dashed\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Logistic Regression\n", "Statsmodels provides logistic regression via the same formula-based interface." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the sake of doing logistic regression, suppose we have the binary outcome \"Was y above 4?\"" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "diab['y_bin'] = 1*(diab['y'] > 4) # multiply by 1 because statsmodels wants 1s and 0s instead of true and false" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.353988\n", " Iterations 7\n" ] } ], "source": [ "logit_model = sm.logit(\"y_bin ~ age\", data = diab).fit()\n", "logit_prediction = logit_model.predict(xpred)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is no built-in `get_predictions` for logistic regression. The code provided below can be used as a replacement. Because it was custom-written by your loving TFs, it will handle polynomial models that use `vander`, but little else. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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30.0550440.2500580.656198
40.0581080.2568600.659458
............
1560.8676310.9878990.999018
1570.8690550.9883220.999074
1580.8704620.9887290.999128
1590.8718530.9891230.999178
1600.8732280.9895030.999225
\n", "

161 rows × 3 columns

\n", "
" ], "text/plain": [ " lower predicted upper\n", "0 0.046716 0.230382 0.646460\n", "1 0.049354 0.236818 0.649700\n", "2 0.052128 0.243377 0.652945\n", "3 0.055044 0.250058 0.656198\n", "4 0.058108 0.256860 0.659458\n", ".. ... ... ...\n", "156 0.867631 0.987899 0.999018\n", "157 0.869055 0.988322 0.999074\n", "158 0.870462 0.988729 0.999128\n", "159 0.871853 0.989123 0.999178\n", "160 0.873228 0.989503 0.999225\n", "\n", "[161 rows x 3 columns]" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.special import expit\n", "import re\n", "def get_logit_prediction_intervals(model, new_data_df):\n", " if type(new_data_df) != pd.DataFrame:\n", " raise TypeError('new_data_df must be a DataFrame')\n", " \n", " # transform the raw data according to the formula\n", " new_data_dict = {}\n", " for x in model.params.index:\n", " # only presently supports Intercept, a named column, and polynmoials created via np.vander\n", " # the trick is finding the correct base column in the raw data\n", " if x == \"Intercept\":\n", " new_data_dict[x] = np.ones(new_data_df.shape[0])\n", " elif x.startswith(\"np.vander(\"):\n", " try:\n", " will = re.match(r\"np.vander\\((.*), ?(.*)\\)\\[(.*)\\]\", x)\n", " column, power, index = will.groups()\n", " except e:\n", " raise ValueError(\"Couldn't parse formula-derived feature {}\".format(x))\n", " new_data_dict[x] = np.vander(new_data_df.loc[:,column], int(power))[:,int(index)]\n", " else:\n", " new_data_dict[x] = new_data_df.loc[:,x]\n", " new_data = pd.DataFrame(new_data_dict)\n", " \n", " variance_mat = model.cov_params()\n", " standard_devs = np.sqrt(np.sum(new_data.dot(variance_mat) * new_data, axis=1))\n", " \n", " linear_predictions = new_data.dot(model.params)\n", " output = pd.DataFrame({\"lower\": expit(linear_predictions - 1.96*standard_devs),\n", " \"predicted\": expit(linear_predictions),\n", " \"upper\": expit(linear_predictions + 1.96*standard_devs)\n", " })\n", " return output\n", "\n", "logit_prediction_intervals = get_logit_prediction_intervals(logit_model, xpred)\n", "logit_prediction_intervals" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A pure logistic model" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = diab.plot.scatter(x='age',y='y_bin',c='Red',title=\"Diabetes data with logit-linear fit\")\n", "ax.set_xlabel(\"Age at Diagnosis\")\n", "ax.set_ylabel(\"Log-odds Log C-Peptide Concentration > 4\")\n", "\n", "ax.plot(xpred.age, logit_prediction_intervals[\"predicted\"],color=\"green\")\n", "ax.plot(xpred.age, logit_prediction_intervals[\"lower\"], color=\"blue\",linestyle=\"dashed\")\n", "ax.plot(xpred.age, logit_prediction_intervals[\"upper\"], color=\"blue\",linestyle=\"dashed\");\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A logistic model wherein the probability is a cubic function of Age" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.194005\n", " Iterations 10\n" ] } ], "source": [ "logit_poly_model = sm.logit(\"y_bin ~ np.vander(age, 4) - 1\", data = diab).fit()\n", "logit_poly_prediction = logit_poly_model.predict(xpred)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = diab.plot.scatter(x='age',y='y_bin',c='Red',title=\"Diabetes data with logit-cubic fit\")\n", "ax.set_xlabel(\"Age at Diagnosis\")\n", "ax.set_ylabel(\"Log-odds Log C-Peptide Concentration > 4\")\n", "\n", "logit_poly_prediction_intervals = get_logit_prediction_intervals(logit_poly_model, xpred)\n", "\n", "ax.plot(xpred.age, logit_poly_prediction_intervals[\"predicted\"],color=\"green\")\n", "ax.plot(xpred.age, logit_poly_prediction_intervals[\"lower\"], color=\"blue\",linestyle=\"dashed\")\n", "ax.plot(xpred.age, logit_poly_prediction_intervals[\"upper\"], color=\"blue\",linestyle=\"dashed\");\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Lo(w)ess\n", "Lowess is available in Statsmodels. It takes a fraction of the data that should be used in smoothing each point. Please note that you are not responsible for mastering lowess - this is merely for your edification." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "from statsmodels.nonparametric.smoothers_lowess import lowess as lowess\n", "\n", "lowess_models = {}\n", "for cur_frac in [.15,.25,.7, 1]:\n", " lowess_models[cur_frac] = lowess(diab['y'],diab['age'],frac=cur_frac)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note** Python's lowess implementation does not have any tool to predict on new data; it only returns the fitted function's value at the training points. We're making up for that by drawing a straight line between consecutive fitted values (scipy's `interp1d`). (There are other more sophisticated interpolation techniques, but the ideal approach would be to predict on new points using lowess itself. This is a limitation of the Python implementation, not lowess itself. R, for example, has a much fuller Lowess toolkit)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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EvA3c4q1HpFYswzCMHSkq8p9KIOA5tHx5ysTZxvffwyl/zqP35pf4g115i5OZznFZlQTHj7F4MC4EdZGqdgcOxWUeMwzDSBt+5hAE2CFBTYpYtw6GDYODDoKP5zXg3ryhLKGA3VnBLdycVUlw/CiCjaq6EUBEaqnqN0C71Ipl5AxZalwz0sv69W6ox68iSOVcAlV4/nnYbz+480445xz47vtqDHn6UOrXKeO6Wg8wne58dO3krAl/7UcRFItII2AS8K6IvIZlETOSwYQJ7p/ds2fWGdeM9LJ0qVvHqgiS3SOYPx+6d3f5bpo1g08+gaefhubNcTuLiuj/7l9p3qyMWz7pkdzGU4gfY/GfVXWVqo4A/gmMBc5IsVxGVaekBPr1Y2jpCB5YfWHWGdeM9LJ4sVvvvbe/8oFJZcnqEaxaBYMHw6GHOmXwyCOuI3vUUSEF8/Opc0wnhl5fnWnT4OOPk9N+qomqCESkmogsCGyr6oeqOllVN0c7zzAqZMkSfqnRgrsYylU8wANcmVXGNSO9/O9/bh1LELlkuJCWl8MTT0DbtjBqFPztb/DddzBgAFSvHvm8AQNgt93gllsSaz9dRFUEqloOzBWR1mmSx8gVCgp4a2M3ALrwBVfxAM+U/jVrjGtGelm82OUgaNLE/zmJzi6eNQuOPNJ1VPfdFwoLYfRofzLssgv84x/w3nvw6afxy5Au/NgIdgcWisj7IjI5sPipXESWiMh8EflKRArDHO8mIqu941+JyPBYv4CRpeTnM/Wwm9idn/iw/mmcUG0al5SNYfJn2WFcM9LL4sWuN+BnDkGAeGcXl5ZC//5w+OHOZfWZZ9wQT8eOsdUzcKCzFWdDr8BPPoJEv0Z3Vf01yvEZqnpqgm0YWcaWLfD212048/9KqX3VFCY23ZMe51Tj7LPhrbegW7dMS5iDlJS4obmCgsS9XZJZF04RdArNfl4BgUllGzdC7dr+zxs8GB57DK6+Gm6+GRo0iK3dAHXrul7B0KHw+edwxBHx1ZMO/PQIenm2gW0L0CvVghlVm88+g9Wr4ZQz60DnztTfsylTpzpj4Omnu264kUaS6cGVZG+wLVucTok1yUw8nkPjxjklcMMNcM898SuBAH//OzRtWvl7BX4UQc8w+072Wb8C74jIbBHpH6HMkSIyV0TeFJEDI5QxqhhTpjjbcI8gD7smTeCdd5y3x0knwddfZ06+nMLz4KK01GnnRDy4klmXx9KlUFbm32MoQKyK4NtvnZH3mGOS9+CuWxeuvdb1cmfOTE6dqSBa9NHLRGQ+0E5E5gUtPwLzfdZ/tKp2xCmOQWFiFM0B2qhqB2AUbq5COFn6i0ihiBSWmHthlWDqVPeHC33jatHCGdhq1IATT9wecdJIIUuWQM2aO+6L14MrmXV5BFxHY+0RBGYX+7ETlJbC2We7oHbjx7v7L1kMGuRecipzryBaj2A8cBow2VsHlsNU9Vw/lavqCm+9EpgIdAk5vkZV13mfpwJ5ItI0TD1jVLWTqnbKz5KZekZkli6FBQugV4QBxn32gbffdtmoevaElSvTK1/OUVAAm0M8wuMNj5DMujziVQSx9AiuugrmzYNnn91+XrKoVw+uuca9/Myaldy6k0W0MNSrVXWJqvYFioEtuKGeen7cSUWkrojUD3wGTgQWhJRpLuL8AESkiyfPb/F+GSM7mDrVrU85JXKZDh3c8FFxMfzpT26UwUgR+fkwdqx7HW7QwK3Hjo3PyJvMujwWL3bumM2bx3ae30xl48fDmDEubtBJJ8UtZlQGDYJdd4V//Ss19SeMqkZdgMuBX4GFuCGh+cA8H+ftBcz1loXAjd7+gcDAoLoXemU+B46qqN7DDjtMjezm1FNV99xTtby84rJvvqmal6d6zDGq69enXracZuVK1Zkz3boS1XXqqart28d3bvv2qqedFvn4N9+o1qun2rWr6pYt8bXhl1tvVQXVwsLUthMJoFAjPFfFHY+MiCwGDlfVSvGm3qlTJy00l5KsZeNG95bWr5+bqemHF15wYVx69YKJE92Qs5E7HHCAC/D26quxn3vKKfDTTzBnzs7HSkudS+fy5fDVV8kfEgpl9Wo3QnbssfBaBnI8ishsVQ3rhOvHa2gZYB1zIylMn+7+gJHsA+Ho08fN6JwyBS66yE37N3KDsjIXXiJW+0CAVq0iG4tTaRcIR8OGMGQITJ4MX36Z+vZiwY9t/AdguohMATYFdqrqvSmTyqiyTJ3qho1jnTA2YAD88Ycbx911V9ebiGWWqZGdLF/ubM/xKoKWLcNPKgvYBa6/Hk726wyfBK68Eu6919kKJk5MX7sV4adHsBR4F6gJ1A9aDCMmVN1b/fHHO2UQK9dd52ZqPvSQm/FpVH3eesutDz44vvMDLqTBmcoC8wWOPhpuvTUx+WKlUSPXE5k0CebOTW/b0aiwR6Cqt4Dz/FHV9akXyaiqfPcd/PCDm2ATDyLwn//A77+7P/Cuu7qudqUmyaEWcoktW+COO6BLl/jDMwQnqNl77+3zBWrVcsllkjlfwC+DB8N997lewSuvpL/9cPjJWXykiCwCvva2O4jIwymXzKhyTJni1rHYB0IRgUcfhTPPdLFgnnoqKaKlBku8kxDPPed06PDh8Q8DhqasDNgFnnkmPXaBcOy6q1MGr77qZKkURHIn0u1uoF8ArYAvg/YtqOi8VC3mPpq9nHCC6oEHJqeujRtVe/RQrVZNdeLE5NSZVFauVK1Tx/kLBpY6dZLjmpkDbNmiuvfeqh07+nMzjsS6de7S//vfquPGuc/XXZc8OePlt99U69dXPeus9LVJFPdRPzYCVDXU7l6WTGVkVH3WroWPPkqsNxBMrVrO2Na5s/MqmjYtOfUmjRSEWsgmXn89sTHwCROct9A//5mYU0Dduu4N/IMPMmcXCEfjxs5w/PLLbpZ9pvHlPioiRwEqIjVF5Fq8YSLD8Mu777ox32iziWOlXj3nhdS2LfTuXcmm76cg1EK2MHs2nHGGG77bujX288vK4PbboX17F4k2UVq1cvdfrVpOwVSWeShDhrh7uDIoJj+KYCAwCGiBCzVxiLdtGL6ZOtX5Ue+U4zVBGjd2cYny850b4KJFya0/KiUlTvuEC4SYglALKSPa94iRsjL35p2X597oX3gh9jpeesl59vzzn1CtWuLyBWwBzzyz3WZQGWjSBK64wn3ftN634Yg0ZlRZF7MRZB/l5aq7767617+mro3Fi1WbN1dt0UL1xx9T1842xo93Y/4NG7r1+PHhyyUzbEMq8Ps9fPLAA24cfvx41YMOUt1/f9WyMv/nl5U5O9IBB3jnJUG+GTNUn3025tPSQkmJat26queck/q2iGIj8GMsfhpoFLS9K/BEReelajFFkH3MmePutCefTG078+apNmqkus8+qj//nMKGqoohOMnfY9kyF7fnpJOc8p8wwVX50kv+63j55e2KpMpc5wq47jpVEdVFi1LbTjRF4GdoqL2qrgrqQfwBHJr0rolRZQm4jaZ6BufBB7shqBUrXMTSVatS1FBVMQQn+XtceaUbGnr4YWfg/etfnf3mttvcU7wiysudb33bts7Xv8pc5wq45ho3cnjbbZmTwY8iqCYiuwY2RKQx/kJTGAbgHs6dOsFuu6W+rSOPdN5EixbBqafC+lRMgawqhuAkfo/XXnPX/eabYc893b7q1V3Kx7lz4Y03Kq7j9dedX/2NN7pzq8x1roD8fBem+vnnnW0kI0TqKgQW4AKcl9Ct3vINcH5F56VqsaGh7KKkxHV7b745ve2+9JKbY9Cxo2pRUQoaCIxdN2iQlLH1jBH0PYpq7avvDns/5iq2blVt3drZBDZv3vHY5s0u5HiXLtHnA5SXqx52mOpee4WEg64q17kCfvlFdZddVM87L3VtkIiNwJ3PgbjcAVcAB/g5J1WLKYIkkgZD5nPPubvsiy9S1kRE3hi3ShvU3aLNmpbpjBkpaKCC67dkiftjv/12CtpOIuW/rNRHrv9R69Ut2/G3ivb9go4VFrrf+Nlb/he27KOPuuM7XIeQuqdMcWXGjg0jYGU3uCeJa65xLy/ffpua+pOhCKoDewCtA4uf81KxmCJIEkn2FolE376q+fmxeY4kBe/7fV2vk7aVbzWv+lZ99NH0NF1erjpmjDOcgmpBgeqmTelpOx4GD3Zy9ujhfqtu3VTLx0W5P0LunbuOelVBdXn9dmHvpY0bVVu2dMmFwp1fPm68Hn64aps2O/cocomff3aX5YILUlN/QorA6wUEMpTNw2eGslQtpgiSwMqVurV2Xb2au/ULOmuqvDG2blXdddfU3dgRCfE2+YOGelK1txVU//731D5sli5VPfFE1/QJJ2x/G3744dS1mQjvv+/ku+wyp8BGjXLbU2v23nb9drg/wnjynMwU3Y9FO5cNYuRId2j6pD92Ov+dmqcoqD7ySEYuQaViyBDV6tVVv/8++XUnqggWA00qKpeuxRRBEpg5U8fUuUJB9XyedrdBgwau+51EPv7YVf3CC0mttmJmznRvm0EPm631G+nQ81coqB57bPJHGcrL3bBGgwbOL3z0aLevvFz16KNV99hDdcOG5LaZKGvWuN7KvvtuTwO6aZPqXi1K9eBqC3Qr1bZfw8D9EXJtN1ND67FGL+OhncsGsWGD6m67qfbosmqH88tBj67+qbZstkk3bkz7Jah0/PSTau3aqhddlPy6E1UEHwA1KiqXrsUUQeL8/l2JNmWlgmorirQ8RT2CG25wbzd//JHUaismiv/5uHHuj9a6teqXXyanueJi1ZNPds1066b6ww87Hp8+3R27++7ktJcMtm51w3Yiqp98suOxCY+uVlB9hvMq7BF8yhFurgBnRu0RqKredZc7/FmtY7eVnUY3BdUH71iTpm9e+Rk82P1vFi9Obr2JKoKxwMfAMODqwFLRed65S7yhpK/CCQEIMNLrdcwDOlZUpymCxLnyStVqUqZ/qz5WQfV/tfZPiY2gQwf39p0RonibFBa6MetddlF98cXEmnn6afeCu8sublglki2kZ0/Vpk3dW3imKStTvfRS9++/Y9DSnR7aZWWqh+35q7aWIi2tnx/ZRtCggd5eY7iCakntlhV69qxdq9qkiepJHZZvO79btem6e6P1Wlqaym+cXSxfrlqrluollyS33kQVwc3hlorO0+2KoGmU472ANz2FcATwRUV1miJIjPnz3dvGZZepLpzxm/PUuD/5T6fiYnd33Xln0qv2TxRvk59+Uj3qKCfjjTfGZ8x+4w13fteuFY/pfvGFK3vrrbG3k0zKy1Uvv9zJclONOyI6C7z3nitzz+CiqF5DJxyzSdu3V9+ePYFewevPrdKPHl2koHrffUn7elWGK65QrVFj595lIiTsNeTqoD5Qz2959acIHgX6Bm1/C+werU5TBPFTXq56/PHOgPvrr267WbPU+C6PGePurvnzk193sti4cfub8Wmnqa5eHdv5PXq4noVf43Pv3u65+/vvsUqaHMrLVa+91n3fa2rc54YEowznnHiiauPGkYf2Nm50w2yDB/uXYdMmF39ozz3dMFqzZtvtE8Z2iotVa9Z092eySLRHcBDwJVDkLbOBAys6zzv3R2COd07/MMffALoGbb8PdApTrj9QCBS2bt06eVcmxwjEcXnooe37zj7bPcwSSf4RjjPOUG3VKvn1JpvyctUHH3S9pP33V/3uO3/nLfKcZG6/3X9b8+a5Mflhw+KTNVH++U8n86C//qzlDRpuVwIRDLyBGFGR5A3YPl57LTY5Ap5KoPrf/8b3XXKBQYNcryBZQRQTVQSfAt2DtrsBn1Z0nld2D2/dDJgLHBtyfEoYRXBYtDqtRxAf69c7A2n79jvO3Hz4YXcXJNMwtXGj85wZODB5daaaDz5w49eNGqm+9VbF5f/+dzeOG6t9/ZxznD0hpUHxwnDbbe53vvRS1bKf/QdzO/dcd6i4eOc6b77ZTYCKxxngwgvdC8jatbGfmyssW+Z6Bf37J6e+RBXBXD/7fNQzArg2ZJ8NDaWJESPcrz19+o77A2+2jz+evLbefdfVOXly8upMBz/84BRltWrOwydSb2bVKqfoLrww9ja+/db1PmIZTkmUe+5xv8e55zpvIVX1Hbrhhx9U8/LCD1Ecc4xqp07xyVRe7tJIGtG57DJ3/ZMRJiVRRTAR+CdQ4C03AZN8nFcXqB/0+VPgpJAyp4QYi2dWVK8pgthZssSN5fbps/Ox8nLn333uuUloyDMYXjVgvdaqlZ1/9LVrVc/0PCHPOy+8738g5n5hYXxtXHKJe9NbulRTEz4hqM4HH3SynnVWSAyfkHLRGDzYKceFC7fvW7/ePaCGDk2e2MbOFBWp5uWV640XL3dvbQncK4kqgl09F8853nI/sKuP8/byhoPm4mYl3+jtHwgM9D4L8BDwP5yb6U72gdDFFEHsnHmme+lbujT88T59XEKXhMbzg8IGtJVv9U/tVyRQWWYpL1f917/cv6Nz5x2HRcrK3ASsI46Iv/4lS9xD9OLj/pf8MB9Bv8PYvAHbDOGJzKYuKXEdh1NP3b7vnXfc9XnzzcRFNqIwfrx+UesY3Vq77vYhvDjvlbgUAVAbyA+zfzegdqTzUr2YIoiNgBtgNLfF0aNdmbintQdNMvqevRVUR+YNyfogYZMmuXhBzZurfvqp2/fmm+5ajRuXWN1DL1+voPoWXjyKZEzqC/odnuICFcr0xGrvaOnSxH+H//zHifi+F5x02DBnyLQx/hQSbmJkAvdKNEUQLR/BSOCYMPt7APdFOc+oJGzZAoMHu/jw114buVy3bm49fXqcDQUlEJlKLwB61ZqW9QlEeveGzz+HunXdNXriCRg1Cpo3h7POSqzuW/osYv9q39CPsfxBI7cz0aQr3u/wLOdxMU9yAu8zqe551P45gTo9rrwSWrd299GmTTBtGnTp4pKvGykiXGKeAElO0BMtwUxXVe0fulNVx4nIDUmTwEgZo0fDwoUwaRLUrh25XLt27uE2fTpcemkcDQUlEJnCKbTjG/Yu+65KJBA58ECYORP69IF+/dy+m2+O/P/0S+12bXgm788csWk6xzCDg5lPs/W/k//qATT70iUradZs+7phQ5f1KyoFBYzfcAYXMZbufMBr9KbOVpLyO9SuDf/+N5x3HtSvD1u3ugQyRgoJl5gnQJIT9ERTBNFuOz+ZzYwMUlICw4fDiSfC6adHLyvi3ng/+MD1Oyt84ISSnw9jx7L+kiuYvrEbg6o/CmPHuv1VgMaN4c03Yeilv/HS67UZcPwKYN/EKs3Pp9OTg3jswkE8Vn4JheWdWVmzNWvuDK9h8vKgadMdlUPouvjr2ly59QmOrTaDyXXPY5etJPV3+L//c9di+nT45hs4//ykVGtEwvtfbXsDKS11Glkk6f+vaIpgpYh0UdWZwTtFpDNQkjQJjJRw440uTeP99/t7sHfr5lLlLV4M+8b5jJtedgybqUWvam8BVespUWPIFdz79IPcA8hxwOWXu3GiROjbl4t79ODiJUugoCHk12TTJqfEA8vKleHXP/zg1mvXBldYn2Orf8IbNf5C3aFDYMCApD4sRFze6VTnnjaC6NsXevRww0D16sG6da4nkOyXrEjGA6ALLkTECOA0b7kFN1v48EjnpXoxY3HFFBa6GaxXX+3/nG++cTaoMWPiaNAzag3lTs1jk26gdkqimWaMwGSL0GXRokxLpqWlqku//FULax2l0+impdRKjuHZqHIQj7FYXU+gC26I6CJvEU8JfJFcdWQkC1W44gr3wjB8uP/z2rbdbieIGc+oNYNj6EQhddiYdGNWRpk5M7b9aaR2bWi15QcOq72Q7kynNpvcgap0/Y2UE21oCFVdiYs2amQJ48bBZ585D5eGDf2fF7ATTJ8eh52goIDSTdUopBNDAg5lSTZmZZQuXWLbn27CGRWr0vU3Uo4ZfasQa9fC0KHQuTNceGHs53fvDitWwPffx3hifj4z//EiW6jJMXVmQ506VcpYzP77O5tAMJdf7vZXBgJGxTp1oEGDqnf9jZQTtUdgZBe33w4//QQTJ0K1OFR88HyCtm1jO3dGzR4AHDX5eujwUNV7CI0aBX//uxsO6tKl8iiBAMFGxVQYE0MpKUlfW0bKEWdD8FFQpK6qrk+xPBXSqVMnLSwszLQYlY7vv3c+7+eeC08+GV8dqtCihVMI48fHdu6f/uR6E/Pnx9e2kUVMmOBcGmvWdENSY8c6RWRUakRktqp2CneswvdGETlKRBYBX3vbHUTk4STLaCTIkCHOcHjHHfHXEWon8MvWrfDpp9C1a/xtG1lCSYlTAqWlsHq1W/fr5/YbWYufAYT7gD8BvwGo6lzg2FQKZcTGlCluuflm5/mTCN27u+Gl777zf868ec69+ZhwAUmMqkW4sAfmoZT1+BpJVtVlIbvKUiCLEQebNrneQLt2zm00UeKJO/Txx25tiiAHMA+lKokfRbBMRI4CVERqisi1eMNERua5/35nH7j//sTj3wDssw/ssUdsimDGe5to3XwTrWrb8ECVJ1EPpZISmDUrvUNJmWgzy/CjCAYCg4AWQDFwiLdtZJgVK+DWW10soZNOSk6dsdoJdPwEZry+imN+mwRt2jhDolG16dsXiorgvffc2q+heMIEd4/07Jm+eyUTbWYhvr2GKgvmNbSd88+Hl16CRYtgr72SV+9jj0H//i6wWLt2UQqWlLC4VXf23bSARxjAAMa4N8SiInMpNHakpMQ9iEtLt+9L9b2SiTYrMdG8hiLOIxCRUUBELaGqVyZBNiNOPvkEnnvOBZdLphIAZzAGF400qiJYsoQZ1Y4DoCueoSBgOMzBP5oRhYCROfihnOp7JRNtZinRhoYKgdm4TGUdge+95RDMWJxRyspcopAWLWDYsOTXv/feru4K7QQFBczYfDiN+Y39A2YjMxwa4ciEkdkM276JFnTuaVV9Ghd4vbuqjlLVUcAJOGXgCxGpLiJfisgbYY51E5HVIvKVt8QQJi13eeIJmDMH7r7bZc9KNr7tBPn5fJx/Bl2rfUa1BvUttIERmUyEwbDQG77xE2JiD6A+8Lu3Xc/b55fBOC+jBhGOz1DVU2OoL6f54w+44QbnqtmnT+ra6dbNBbD79lvYbz9vZ0hYgZ9/hu9/bsDfhneDU9+zcAPZTqrDRqQ7DEam2sxC/HgN3Ql8KSJPichTwBzg334qF5GWwCnA43FLaOzAiBHw++8wcmQcmcRiIDCf4IMPvB1hvC8++cQdOubkei7Snf3Jspd0edfk56f/XslEm1lGhYpAVZ8EDgcmesuR3pCRH+4HhgLlUcocKSJzReRNETnQZ705yYIF8NBDLvHUIYektq2994aWLT07QYSwAjPe2UCdOtCxY2plMVKMhY3IeSIqAhHZz1t3xA0FLfOWPbx9URGRU4GVqjo7SrE5QBtV7QCMAiZFqKu/iBSKSGFJjt6cqjB4sBvqvPXW1Le3g53gxyVhwwrM+Eg5/PDkTGQzMoiFjch5ovUIrvbW94RZ7vZR99HA6SKyBHgeOF5EngsuoKprVHWd93kqkCciTUMrUtUxqtpJVTvl52j37tVXYdo0uO02aNIkPW126+Zy5H6zZe+dvC/Wbq7FV9/tYmElqgLmXZPzRPMa6u99PFlVuwcvQK+KKlbVYaraUlULgHOAaap6XnAZEWku4ka6RaSLJ89vcX6XKsuGDXD11dC+vZvolS62xR2a13gn74vPrnqB8nIxRVAViMW7xsI1VEn8GIs/9bnPFyIyUEQGeptnAQtEZC4wEjhHs22qcxq46y5YutQZiGukMZXQXntBq1aewTgkrMDHed2pVg2OOCJ98hgpxE/YCAvXUGWJGGJCRJrj4gs9B/wfLnE9ODfQR1R1v7AnpphcCzFRVOTcN3v3huefT3/7F1wAb70Fv/yyo5dS9+4uNWYO/RS5jYVryHriTUzzJ5wtoCVwL9vtA1cDNyRbSCM8117rHsB33ZWZ9rt1c8+Ar4PizW7eDJ9/bmGncwozKFdpIg40eC6iT4vImar6ShplMjymTYOXX3ZeQq1aZUaG4PwEBxzgPs+ZAxs3WkaynMIMylUaPzaC6SIyUkTmiMhsEXlARNLkt5K7bNni4gntuafrFWSKPfcMshN4zJjh1qYIcggL11Cl8WN6fB74CDjT2z4XeAHokSqhDBg9GhYuhEmTXC7iTCHi7AFTp7q5DCJOEbRtC7vtljm5jAxg4RqqLH56BI1V9VZV/dFbbgMapViunKakBIYPhxNPdElnMk23bvDrry7vQXm5C4FtvYEcxcI1VEn89Ag+EJFzgBe97bOAKakTybjxRli/3qWfTGU8Ib+E5jH+/XczFBtGVcKPIhiA8xR6DpeopjqwXkSuBlRVI0UVNeJg9mx4/HGXkH7//TMtjaOgAFq3doogMI/BegSGUXWoUBGoav10CGK4MfgrrnC97uGVKDNDIO7Q1KnOg7B5cxeUzjCMqkGFNgJxnCci//S2W3nhIIwkM24cfPYZ3HknNGyYaWl2pHt3ZyeYONENC1WGISvDMJKDH2Pxw8CRuNnFAOuAh1ImUY6ydi0MHerscBdemGlpdiZgJygttWEhw6hq+LERHK6qHUXkSwBV/UNELPBwkrn9dvjpJ/fGXc2Pek4zBQUuwkBRkRmKDaOq4eeRs0VEquMMxYhIPtETzRgx8v33cO+9cNFFcPjhmZYmMj17QuPGLgqqYRhVBz+KYCQuM1kzEbkd+BifqSoNfwwZ4iaN3XFHpiWJzl13uRhD1atnWhLDMJKJH6+hcSIyGzgBF4H0DFX9uoLTDJ9MmeKWu+923jiVmUaN3GIYRtUioiIQkcOBMcDewHygn6ouSpdgucCmTa430K6dcxs1coiSEgvVECt2zVJGtKGhh4BrgSa4MNT3pUWiHOKBB5x94P77Le9vTmEJXmLHrllKiZaYZo6qdoy0nSmqSmKaFStcT+D44+G11zItjZE2LMFL7Ng1SwrREtNEsxE0EpG/RNpW1VeTJWAuct11LtT0vfdmWhIjrQQSvAQ/1AIJXuyhFh67ZiknmiL4EDgtwrYCpgji5JNP4LnnXHA5C9WQY1iCl9ixa5ZyomUouzgZDXhzEAqB5ap6asgxAR4AegEbgItUdU4y2q2slJW5hDMtWsCwYZmWxkg7gQQv/fq5t9otWyzBS0XYNUs5fmYWb0NE3gh9mPtgMPA1Lul9KCcD+3rL4cBob11leeIJl+pxwgSoWzfT0hgZwRK8xI5ds5QSkyIAWsRSWERaAqcAt+NCWYfSG3hGncX6cxFpJCK7q+pPMcqVFfzxB9xwgwvR0KdPpqUxMkp+vj3MYsWuWcqINarNlzGWvx8YSuSQFC2AZUHbxYRRNiLSX0QKRaSwpKQkRhEqDyNGuKQuI0da9E7DMCoPERWBiOSLyAHB+1T1EhE50Is3FBURORVYqaqzoxULs28nf1ZVHaOqnVS1U36WvhEsWAAPPQQDBsAhh2RaGsMwjO1E6xGMAsI9dVviDLwVcTRwuogsAZ4HjheR50LKFAOtQupe4aPu+CkpgVmz3DpNbajC4MHQoAHcemvqmk056bh2hmGknWiK4GBV/TB0p6q+DVQYf1JVh6lqS1UtAM4BpqnqeSHFJgMXeMlvjgBWp9Q+kI7ZiWHaePVVmDYNbrsNmjRJfpNpwWZ2GkaVJdrM4u9UtW2EY9+qajvfjYh0A65V1VNFZCCAqj7iuY8+CJyEcx+9WFWjThuOe2ZxOmYnhmljQ+3G7N90JY0aV2f27O05f7MKm9lpGFlPvDOLvxeRXqo6NaSyk4EfYhFAVacD073PjwTtV2BQLHXFTTpmJ4Zp4y69hqXF1XnmuSxVAmAzOw2jihPt0TQEeENEzgYCBt9OuLSVsc4lyDzpmJ0Y0kYRrblz0xD6nLGR446rnbx20o3N7DSMKk1EG4GqfgccjAstUeAtHwLtvWPZRWB2Yp06zmpbp07yZyeGtHFttfuQmnncNTKLlQCk59oZhpExItoIKisJRx9NR0zzkhKmvfQbJwzaj1tvhZtuSk0zacfiwRtG1hLNRpB7iiANbN3q5gps2ACLFrk0lIZhGJkkXmOxESe33w4LF8LEiaYEDMOo/MQaYsKogJdecqEkzj8fevfOtDSGYRgVU2GPQETms3PYh9W40NK3qepvqRAsGykshAsvhKOOgsces3hChmFkB36Ght4EyoDx3vY53noN8BQ7Jq/JLYKMp8s359O7t7OhTpwItWplWjjDMOImxxwj/CiCo1X16KDt+SLyiaoeLSKhISNyhwkTXKKMmjXZsKk6Z+zxHWvWNOGTT6BZs0wLZxhG3AT9t9m82blK9+2baalSih8bQT0R2ZYsRkS6APW8za0pkaqyU1LibpTSUspXr+GijaOZ/cOujB+9mvYVRmEyDKPSEvTfZvVqt+7Xr8oHWvSjCC4FHheRH71Ioo8Dl4pIXeCOVApXaQmEXAD+xXBe4mz+W2s4p7XLvnl2hmEEEfTf3kYgnEoVpsKhIVWdBRwsIg1x8w5WBR1+MVWCVWq8kAvP04dbGMHFPME1ci8UDM60ZIZhJEKOhlOpsEcgIg1F5F7gfeA9EbnHUwq5S34+M4dN5GKepGv1Txld+2rkCQu5YBhZT46GU6lwZrGIvAIsAJ72dp0PdFDVv6RYtrBUhpnFxcXQuTPUrlnGzMfmkX9oyyp/oxhGTlEFvYYSnVm8t6qeGbR9i4h8lRTJspD1691EsfXr4d13q5N/0KGZFskwjGSTn19lFIAf/BiLS0Wka2BDRI4GSqOUr7KUl7sJY199Bc8/DwcdlGmJDMMwEsdPj2Ag8EyQXeAP4MLUiVR5uflmeOUVuOce6NUr09IYhmEkBz9eQ3OBDiLSwNteIyJXAfNSLFulYvx4l3O4Xz8YMiTT0hiGYSQP30HnVHWNqq7xNq+uqLyI1BaRmSIyV0QWisgtYcp0E5HVIvKVtwyPQfa08fnncMklcOyx8PDDFkPIMIyqRbxhqP08CjcBx6vqOhHJAz4WkTdV9fOQcjNUtdKmvly6FM44A1q0cMNCoXNNDMMwsp14FUGF2Wy8xPTrvM08b8mqLDjr1sHpp7tZ5tOmQdOmmZbIMAwj+URUBCKylvAPbgHq+KlcRKrjEt/vAzykql+EKXakiMwFVgDXqurCMPX0B/oDtG7d2k/TCVNe7nIKzJ8PU6bAAQekpVnDMIy0Ey15fX1VbRBmqa+qvnoSqlqmqocALYEuIhLqcDkHaKOqHYBRwKQI9YxR1U6q2ik/Tb69N90EkybBvffCSSelpUnDMIyMkJYMZV58ounASSH716jqOu/zVCBPRDI+APPss3DHHdC/P1x5ZaalMQzDSC0pUwQiki8ijbzPdYAewDchZZqLOB8cL7x1NSCjGc8+/RQuvRS6dYMHH4zgIVRSArNmVfnQtIZRqbH/YdJIZY9gd+ADEZkHzALeVdU3RGSgiAz0ypwFLPBsBCOBc7Si4EcppKgI/vxnaN0aXn7ZRZ/diQkToE0b6NnTrSdMSLuchpHz2P8wqVQYdK6ykaqgc2vXQteuThl8/jnst1+YQiUl7qYrDYqwUaeOOymH4pIYRkax/2FcRAs6lxYbQWWnrMxlolu4EF58MYISgJxNWmEYlQr7HyadeOcRVCn+8Q/nIvrww3DiiVEK5mjSCsOoVNj/MOnkfI/g0Ufhvvucd9Bll1VQOEeTVhhGpcL+h0knp20E773n5giceCJMngw1/PaPqmDSCsPIOux/GBOJJqapknzzDZx1Fuy/v8st4FsJQM4lrTCMSon9D5NGTg4N/fornHIK1KoFr7/uepeGYRi5Ss71CDZtgr/8BZYvhw8+MPuSYRhGTikCVRgwAGbMcPNPjjwy0xIZhmFknpwaGrrzTnj6aRgxAs45J9PSGIZhVA5yRhFMmgQ33OAmjg2vlHnQDMMwMkPOKIJOnVwwuSeesFSThmEYweSMjaBlS3jssUxLYRiGUfnImR6BYRiGER5TBIZhGDmOKQLDMIwcxxSBYRhGjmOKwDAMI8cxRWAYhpHjmCIwDMPIcVKmCESktojMFJG5IrJQRG4JU0ZEZKSILBaReSLSMVXyUFICs2a5tWEYhrGNVPYINgHHq2oH4BDgJBE5IqTMycC+3tIfGJ0SSSZMcMmue/Z06wkTUtKMYRhGNpIyRaCOdd5mnreEpkPrDTzjlf0caCQiuydVkJIS6NcPSkth9Wq37tfPegaGYRgeKbURiEh1EfkKWAm8q6pfhBRpASwL2i729oXW019ECkWksCTWB/iSJVCz5o778vLcfsMwDCO1ikBVy1T1EKAl0EVEDgopEi78205JlFV1jKp2UtVO+bGmpisogM2bd9y3ZYtlpDEMw/BIi9eQqq4CpgMnhRwqBloFbbcEViS18fx8GDsW6tRxOSnr1HHbluvUMAwDSK3XUL6INPI+1wF6AN+EFJsMXOB5Dx0BrFbVn5IuTN++UFQE773n1n37Jr0JwzCMbCWVYah3B54Wkeo4hfOiqr4hIgMBVPURYCrQC1gMbAAuTpk0+fnWCzAMwwhDyhSBqs4DDg2z/5GgzwoMSpUMhmEYRsXYzGLDMIwcxxSBYRhGjmOKwDAMI8cxRWAYhpHjiLPXZg8iUgIUZVqOMDQFfs20ED7IBjlNxuSRDXJmg4yQHXJGk7GNqoZ1ncw6RVBZEZFCVe2UaTkqIhvkNBmTRzbImQ0yQnbIGa+MNjRkGIaR45giMAzDyHFMESSPMZkWwCfZIKfJmDyyQc5skBGyQ864ZDQbgWEYRo5jPQLDMIwcxxSBYRhGjmOKIEFEpJWIfCAiX4vIQhEZnGmZIuFljPtSRN7ItCyREJFGIvKyiHzjXdMjMy1TKCIyxPutF4jIBBGpnWmZAETkCRFZKSILgvY1FpF3ReR7b71rJZTxLu/3niciEwPh6zNFOBmDjl0rIioiTTMhW4gsYeUUkStE5FvvHv2vn7pMESTOVuAaVd0fOAIYJCIHZFimSAwGvs60EBXwAPCWqu4HdKCSySsiLYArgU6qehBQHTgns1Jt4yl2Tv50PfC+qu4LvO9tZ5Kn2FnGd4GDVLU98B0wLN1ChfAUO8uIiLQCegJL0y1QBJ4iRE4R6Y7LBd9eVQ8E7vZTkSmCBFHVn1R1jvd5Le7BtVPe5UwjIi2BU4DHMy1LJESkAXAsMBZAVTd72e0qGzWAOiJSA9iFZGfVixNV/Qj4PWR3b+Bp7/PTwBnplCmUcDKq6juqutXb/ByXqTBjRLiOAPcBQwmTTjcTRJDzMuBOVd3klVnppy5TBElERApwORi+yLAo4bgfdxOXZ1iOaOwFlABPekNYj4tI3UwLFYyqLse9ZS0FfsJl1Xsns1JFZbdA1j9v3SzD8lTEJcCbmRYiFBE5HViuqnMzLUsFtAWOEZEvRORDEens5yRTBElCROoBrwBXqeqaTMsTjIicCqxU1dmZlqUCagAdgdGqeiiwnswPZeyAN8beG9gT2AOoKyLnZVaqqoGI3Igbah2XaVmCEZFdgBuB4ZmWxQc1gF1xw9T/AF4UEanoJFMESUBE8nBKYJyqvpppecJwNHC6iCwBngeOF5HnMitSWIqBYlUN9KheximGykQP4EdVLVHVLcCrwFEZlikav4jI7gDe2tdQQboRkQuBU4FztfJNbtobp/jnev+hlsAcEWmeUanCUwy8qo6ZuBGACg3bpggSxNO2Y4GvVfXeTMsTDlUdpqotVbUAZ9icpqqV7i1WVX8GlolIO2/XCcCiDIoUjqXAESKyi/fbn0AlM2iHMBm40Pt8IfBaBmUJi4icBFwHnK6qGzItTyiqOl9Vm6lqgfcfKgY6evdrZWMScDyAiLQFauIjYqopgsQ5Gjgf95b9lbf0yrRQWcwVwDgRmQccAvw7s+LsiNdbeRmYA8zH/YcqRegBEZkAfAa0E5FiEekH3An0FJHvcR4vd1ZCGR8E6gPvev+fR6JWkhkZKx0R5HwC2MtzKX0euNBPD8tCTBiGYeQ41iMwDMPIcUwRGIZh5DimCAzDMHIcUwSGYRg5jikCwzCMHMcUgZE1iMifvciP+6WhrW4iEnaimIhcJCIlXhiM70Xk7eCyIvIvEemRahmjURlkMLIHcx81sgYReRHYHRdNc0SK2xoBrFPVnaI3ishFuOijl3vb3YEJQHdVrcyTywwjLNYjMLICL5bT0UA/gsI+i0g1EXnYi73+hohMFZGzvGOHeYG3Zntv7buHqfc0L0DXlyLynojs5gUPHAgM8SY4HRNNNlX9ADeprL9X51NBMgwXkVnicheMCcR9EZHOXvz9z8TF41/g7b9IRF4Vkbe83sa2ePIi0ldE5nt1/cfbV91rb4F3bEgYGe4UkUVee77CEhu5hSkCI1s4A5en4DvgdxEJxCD6C1AAHAxcChwJ2+I/jQLOUtXDcDMubw9T78fAEV6Qu+eBoaq6BHgEuE9VD1HVGT7kmwOEG7J6UFU7e7kL6uDi6QA8CQxU1SOBspBzDgH6eN+pj7jkR3sA/8GFDzgE6CwiZ3ifW6jqQap6sFfvNkSkMfBn4EAv3v9tPr6LkWOYIjCyhb64BzXeuq/3uSvwkqqWe7FfPvD2twMOwgtbANxE+Dj3LYG3RWQ+LlrjgXHKFynCY3evxzEf9xA/UFwGrvqq+qlXZnzIOe+r6mpV3YiLtdQG6AxM94LdBSJ0Hgv8gAspMMqL2RMa+XYNsBF4XET+AlS6WD5G5qmRaQEMoyJEpAnuIXqQiCguK5iKyFAiP4AFWOi9cUdjFHCvqk4WkW7AiDjFPJSQ4HPiUlg+jLMnLPPsDrWjyBxgU9DnMtz/NOw5qvqHiHQA/gQMAs7GxfQPHN8qIl1wwfHOAS7HC0pmGAGsR2BkA2cBz6hqGy8CZCvgR1xv4GPgTM9WsBvQzTvnWyBfvJzHIpInIuHe9hsCy73PFwbtX4sLhFYhInIczj7wWMihQC7jXz0bx1ngHt7AWhE5wjvuJ9XlF8BxItJURKrjekQfisudW01VXwH+SUjYbq/dhqo6FbgKN5RkGDtgPQIjG+jLzlEzXwH+D/cWfAKwAJfv9gtc1rDNnrF0pIg0xN3r9wMLQ+oZAbwkIstxaRL39Pa/DrwsIr2BK8LYCfqISFdcqsofgTNDPYZUdZWIPIaLUroEmBV0uB/wmIisB6YDq6NdAFX9SUSG4Ya+BJiqqq95vYEnRSTwUhea77c+8JrXOxFgSLR2jNzE3EeNrEdE6qnqOm8IaSZwdCWNFb+NgMze5+uB3VV1cIbFMnIU6xEYVYE3PANsTeDWyq4EPE7x3vBrAEXARZkVx8hlrEdgGIaR45ix2DAMI8cxRWAYhpHjmCIwDMPIcUwRGIZh5DimCAzDMHKc/wfYt4UTo4Al7QAAAABJRU5ErkJggg==\n", 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.interpolate import interp1d\n", "for cur_frac, cur_model in lowess_models.items():\n", " ax = diab.plot.scatter(x='age',y='y',c='Red',title=\"Lowess Fit, Fraction = {}\".format(cur_frac))\n", " ax.set_xlabel(\"Age at Diagnosis\")\n", " ax.set_ylabel(\"Log C-Peptide Concentration\")\n", " lowess_interpolation = interp1d(cur_model[:,0], cur_model[:,1], bounds_error=False)\n", " ax.plot(xpred, lowess_interpolation(xpred), color=\"Blue\")\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As the fraction of data increases, Lowess moves from high-variance to high-bias" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = diab.plot.scatter(x='age',y='y',c='Red',title=\"Large variance, low bias smoother\")\n", "ax.set_xlabel(\"Age at Diagnosis\")\n", "ax.set_ylabel(\"Log C-Peptide Concentration\")\n", "lowess_interpolation = interp1d(lowess_models[.15][:,0], lowess_models[.15][:,1], bounds_error=False)\n", "ax.plot(xpred, lowess_interpolation(xpred), color=\"lightgreen\")\n", "plt.show()\n", "\n", "ax = diab.plot.scatter(x='age',y='y',c='Red',title=\"Low variance, large bias smoother\")\n", "ax.set_xlabel(\"Age at Diagnosis\")\n", "ax.set_ylabel(\"Log C-Peptide Concentration\")\n", "lowess_interpolation = interp1d(lowess_models[1][:,0], lowess_models[1][:,1], bounds_error=False)\n", "ax.plot(xpred, lowess_interpolation(xpred), color=\"lightgreen\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Splines (via knots)\n", "Here, we flash back to OLS and logistic regression. So far, we've made \"design\" matrices by taking powers of the raw data's columns and asking the solver \"how much of each transformed column is there\"? That's fine if there's an a-priori theoretical reason to think the relationship truly is polynomial. But in most cases we can use *much* richer and better transformations of the raw data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function below is one such better transformation of the raw data. It (depending on the parameters) applies a RELU or truncated cubic to the input data. Let's see what that looks like" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "def h(x, knot, exponent):\n", " output = np.power(x-knot, exponent)\n", " output[x<=knot] = 0\n", " \n", " return output" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Transforming the x values [0,10] with a knot at 4, power 1. Everything below 4 is zeroed out, values above 4 increase at slope 1. (If we had applied \"square the data\" we'd see a parabola below)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "xvals = np.arange(0,10.1,0.1)\n", "\n", "plt.plot(xvals, h(xvals,4,1), color=\"red\")\n", "plt.title(\"Truncated linear basis function with knot at x=4\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$(x-4)_+$\") #note the use of TeX in the label\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Transforming the x values [0,10] with a knot at 4, power 3. Again, inputs below 4 are zeroed out, the rest grow cubically with their distance from 4." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(xvals,h(xvals,4,3),color=\"red\")\n", "plt.title(\"Truncated cubic basis function with knot at x=4\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$(x-4)_+^3$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The sum of three RELUs with different knots and different coefficients can create a complicated shape, and thus fit complicated data. Below we see $3\\cdot RELU(x,\\text{knot=}2) - 4\\cdot RELU(x,\\text{knot=}5) + 0.5\\cdot RELU(x,\\text{knot=}8)$. Can you see how much the slope changes at each knot (i.e. at 2, 5, and 8)? " ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(xvals, 3*h(xvals,2,1) - 4*h(xvals,5,1) + 0.5*h(xvals,8,1), color=\"red\")\n", "plt.title(\"Piecewise linear spline with knots at x=2, 5, and 8\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Above, but with a starting slope and intercept \n", "(intercept=2, starting slope=1)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(xvals, 2 + xvals + 3*h(xvals,2,1) - 4*h(xvals,5,1) + 0.5*h(xvals,8,1), color=\"red\")\n", "plt.title(\"Piecewise linear spline with knots at x=2, 5, and 8\\n plus a starting slope and intercept\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using OLS, we can find optimal coefficients for RELUs with pre-specified knots, just like we can find optimal coefficients for $x^2$ and $x^3$" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "# generate some fake data to fit\n", "\n", "x = np.arange(0.1,10,9.9/100) \n", "from scipy.stats import norm\n", "y = norm.ppf(x/10) + np.random.normal(0,0.4,100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that we can apply the function h(x) directly in the formula, because we defined it earlier in the notebook." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fitted_spline_model = sm.ols('y~x+h(x,2,1)+h(x,5,1)+h(x,8,1)',data={'x':x,'y':y}).fit()\n", "\n", "plt.scatter(x,y,facecolors='none', edgecolors='black')\n", "plt.title(\"3 knots\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$\")\n", "plt.plot(x, fitted_spline_model.predict(),color=\"darkblue\", linewidth=2, label=\"Spline with knots at 2,5,8\")\n", "plt.plot(x, norm.ppf(x/10), color=\"red\", label=\"Truth\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "More knots" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fitted_spline_model = sm.ols('y~x+h(x,1,1)+h(x,2,1)+h(x,3.5,1)+h(x,5,1)+h(x,6.5,1)+h(x,8,1)',data={'x':x,'y':y}).fit()\n", "\n", "plt.scatter(x,y,facecolors='none', edgecolors='black')\n", "plt.title(\"6 knots\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$\")\n", "plt.plot(x, fitted_spline_model.predict(),color=\"darkblue\", label=\"Linear Spline with knots at\\n1, 2, 3.5, 5, 6.5, 8\")\n", "plt.plot(x, norm.ppf(x/10), color=\"red\", label=\"Truth\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "More knots (writing out all the knots in this formula is getting old...)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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dCwCwtbXF4cOHMWHCBDx+/BjVq1dHkyZN0LJlS8TExKBDhw64e/cuHBwcsHnzZrH9oSDkM8nJyWjatCksLCywfPlyJCQkYNasWWkLLO7evRsNGzYEADx8+BB169ZFSkoKfHx80ta96tatGzw8PLB27VqMGDFC3nBoKLBjBzBsGKCri6SkVAwadBIbNtzDtm1Aly4FcNE5SZLUIU8CW0ju/eoGR44EPi4XnGuqVwcWL/7iakFBQTh9+jRUVVUxbdq0DI+ZM2cO7t69m7bE8blz5+Dn54d79+7B1NQUzs7OuHTpUto6/oIg5A/79++Hqqoqtm7dmvZFzdnZGaVLl4a1tXVaEgAAKysruLm54eLFiwqLH0qShN69e+Ovv/76fyJYuhQggZ9+QkREAtq3P4gzZ55j2rS66Nz5y9cHy4rSh4Yk+bu3FkAAyYXKjie3dezYEaqqql9cr3bt2jAzM4OKigqqV6+e4TLMgiAo17Vr19CmTRuF3nqRIkVQpUoVJCYmppVFRESgV69e2Lt3L169eoU6dergn3/+Sfv927dv/78YY3Q08NdfQIcOeCbpwdl5Gy5eDMXffzfH1Kl182RkID/0CJwB9ABwR5Ik/49lv5DM+aIaOfjmnlc+XeBMTU0tbbVMAGlLSmckoyWSBUHIX0qXLo1bt26lK09ISEBgYCBevnwJU1NTtG/fHpaWlrC0tIRMJkOFChXQsmVL3Lx5E6qqqpg3b97/7xMuXgxERuJ+895wc9yCxMRUnDjRAa6u5unOk1uU3iMg6UNSIlmVZPWPr69bWSmfsrCwSFuu+ObNm3j69CkAoHjx4oiOjlZmaIIg5ED37t1x7NgxbNu2DTKZDMnJyVi0aBHCwsLwyy+/wNHREUOHDoW/vz+uXr2KunXr4vjx4/Dz8wNJNGzYEFWqVMGAAQPQtGlTIDgYmDULL+o2R60hgShaVA2XL/+Qp0kAyB89gkKjffv2aTuR1apVCxUrVgQgn3Hk7OwMW1tbNG/eHC1btlRypIIgZIeRkREOHz6MgQMHYtSoUUhKSkLx4sWhqqqK9evXw83NDQ8fPoSOjg7mzZuHZs2aQUVFBbdv38a0adNw/vx5XLt2DYaGhvIGR41Csgyoc7kGqtQyxKFDHihZ8vObUOUGsQy1IOQR8Xey8CCJ4OBgdO3aFRYWFhg/fjxUVFTg5eWFe/fu4eXLlwgODkbRokXT6vTq1Qu2trYYN24cACD1yFGotmqJCWiOB+0GYsuWltDSyt3nBzJbhlr0CARBEL6SJEkICgpCYmIitm7dChUV+aj7pk2b4OjoiCpVqqBdu3b47bffYGhoiLVr1+LcuXNYtGgRACD2fTQiO/dHNIyQMnwkdi9qDFXVbzdyLxKBIAhCLvD19YW7u3taEgDkCcLd3R2SJKFo0aLo3r07oqOj0axZM1y8eBH6+vp4/ToWR+y7o1/sK+z/8Q/MX9r0m8eu9JvFuel7HOYSCibxd7HwsbCwSHsW6FP+/v4oX748Jk6ciAcPHuDly5dYt24dzM3Nce9eGEZV+xV9Xh/CczdPtFs+9NsHjgKUCDQ1NREeHi7+AQpKRxLh4eE52g9a+H55enriwYMHmD9/PhISEpCYmIglS5bg9u3b6NixY7rjz5x5jrZ1/sLisLVIKlsO5gc3KvyeJK5evYpNmzbBz88vT2MvMENDZmZmCA0NRX5ch0gofDQ1NWFmZqbsMIRvSFNTE6dPn8aQIUMwffp0AICjoyNOnToFLS0thWP//vsuBvQ7jtNFt8NYLRHSgT3AJ88cRUREoG3btnj16hVq1aqFyZMno1q1atixY4fCDefcUmBmDQmCIOS1Dx8+4PLly9DX14ejo6PC/YBPRUREAAB0dXUVykli+vTLmD79CtaU90W/x9uBP/8EhgxROK5///5QVVXFihUroKKigpSUFHTp0gVWVlaYPXt2juPPbNaQSASCIAjZsGjRIkyfPh21a9fGy5cvQRL79++HlZVVtuonJqZgwICT2LTpPpY3fI8fz80GunYFtmwBPlk2IjU1FTo6OggODoaRkVFaeUBAAJo2bYqQkJAcX4OYPioIgpBD586dSxvvNzc3B0ksX74c7du3x61bt7Jc/+fDhwR4eh7AuXMhWNdfB703TQacnYF16xSSAIC0J5SLFy+uUK6rq5t+qepcUmBuFguCIOSV9evXY+zYsTA3ly/1IEkShgwZgsTERPj6+n627tOnEahbdysuX36J/Qts0Wf/JEhlygD79wMZTChQV1eHq6sr1q5dq1C+cuXKPFt1QPQIBEEoVOLj4xEeHo6SJUtCPZs7f0VGRqJkyZIKZZIkwdjYGJGRkZnWu3btFdq02YfkZBnOb3SC04Qf5MtLHz0K/LusRAYWLlyIxo0b4+bNm3B0dMTZs2dx5coVXLhwIXsX+YVEj0AQhEIhJSUFEydOROnSpVG7dm2Ym5tjxYoV2arbpEkT/P333wrT04OCgnDv3j04OjpmWGfv3iA0bLgDxYqp4589LnD6pTsQESHfkD6L+wpVqlTBrVu3UKlSJfzzzz9wcnKCv79/Wo8kt4kegSAIhcL06dNx7do13L59G2ZmZrh79y7at28PPT09dOnS5bN1+/Tpg82bN6NFixbo3r07Xrx4gSVLlmDu3LkoVqyYwrEksXixL8aMOYfatU1weFVtGHZoAYSFAadPAzVqZCteY2Nj/Pzzzzm93C8iZg0JglDgJScno1SpUvD19YWFhUVa+bFjxzB9+nRcvXo1yzbi4+OxadMmnD59Gvr6+ujTp0+63kBKigwjR57Bn3/6w9PTClumV4Rmm5byJHDyJODklNuX9kXE9FFBEAqt9+/fw9LSEhEREQozfEJDQ1GrVi28evXqq88RE5OErl0P4/DhJxg7tibmdi4OlRbNAZlMfk+gdu0M6+3btw9//vknXr9+jbp162LChAkoV67cV8eTkcwSgbhHIAhCgaerqwtDQ0NcvnxZofzo0aOoVavWZ+sGBARgzZo1OHToEJKTkzM85uXLGDRosANHjz7Fn382glezVKi4uQJFiwKXLmWaBJYtW4aff/4ZgwcPxpYtW9L2KP/mW9OS/O5eDg4OFARByI4nT55w0qRJdHFxoZ6eHjds2MCgoCD+8ccfNDQ05D///JNhvdTUVA4aNIglS5Zkr169WL9+fVpaWjIgIEDhuNu337JMmZXU1l7Mw4cfkcuXk2pqpK0tGRqaaVxxcXE0NDRkUFAQSVImk3Ht2rU0MjKiuro6GzZsyHPnzuXeG0ESwA1m8Jmq9A/1nLxEIhAEITvOnDlDQ0NDjh49mmvWrKGjoyO1tbVpaWnJ9u3b88aNGxnWi4uL48yZM2lvb8/o6Oi08pUrV9LBwYEymYwkefLkU+roLKGJyXLevBZCDhki/1ht0YKMjPxsbLdv36aNjU3az4sWLWKVKlW4fPlyVq9enVu3bqWRkREvXbqUC++EnEgEgiAUKjKZjJUqVeKRI0cUyvv168eJEydmWm/x4sU0MDCgtrY2tbS02KtXL8bGxpKU9xLMzMwYGBjIRYtuUFV1Pu3s1jP0RhDZsKH8I3XsWDIlJcv43r59S11dXUZFRTEpKYklS5ZkQEAA165dy3bt2pEkV69ezdatW3/Fu6Aos0Qg7hEIglAgBQcHIzo6Gs2bN1coHzBgAI4ePZphnd27d2P58uW4evUqHBwcsGnTJiQkJGDkyJEAABUVFWhoFMOYMTcwatRZtG5dHlfnmqF0Kxfg2jXg778BLy9AVTXL+IyMjNCqVSsMHjwYDx8+hCRJiI2NxbRp0zB8+HAAgKurK+7cufN1b0Q2iEQgCEK+l5CQAG9vb5w7dy7TG7b/paWlhfj4eCQlJSmUf/jwAdraGW8I/+eff2LOnDmoUKECWrdujY0bN2LZsmXYsWMHoqKisGXLUYSEtMaRI68wc5oT9tS6D61W7kCJEvJE0LPnF13XypUrUaRIETg5OeHt27do0aIFfv/9d7i5uQEArl27hooVK35RmzmSUTchv7/E0JAgFB5HjhyhsbEx69Spw1q1atHU1DTbN1Hd3d05derUtDH96Oho1qlThytXrszw+EqVKvHu3bskydjYWNarV4/Ozs4sUaIEmzb9kZI0nVpaC3hq7QWyQQP5UFDnzmRU1Fdd44cPHzhy5EjWrl2bd+/epUwm44kTJ2hiYsJTp059VdufgrhHIAjC9+bly5c0MDBQuGF68uRJGhoaMiIiIsv6oaGhtLe3Z5UqVdihQwcaGhpy0KBBTE1NzfD4Pn36cMaMGWk/JyUlcebM31ikSGOqqMxjhfIr+WLBarJECbJYMXLDBvJjkvlaqampnDNnDkuVKkU1NTXa2tpy3759udL2vzJLBOKBMkEQ8q2FCxfi/v37WLNmjUJ5hw4d0KJFC/Tt2zfLNkjCx8cHL168QK1atVC+fPlMj3348CHq16+PgQMHolWrVvD1vYMxY64iPr4S+rQwwiq1/VA/uF/+hPDmzcBn2sopkkhKSoKGhkauty32IxAE4bsTERGBUqVKpSs3MTHBhw8fstWGJEmoX79+to61srLC5cuXMX/+fPTrNw7Pn7shIb4i9neKQ5vToyHFxABz5gBjxgBqefPxKUlSniSBzxE3iwVByLeaNGmCnTt3Ij4+Pq0sOjoae/fuRdOmTfPknOXKlUO7dj/jxYuOKAfijcNhtN05FZKVFeDvD4wfn2dJQFlEIhAEId+qV68eateuDRcXF6xfvx6rV69G3bp10a5dO9jZ2X1V2z4+Pmjbti0qVaoEDw8PXLlyBSQxZ841tHbfjilFzsM3cS6MHtwEliyRLxVRuXIuXVn+UrDSmiAIBYokSdi4cSN2796NvXv3QlVVFb/99hvatGnzVe2ePHkSPXv2xO+//445c+bAx8cHbdp0hI3NNGheuIanxY/B9M0LwMMDWLoUMDPLpSvKn0QiEAQhX1NRUUGnTp3QqVOnXGtz8uTJWLlyJdq1awcAUFMrBWv15xh5YTE8cA8sZQXsOAr852G0gipfJAJJktYBaAXgLUlbZccjCELBRRI3btxAq1atAAAndvghqOdYeCedRxJkwOzZkEaNAr7xDVtlyi/3CDYAaKbsIARBKPgkSYKZmRnu3PDFieYj4dClHoYmncWrxs3QpKw5MGFCoUoCQD5JBCQvAHiv7DgEQVCulJQU3L59O2/X45fJsNSxHvSdm8L9+BK8LmWFp7v3of2H1/hhzJi8O28+li8SgSAIwr59+2BhYYFOnTrB0dERrq6uCA0Nzb0TkMD+/UiwtkW73dsQLiuG1hoOaK72Ho6D+sHDwwPDhg3LvfN9R76bRCBJ0kBJkm5IknTj3bt3yg5HEIRcdOfOHQwePBi7du1CYGAgQkND4erqinbt2uGrVz8g/79VpIcHQh6FY2Dx3og+cxm7Inxw8eIFhIaGYtKkSQrbWBYm+WaJCUmSLAAczs7NYrHEhCDkf/LVOrfg3r17qFSpEnr06AFdXd0Mjx0xYgQMDQ0xZcqUtDKSsLa2xqZNm1D741aPJHHs2DHs2LEDKSkp8PDwgKenJ1RUMvhOSwLHjgHTpgHXr+ODrglGRdTHg5otsHOvB8qU0cmDq87fxJ7FgiB8MyEhIahWrRq8vb1RsWJFXL58GXZ2dnj06FGGx79+/RoVKlRQKEtMTISuri7Onz8PmUwGABg7dizGjh0LJycnuLq6Yvbs2ejVq5dir0EmA/bsAWrWBFq2ROqbt1hi9yOMI36Cat8+OHuxW6FMAp+V0Up03/oFYBuAVwCSAYQC6Pe548Xqo4KQv3Xr1o1TpkxRKJs3bx7btm2b4fFLliyhp6dn2s+7d++moaEhVVVVWbFiRVpZWXH37t0sVaoUP3z4kHZcfHw8K1asyPPnz5NJSeTff5M2NvKFlStUYOj0RbQuv4Lq6gu4fLlf2nLUhRXEMtSCIHwrxYsX55s3bxTKYmJiqK6unuES0FFRUbS1tWXPnj25ceNGFi9enOXLl+ekSZMok8m4detWlihRggMGDEhXd+aECTzUuDFpbi7/SLO1Jbdu5e7td6mtvZilSi2nj0/mm8gXJpklAjE0JAhCrtPU1ERsbKxCWWxsLNTV1TO8IVu8eHFcuHAB5cqVwy+//AIDAwPMmjULM2fOhCRJ6Nq1K0qWLKm4beOrV8CkSRi1aBFanT4NlC0LHD6MVD9/TLhVGh26HIOdnSF8fXvA2bl0Xl/ydy1fPFksCEL+8c8//2Dbtm1ITExEmzZt4O7u/sWzabp164apU6diw4YNUFFRAUlMmTIFP/zwQ6Zt6enpYerUqXj79i2srKzSLSlRtWpVHD9+HFf/+gtOV68CW7aAyck4o6aG2nv3oqSHB8LD4/FDy304eTIYgwZVw5IlrtDQEB9zWRE9AkEQ0sydOxft27eHgYEBKlSogDFjxqB///5fPIVzxowZePHiBSpXrox+/frB1tYWd+7cwbx587Ks6+bmhu3btyM1NTWt7P27d1A/fhyPypaF06BBiP/7b+w1NISjri5Sd+5ESQ8P+Pu/Rc2am3DuXAhWr26KlSubiCSQTflm+uiXENNHBSH3hYSEoHr16rh79y5MTEwAAHFxcbC3t8fKlSvh6ur6Re2RxJUrV9Kmj9avXz9bPYuUlBS0atUKSUlJGNa9O0yPH0fp/ftRJjkZMDNDyo8/4pKNDRKKFoWLiwuKFi2KrVsD0L//cWhqEr16SRgwwB02NjY5eh8Kssymjyr9xm9OXuJmsSDknsjISI4bN44GBgYsVqwYx40bx8jIyLTf//bbbxwzZkzazzKZjBs3bqSTkxMtLCzYrVs3BgQEZPt8T58+5dChQ+ng4MDWrVvzxIkT6Y5Jun6dAfXrM15VlQQYVqUKZTt2yGcG/XtMUgoPHXrE9u33E/CiuvoINmvWkYMHD2apUqU4cuTIQj9L6L8gbhYLQv7z7NkzzJo1C+PHj8fp06e/eAjma6WmpqJZs2Z4/fo1xo4di5o1a+LNmzdwd3dPG5qJiIiAlpZWWp25c+di7ty5mDJlCk6dOgU7Ozs0aNAAjx8/zvJ8wcHBqFu3LnR0dPDnn3+iffv2GDBgANauXQskJMj3Aa5XD+q1asH6xg1o9ukD+PnB4O5dSJ064XV4ErZvD8TAgSdRuvRKtG69D+fOhaBYsWvYt685jh3biRUrViAwMBAnT57E4cOH8+y9K1Ayyg75/SV6BEJBsGfPHhoYGHDYsGGcMWMGK1euzM6dOzMlJSXD4zMr/xqHDx9mzZo1KZPJGBkZSQMDA54/f561atXioUOHGBQURCMjo7Rv/DExMdTT02NwcLBCO7/++it//PHHLM/3448/8pdfflEoCzhwgMu1tCgzMJBP/7SyIhcsIN+/Z1hYHPfsecChQ0/RxmYdAS8CXtTRWcIOHQ7wwIGHPHHiNGvVqpXuXCtXrmT37t2/4t0peCCeIxCE/CM2NpYGBgb09fVNK0tISGDNmjW5Y8eOtDKZTMbFixezTJkylCSJdnZ23Lt3b67FMXPmTE6cODHt55MnT9LAwICWlpa0trZmiRIluGbNmrTf+/n50dbWNl07ly9fzvDD+L+qVavG69evk/Hx5NatZMOGJMAkgJFNmzL6wFEe3B/EUaPOsFq1DZQk+Qe/tvZiurvv4pw5V/nPPy+ZnPz/ZxFOnjxJZ2fndOdat24dO3fu/KVvSYEmEoEg5CPHjx+ni4tLuvI1a9awa9euaT/PmzePNWrUoJ+f/KnYkydPsnTp0jx27FiuxLFlyxa6u7srlMXExNDe3p5Dhw5lWFiYwu/evn1LXV1dhXsIJLlixQp26tQpy/MNqlePAc2akfr6JMBUCwve6fYTy6g3p739eqqozCfgRQ2NhXRz28GZMy/TxyeUiYmZ94bi4uJoaGjIa9eupZXFx8ezZs2a3L59e3behkJDJAJByEe8vb1Zu3btdOV//vkne/XqRZJMTk6msbExAwMDFY7ZsWMHXV1dcyWO+Ph4WlhYcO7cuYyLi2N8fDznzZtHCwsLxsXFZVind+/ebN++Pd+8eUOZTMbz58/TxMSEPj4+GZ8kIoJctYqsXZsEmAiJ18s78yebCVRXlX/jV1GZy3r1tnLKFB+ePfuM8fHJX3QdBw4coL6+PgcPHsxp06bR2tqaXbt2/aLhtPj4eD58+JDR0dFfdO7viUgEgvCVUlNT+fLly0w/IL9EUlISTU1Nefz48bSy9+/fs1KlSmnf9t+9e0c9Pb10dZ8/f05TU9OvjuFfjx8/ZrNmzailpUUtLS02a9aMjx8/zvDY58+f8+rVqxw4cCB1dHRoYGDAChUqcM+ePYoHpqaS3t5M+aEbUzQ0SYBPtMw4TrUNDTGVwFxqao6jhkY7urkN5uvX77/6OkJCQjh37lxOnDiRZ86cyfaMIZlMxnnz5tHQ0JCWlpbU1dXlmDFjmJz8ZcnoeyASgSB8ha1bt7Js2bI0MjJiiRIlOGLECCYkJHxVmxcvXqSRkRFbt27Nfv360djYmOPGjUv7AEtJSaGJiQnv3LmjUG/Tpk1s0qTJV507I9HR0YyKisrwd69fv6a7uzsNDQ1ZuXJllipViuvWreOrV68U1g5KDnjA0L4j+UHPhAT4AZpcASfWxnDaV9/A0aPP8PDhR3zzJpJ37tzh27dvc/06vtTatWtpa2vLhw8fkiRfvXpFNzc3/vrrr0qOLPeJRCAIOXTq1CmamZnxypUrJOUfFK1bt06bJfP69Wvu3LmTJ06c+OJvkdHR0dy8eTP//PNPPnjwIK08MTGRe/bsYYcOHWhpackLFy4wOjqau3fvZsmSJXnmzJncu8BsaNCgAcePH8/ExESSpK+vL01MTHjt2jXK3r+n/9DfeFe/MgkwFRKPoyLHmg3k6B+PcO/eIIaHf30vKq9Uq1Yt3fv5+PFjGhgY5MlMLWUSiUAQcqhVq1b8+++/FcrCwsJYokQJzpgxg7q6umzbti2dnJxYtmxZ+vv7f9X5goKCaGlpyYYNG3LQoEE0MDCgjo4OtbS0WLduXZ48efKr2v9S9+7do5mZmeKHYlIS9/Tuw3PGFZggqZMAg9RKck/tvjyw/Bxfv475pjF+DUNDQ75+/VqhTCaTsWjRogXufoFIBIKQQ7a2tvTz80tXbmpqSlNTU4aG/n+J482bN7NcuXJf9U3S2dmZS5cuTfs5ISGBjRo14uLFi3Pc5tfw9vZm/fr1SZmMvHyZHDqUybryWT9voc2VGnXprGFP3RL6tLS05ObNm5USZ061aNGCf/31l0LZqVOnaGNjU+CeTBaJQBByqHfv3pw1a5ZCWWBgIDU1Nenl5ZXu+GrVqvHChQs5OldISAgNDQ3TDTGdOnWKTk5OOWrza0Vcvcq5GhpM/rjef6JqEW5HdXqo92TlCl3ZsGEjPnv2jCR55coVmpub8+jRo0qJNSeuXbtGQ0NDLlq0iLdv3+a6detoYmLCffv2KTu0XJdZIhBL8wnCJ65du4Z58+bh/v37qFSpEsaNG4eff/4ZDRo0QJEiRdCmTRsEBgZi7NixqFy5MoyNjdO1YWBggJiYmBydPzk5Gerq6un24NXQ0EBycnKO2nz58iUuXLgAAwMDuLq6Qk0tG//sQ0OBHTuALVtQws8PYyUJF1/HYZtmZ2xPtIVZlXjExu5DRNgrnDp3F6VLy9f7d3JygpeXFxYuXIjmzZvnKN5vrXbt2jh16hTmzZuH1atXo0KFCti2bRsaNGig7NC+nYyyQ35/iR6BkJyczLVr17J58+Zs0aIF161b99U39s6ePUsjIyOuWLGCd+/e5erVq1myZEmeOHGCd+/eZZcuXWhpacl69epxx44dXL9+PRs0aKBw3sDAQOrp6WU6+yYrMpmMdnZ2Ck8Xp6amskOHDpw5c+YXtzd9+nTq6enR09OTtWvXpqWlJe/evZvxwe/ekStWkC4upCTJBwxq1eKzUdPZvPoyAl7U05tEOzt3Tpo0if7+/hlOY33w4AHLly//xbEKeQ9iaEgoKGQyGTt27Mh69epx9+7d3LVrF+vWrcsuXbp81Zhu/fr10z2Jun///gwf/CLlM3uaNGlCZ2dnrly5ktOnT2epUqW4du1avnz5kj179qSOjg719PQ4aNAghoeHZyuOa9eu0cjIiD179uTs2bNZp04d1q1b94tvXB47doxWVlYKW0auW7eOlStXpkwmY3BwMFfPn8+zffow0c2N/LjSJytXJmfMYPjVWxww4AQlyYulSi3npk33FN7fpKQkmpiY8Pbt2wrnXbZsGTt06PBFsQrfhkgEQoFx/vx5VqxYUWEef3x8PMuXL89Lly7luN0iRYowNjZWoSw5OZmSJGW4zy4p/zDcunUre/fuzZEjR9LPz4/x8fGsVKkSf/75Z7569YohISEcPHgwa9asmWk7//Xu3TsuWrSIY8eO5Z49e5j0yfLL2dW1a1euXLlSoUwmk7FGxYr8u1kzHlFXZ9LHD/9gFRUGeHiQ/v5MSU7h8uV+1NNbRlXV+Rw16gwjIzN+ZmLFihW0srLioUOH+OzZM65YsYKGhoYKayhlJSYmhj4+PgrTZ7Pj3+WwmzZtynr16nH27NkKyfLOnTv09vZmRETEF7Wb3XNfuHCBEydO5G+//ZbpA3j5jUgEQoExY8YMjh8/Pl352LFj093U/RLly5fnP//8o1B269YtmpmZfVE7mzZtYtOmTRXKZDIZa9SokWtrBGVHmzZt/j/EFBtL7txJtm/P+I/DPiklS5IjR5JXrtDv5k3q6ury+PEA1qixkYAXGzbczrt332V5nh07drBOnTo0NTVl27Zt5YvKZdPy5cupr6/PWrVq0dTUlA0bNuSrV6+yVXf48OF0cHDg7t27eerUKXbo0IGOjo588uQJnZ2daW5uzvr161NXV5cLFizIdkxZkclk7NevH8uXL88pU6Zw+PDhNDAw4JYtW3LtHHlFJAKhwFixYgW7dOmSrrxjx47ppgF+iaVLl9LBwYFPnz4lST579oxOTk4Zzgz6nAkTJvC3335LVz5y5EjOnz8/x/F9qdVLlnB61aqUdexIammRAJMMDLhCVZV/du4sXwbiozdvYli27DgCXjQ1XcFt2wJyNMx28OBB1q9fnyYmJmzatCnPnz+f6bHe3t40NzdnUFAQSXnva9KkSWzYsGGW53n06BENDQ0VFr+TyWR0c3OjtbU1p0yZknbvJjg4mOXLl8+1mUxHjx5llSpVGBPz/2cl7t69S11d3TzpfeQmkQiEAiM8PJyGhoY8dOgQSfkHwIEDB2hkZMQPHz7kuF2ZTMaZM2dSX1+fZcuWpb6+PqdMmZLt4Zx/bdiwgS1atEjXdu3atXn48OEcx5ctsbHk7t1k586UaWuTAN+rq/OuiwvXduvGkoaGdHV15ejRo0mSycmpXLrUlyVKLKWKyly6uy9ldHRijk69fft2lilThnv37mVISAg3btxIY2PjTJ+C7tKlS7qhq+TkZJqYmGQ5TLRx48YMvwxMnTqVWlpa6abfrl27lp6enl94RRkbOHBghs90NG/enLt3786Vc+SVzBKBmD4qfHf09fWxf/9+9OjRAz///DNIIjk5GQcOHICurm6O25UkCZMnT8bYsWPx8uVLmJiYoGjRol/cTseOHTFz5kxMnToVo0aNQkpKCn7//XckJiaiWbNmOY4vU7GxwNGjwO7dwJEj8p+NjCB164ZkDw8ce/sWp8+dQ3R0NDS0tHD//n2cP38eZ848QWJiSwQERKBePWPcvr0U69dfQLFiRb44BJKYOnUqNm/eDBcXFwBAjx49oK6ujpkzZ8LV1RUkERMTA21tbaioqODdu3coW7asQjtqamowMzNDWFgYKlasmOn5SpYsmeGOaEFBQShevHi6KbJmZmZ4//79F19XRtTU1JCUlJSuPDExEerq6rlyjm8uo+yQ31+iRyCQ8mmV169f540bN774W3teiouL46NHj9ipUycWKVKERYsWZa9evXJ3gbWoKHLbNtLTkyxaVN65NzYmBw8mvb3J/3wjfvjwIQ0NDXny5Em+fBnNypWnf1z++Ve2bDmBhobyabM5FRsbSw0NjXTDSeHh4dTV1eW2bdtoZWXFokWL0tjYmLNmzeKMGTPSltz+14MHD6ivr68w7JKRlJQUVqxYkUuWLEkbAjpz5gwNDAyor6+fbopsz549OWPGjBxf36fOnz9PCwsLvnv3//snFy9epKGhYbrJBvkNxNCQIOSdxMQUHjhwhVWrdqWqqhvV1V3YrNlAPn/+mjKZjBcvXuTw4cM5ZMgQnjp1KmfTXD98IDduJNu2JTU05P98S5Uihwwhz54lP/McxYQJEzh69DguXHidxYsvYZEiC9mnz3YaGJiwX79+6fY8+FKpqak0MTHhvXv3FMpPnTrFcuXKsUyZMrxw4QJlMhkDAwPp5OTECRMmsFKlSuzZsyePHj3KFStW0NzcnMuXL8/WOR89ekQnJyeamJiwYsWKLFu2LI8fP87169fT1NSUixYt4r59+9i1a1dWrlyZ799//VLX/5oyZQoNDQ3Zr18/enp6Ul9fnydOnMi19vNKZolAkv/u+1KzZk3euHFD2WEIAiIjE7Fs2U0sWHAdERHphwsAwtBQhri4R2jQoALKlFGFt/dGNG/eAEuXLoUkSZ8/QVgYcOCAfNjH2xtITgbMzID27YEOHYC6dYH/PIWcEXf3Ibh71wovX6aieXNLLFniBisrPbRv3x6dO3dGp06dcvYGfMLLywu7du3C5s2bUbFiRfj5+aFz585QU1PDzJkz0b59+7RjHz9+DCcnJ9y9exerV6/G+fPnYWhoiIEDB8LV1fWLzvvo0SPExcWhSpUqUFVVBQBcuXIFf/31F96+fQsXFxcMGjToq4YNMzvviRMnoK2tjXbt2uV6+3lBkiRfkjXTlYtEIAhfLiIiAUuX3sSiRb6IiEhE5cqEoeFLzJ//MypW1ENERCL8/N6gb98piInRgbFxdbx8GZdWX1U1CnXrWsDNrRLs7UvC3t4YZcoUlyeGly+BffuAvXuB8+eB1FTA0vL/H/61amXrwx8AXryIxtix57F9eyC0tBKwdWtntGlTAZIkISoqCuXKlcONGzdgYWHx1e8JScydOxeLFi1CUlISihUrhl9//RUzZszApUuX0t0PMDQ0xP379zNcpkPIGyIRCEIu+PAhAUuW+GLx4puIjExE27YVMGVKHaxc+Stq1KiBwYMHKxxfq1YtFCtWDGfPnkVYWBz8/d/Bz+8NNmw4jTdvVPH+vSpIwALv0UMrEJ3U78E2MggAkFjOCuqdOkClU0egenUgg94DScTHx6No0aIKvYukpFQsWeKL6dOvICVFhtGjq+PAgVFwdKyBAQMGIDw8HDNnzkTt2rWxbNmyXH2PUlJSEBkZCV1dXaiqqqJly5Zo3749+vbtm3aMv78/WrVqhWfPnqV9ixfyXmaJQOnj/Tl5iXsEwrcWHh7HX3+9SB2dJQS86OGxn35+/1+64Y8//ki3rEJSUhL19fXTbQ5PkkOGDOHq0aOZOGU6oyvZycf7AQYWNec01WasjLEEvFi06CLWrr2Jgwad5MqV/rx27SXj4uRPGW/cuJEVKlSghoYGS5cuzUWLFlEmk/HUqWBaW68l4MU2bfby8eMPJOVbYU6ePJk1atSgi4sL165d+01usvv4+NDIyIgbN27kmzdveOLECVpZWaWbOirkPYh7BIVTQkICHj9+jJIlS8LQ0FDZ4eRrMpks3aqf4eHxWLjwBpYt80N0dBLat7fClCl1UbWqkcJxUVFRsLe3R6dOnfDjjz8iKioKU6ZMQVxcHK5fv45jx46hdq1agJ8f3q1ahfdr1qCSTCavXKcO4OkJeHoiQl8f7969R1ycNm7dCoOf31v4+b2Bv/87REYmAgBUVSWYmqrh/fu76NvXHc2a1cCtWw+xdOlm6OtXx/37RPnyuli61A0tWpT7Ju9dVi5cuICZM2fCz88PlpaWGDVqFH744Qdlh1Xo5OseAYBmAB4AeARgQlbHix5B9ixbtoyGhoa0tramrq4ue/TokeW0vOy4f/8+J0yYwCFDhnD//v35fju/9+/f89mzZxl++5XJZFyxYgUtLS0JgLa2tty1axffvYvlhAnnWazYYkqSFzt2PMDbtz8//TM0NJR9+vShsbExy5Yty0mTJjE+JoY+c+bwTw0NvtaUb+KeDPBVlSrkH3+QL16QJCMjI9mtWzfq6OjQ1NSUFhYWChvCy2QyPn78gXv2PODkyRdZosQoGhgsIuCl8FJRmcoZMy4xPr7gbbwufD3k1+mjAFQBPAZQDkARALcA2HyujkgEWdu3bx/Lly+fNi0wMjKSP/zwA/v06fNV7W7atIlGRkacOHEiFy5cyBo1arBt27ZfvFfvt/D+/Xt26tSJOjo6LFWqFK2srHjkyBGFY5YtW8YqVarw2rVrTE1N5e7dx1i8eGdqas6nJHmxS5dD2VpvR0FiInniBDloEFmyJAlQVqQIXzo48J/Bgxnx6FG6Kh4eHuzbt2/aEgUXL15kqVKleO3atQxPoaenx3fv3vHNmxheuBDCbdu82bRpSwJg9erVuX79ej5+/PirnrQWCp78nAjqADjxyc8TAUz8XB2RCLLWuHFj7ty5U6Hsw4cPLFGiRI4/HKKioqinp6cwVzwpKYlOTk7cunXr14SbJ5o2bcohQ4YwKiqKMpmMp0+fprGxMW/dukVSPvfdzMyM/v7+fPMmhuPGnaOW1iJKkhcNDUfw3r0vSACxseTevWT37mSJEvJ/WtraZKdO8ge/PlkT57+Cg4NpaGjI+Ph4hfJFixaxZ8+eGdZxcXFJ+/O9fv06DQ0N+csvv9Dc3JwTJ06kmpoa9fT0qKOjw169ehW4vXeFnMksEWRvDlreKg0g5JOfQz+WKZAkaaAkSTckSbrx7t27bxbc9+rVq1fpHtHX1dWFrq4uwsLCctTmhQsXYG9vDxsbm7QydXV1DBgwAIcPH/6qeHNbYGAg7t69i8WLF6N4cfm0zEaNGmHEiBFYuXIlACAuLg5hYYnYuPE9LCxWY8GCG/DwsMKlS+0gk22GjU3G91QiIyPh5eWFTu7uWOXignBXV8DQUD7Of/Qo4OEhn/v/7p18l68uXQAdnUxjffHiBcqVKwdNTU2FcltbW4SEhGRYZ/LkyRgxYgR27dqFGTNmoFOnTti+fTt++OEHbNy4EVu3boW6ujoePXoEmUyGgQMH5uh9fPbsGWbPno1ffvkFFy9e/PfLmlDA5IdEkNETNen+tpH8i2RNkjWNjIwyqCJ8qm7duti3b59CmZ+fH5KTk9PN586uokWLIjo6Ol15dHR0jtbkyUshISGoVKmSwtovt27dwuXLl7Fv3z7MmLEYEyZcQmLiKCxe7IsOHSoiIKAPNm9uiVevbqNKlSoZthv58CEWVq6MJosWYfuZMxh08SKSLlxAQJ06wOnTwJs3wPr1QJs2QDbfExsbGwQFBeHFixcK5YcOHULt2rUzrNOkSRNs3LgRf/zxB44cOYILFy5gzpw5ePToEaZOnYqOHTtCXV0dCQkJWLFiBY4fP47Xr19n892T27lzJxwcHPDixQuoq6ujb9++6N+/v0gGBVFG3YRv+YIYGsoTjx49YqlSpThp0iRevXqV69evZ5kyZbhhw4Yct5mcnMwyZcpw//79aWWvX7+mpaVlpitMKsubN2+oq6ubth7Mrl27aGxsTDs7Z1aoMIYqKnMIzGWxYv2oo1OOO3fuZGxsLA8ePEhTU1PFfQOePSMXLyZdXJj67xaO5cuTY8eSV67w7u3bNDQ0ZFxcXI7jnTlzJm1tbXnw4EHevn2bv/zyC0uXLs3Q0NAs67q7u3Pz5s0kSScnJ/r4+DAkJIR6enppMdna2tLPzy/b8fw7DPjvMBop30DG1tY2bdVX4fuDnN4jAHAaQLWsjsvpC4AagCcALPH/m8VVPldHJILsefLkCYcMGUIHBwe2adOGp06d+uo2r127RhMTE7q6urJz587U09PL0V66XyIkJITr16/n7t27v+jDdvz48axRowYPHDhAfX1LVqz4M4HZVFHxYtGivWhn15C9evVis2bNqKamxiJFirBWrVryD7oHD8hZs8iaNfnvHH/a2XGDhQV9li8n/7NWUI0aNXjlypUcX6NMJuPmzZvp4uJCa2trDho0iMHBwdmqe/LkSZYuXZpnz57l8OHDOXDgQLq4uHDixIkkycePH1NfX/+LFkTbv39/us11SPnN9b59+2a7HSF/+ZpEUAPAGQDrAZhkdXxOXgBaAAiCfPbQpKyOF4lAueLj47lv3z5u2LCBISEheXquWbNmUU9Pj126dGGTJk1obGxMHx+fbNWVyWScP381DQz6f0wA89ilyx6amVXjhQsXeObMGdatW5ckOeXXXznNw4OcMoWsUiXtwz+ycmX6tGrF08uXMzk5me3bt+fatWsVzpOcnExTU9O0DVaUYffu3bS2tqampiZVVFTo4uJCX19f7t69mxUrVuTChQu/qL3Dhw9nuEHMggULOHDgwNwKW/jGcpwI+P8P6/Yfv61PBVA0u/Xy4iUSQeFw8eJFmpubK2xdeOzYMZqYmDAx8fObpzx/HskffzxJdfUFVFefT03N7gwKCuOzZ89oYmJCmUzGbVu3clTduuS4cUwoU0b+z0FFhWzQgInz5rFrvXqsXLkyhw0bRmdnZ1pbW3PTpk0sV65c2rf1lJQUTp06lS4uLnn6XmSHTCZjVFQUHz58yIEDB9LGxoZubm452iwlLi6ORkZGCjuMhYWFsXz58vT29s7NsIVv6KsSAeQ3dG0BDAYQBvnMnh7ZqZsXr4KWCGQyGXfs2MGWLVuyYcOGnDdvXqGb7ieTyXjp0iXOnTuXGzZs4M6dO1m1alW6u7unGyJxdnbOdO/fly+jOWzYaRYpspDq6gs4ePBJBgdHsGHDhpw2bRo/hIWxmZYW3/fsyZdqavJ/AmpqfFOjBudWqEC+kS8bMXnyZHbo0EHhYblp06axTZs2XLBgAXV1dVm/fn2WLVuWderUydZY/vfm5MmT1NfXZ/v27Tlw4EAaGxvzl19+UXZYwlf4mqEhHwAvAZwCMBNAKwAVACwD8FdW9fPiVdASwbhx41i1alVu27aNx44do6enJx0dHdPNKy+okpKS6OnpyQoVKnDEiBE0Njamuro6K1euzIYNG9LAwEDhBmWzZs24b98+hTbCw+M4btw5amouopraAg4YcILPnn2cu5+czHfbt3OXkRHfqqqSAOMB3reyomzDBobeuUNbW9u0G64kWaFCBfr7+yucIyYmhlpaWoyOjmZERAS9vb15+/btPHtf8oMPHz5w3bp1XLJkSZbbRwr539ckAlt8XKU0g98FZFU/L14FKREEBwdTX19fYdMMmUzGxo0bc/369coL7Bv6448/6ObmxsTERK5evZoNGjTg2rVrWbZsWTo4OPDcuXMsWbIkExMTGRgYqLBJeFxcEufOvcYSJZZQkrxYp84SXr78gExKIo8fJ/v3Jw0MSIAyLS2GN27MyyNHsnOLFtTX16eDgwN1dXX522+/KWwWY2Fhwfv37yvEmZCQQG1tbYUN0wXhe/LV9wgyrAyU+5r6OX0VpESwdevWdKtWkuSqVau+ejmIzMTExHDp0qVs3bo1e/TowbNnz+bJebLLxcWFR48eJUm2bt2aO3bsYGpqKk1NTdmsWTNWrVqVZmZm7NatG42Njbl+/XqmpKRy7drbLF16BQEvqqkNYpMGnTnHxYVbihRhvJaW/K938eLkDz+Qe/bIn/79REhICK9evZrhB/vIkSM5YMAAheSwbNkyNmrUKG/fDEHIQ5klgq/avJ7kk6+pLwDGxsZ48iT92/jkyZM82bAjLi4Obm5uKFmyJHr27InXr1+jd+/eGDVqFH766adcP192yGSytDXpNTQ0EBcXB0mSoKamhgULFuDp06fo0aMH1NTUcObMGTx5oomqVf/G/fvhqF1dD07hy7GykQ0MfXyAyEjIihfH7uRkOC1bBvP+/YH/PLH7LzMzM5iZmWX4u19//RVubm5wc3ODu7s7bt68iUuXLsHb2zvP3gdBUJqMskN+fxWkHkFKSgorVaqksAn3pUuXaGRklCdjssuXL2fLli0VvukGBwdTV1dXaQuULVy4kM2aNWNycjL37NlDOzs7rl+/njY2Nmk30itUqMCLF0NYr95WqmM2B5iO4NOGHkz8d+P2EiXIXr3IQ4fIhASOGzeOv/7661fFlZCQwG3btvHnn3/mihUr0oajBOF7BbEfQf716NEj/PDDD3j16hVKlCiBiIgILF++HG3atMn1c7Vv3x4dO3ZEly5dFMobN26MMWPGoHnz5rl+zqwkJiaibdu2ePXqFdq0aYOdO3fi4cOHaNmyJRITE+Hv/wLVbEZD9fwV9Na8Bw/pHjTio4ESJfDAxgaHihbF2GPHgCJFAAARERHo3bs3YmJisGLFClhZWX3zaxKE/Ciz/Qi+amhIyB0VKlTAP//8gwcPHiAmJgbVqlWDmlre/NHo6+unW9OGJF68eAEDA4M8OWdWNDQ0cPToUZw+fRo+Pj4YOXIkHBwccPbUPwjf8xCd3kXB8/wI6CMOLKIDqZ0H0KkT0KQJtN++xayqVdH5zRuUKVMGJ0+eRJcuXZCUlAQ3Nzc4Oztj0KBBmDlzplKuTRC+Cxl1E/L7qyANDeVUREQEly9fzjFjxnDjxo3Znmp65coVli5dOm3YSSaTcfHixaxatarCcJHSpKYy6uhpXq7hwdcoRgKMVy/KeM9O5IEDZEJCuiqLFi1iqVKlOG7cOGppadHU1JTDhw+nTCbju3fvaGlpyXPnzinhYnLfnTt32K9fPzo7O3PgwIEMCAhQdkjCdwT5eBlq4Qs9ePAAVapUwdmzZ2FsbIzNmzfDwcEB2Vme28nJCVOnToWTkxPq16+PihUrYv369di7d6/C5ueAfLnlHTt2YOvWrXj//n1eXY58MYebN5EyagyiDExRvEVjVL95CMHm1fDmjw3QjAyH5p4d8hU9NTTSVR85ciSOHz+Op0+fwtDQENu3b8eSJUsgSRIMDQ0xZMgQ7NixI+/i/0Z8fHzg5uaGChUqYNasWShTpgxcXFxw/fp1ZYcmfO8yyg75/VXYewTu7u5cvHixQtnw4cM5ZMiQbLcRFRXF06dP88aNGxn2BPbt20c9PT22atWK7dq1o66ursIDV9nx5MkTnj17lm/fZrLF44MH5LRplFWsSAJMggoPojJn2w6n/8X0u3hlZe/evWzWrFm68iVLlrB///5f3F5+U69evXQbAK1Zs4ZNmjRRUkTC9wb5dYeynLwKUiJ49OgRAwICsj0sExsbS01NzXRDQY8ePaKpqWmuxPTmzRvq6enxxo0baWX37t2jvr5+tlbEjI6OpoeHB42MjFi/fn2WKFGC48aNk+8Z/PIluXBh2qqeMkniP9qVOADt6Vr1T546lXX7mYmMjKSenh7v3LmTVhYTE8MqVaqk26Lye5OamkpJkpiUlKRQHhUVRU1NTSVFJXxvMksE4maxkgQEBKBnz5548eIFihQpgqJFi2LNmjVwdnb+bD0VFRVIkoSkpCSFHa0SEhIUNmHJSGpqKp4/fw49PT3o6upmetzevXvRokULODg4pJXZ2Nigc+fO2LFjB37++efPnmfkyJEoXrw4QkJCoKGhgbDgYPzRqBFeHDqEMkFBgEyGWGs7/F2+B35/XBaaJc3x++/1sbJTJaioZLRPUfbo6Ohg+fLlaNCgAbp27QoDAwNs2bIFrq6uSpkNlZtUVFRgaGiIp0+fKuw89/jxY5QsWVKJkQkFgbhHoASJiYlo1qwZ+vfvj9DQUDx9+hRz5syBh4cH3r59+9m6mpqaaNmyJWbPni3v0kH+Af/bb7+ha9eumdbbtWsXypUrBxcXF5QtWxY9evTIcLcxAIiPj4dOBlsr6ujoID4+/rPxxcXFYefOnVg4bx40zp4FunWDQZUqmPbkCVKDgnDGyQ3D3BahWGBPTItyxMRlHggI6IsuXay/Kgn8q0uXLvD19UXp0qWRkpKCDRs24K+//kp3/+N79OOPP2LYsGH48OEDACA8PBwjR47E4MGDlRyZ8N3LqJuQ31/f+9DQrl276Obmlq68T58+XLBgQZb1X758STs7O9auXZtDhgyhtbU13dzcGBMTk+Hxly5doomJCS9fvkxSPuOoT58+GS5tQZIPHjygsbGxwtj++/fvWbJkSW7cuJHJycmZxvb+3DkuLVKEslKlSIApOjr8W0uLY+s0okaRLpSkeZSk3zl8+CFGRqafASRkLikpiUOGDKGurm7aGkkjR45UWCFVED4H4oGy/OOPP/7AvXv3sGLFCoXy2bNn4/379/Dy8sqyjdTUVJw8eRKPHz9GtWrVUK9evUy/9Xbr1g116tTBsGHD0sri4+NRpkwZ+Pv7Z7jMwvTp07Fu3ToMGDAA4eHhWL58OTQ1NWFubo4PHz7gr7/+QosWLeQHv3sHbNkC/P034O+PZElCuJMTSo0di5bL1yJVrRHOnk1FcjLw44/2KFbsKp4/v4dt27Z9wbsm/Ovdu3d4+vQpypcvr7RnP4TvU2YPlCn9231OXt97j8DX15fm5uYKN3xTU1Pp6OjIvXv35vr56tevn+Gewg4ODrx69Wqm9S5fvszhw4dTR0eHY8eOld/sJXn+/HmWMjDg61WryHbtyH/X9a9Zk1y2jGd37aKBgTkbNZpFYCoBL2pq9ufp0/4kybdv37J48eIk5d9yg4ODM+3NCIKQeyCeI8gfIiMj8eTJE5ibm6Nx48Y4cuQIvL294enpCU1NTbRu3TrXz+no6IhDhw4plD1//hyPHz+GjY1NpvXq1KkDd3d3VK1aFV5eXlBRUQECAuBy6BCC4uNRctAg4MoVYORI8M4dhO47gwNlmmHrSR3ExPwEb291AC/QqdNrPHo0DY0aVQMgXwJCW1sbq1evRtmyZeHs7IzSpUtj5MiRSEpKyvXrFwTh88SsoW9o165dGDRoEOrUqQMtLS34+Phg/PjxKFGiBNq1a4ehQ4fmydISP/30ExwdHVG0aFF06tQJT58+xaRJkzB+/HgUL178s3Xfvn2LSmZmwPr1wJo1wOXLoJoaQstXxnat8qD7T7juH4abjS7g7ds4AICmphp69rTFyJE1sHTpZCQnf4CJiQkAICUlBZMnT4ajoyPmzJmD48ePo2rVqnjz5g369u2L8ePHY9GiRbn+HgiCkDlxj+AbCQ0NRbVq1XDmzBlUqyb/Zuzr64smTZogMDAwT5ac/lRwcDDmzp2L8+fPo2TJkhg0aBA6d+78+dk0N28i0ssLKtt3oDiItwbmOGDQAAvfWSPwg3yBN1VVCaVKSTA2TkKDBhXQsWMdVK9uDC0t+VTWqKgoeHh44NmzZ3B0dISPjw/s7OwQHR2Nn376CZ6enmmne/XqFSpXroyXL19CS0srw5Cio6Nx7tw5FClSBK6urijycaE5QRCyltk9ApEIvpGFCxciICAAq1evVijv2bMnnJycMGTIECVF9n8k8eR2KD78uR6lDm6B2ZsgxEMdO1EVq+GIqyoWKGuhieTkYGhqhmHUqE6YMmUAGjduAHNzc+zbtw/29vbYsmWLQs+GJG7cuJG2NIa9vT3Kly+PY8eOKcyJBwATExPcuHEDpUuXThff1q1bMWzYMDg4OCAuLg5Pnz7Fzp07Ua9evTx/bwShIBCrjypZXFxchg9x6erqIjY29pvHI5MRjx59wM2bb+Hr+xrh52+gzq0D6Jx0HeWRiDswweYyPfHKtS0q1ymH5uG3oXNpN5KT49GqVSv06zcdVatWxYYNq9GyZUsAwIwZM+Dm5oZNmzahT58+aeeSJAm1atVCrVq10spq1aqFI0eOKCQCX19fqKmpZfiA1MOHD/HTTz/hwoULsLW1BQCcOHECnp6eePr0KbS1tfPqrRKEgi+jO8j5/fU9zhry9fWlmZmZwuYm4eHhLFWqFO/evZun505NlTEgIIybN9/jqFFn2KDBNuroLKE6ZrMTuvGCVI4EmKSqzmvW9TihQQcOGvgjz58/n2mb169fp42NTbrynTt3smXLllnGdPv2bRoZGXH+/Pm8f/8+t2/fzrJly2a6T/OUKVM4evTodOXNmzfn9u3bszyfIAiZzxoSPYJvpEaNGujQoQNq1aqFgQMHQiaTYdWqVejVqxeqVKmSq+dKTk7FhQuhuHgxFJcvv8TVq68QHS2fjaOpqQZXmyLYUskXrkHHoB35DrSwBAfPxfh793Dixg0MaNceeklJ6NWrF3r27Inp06dneB5mMKyYUVlG7Ozs4O3tjTlz5mDVqlUoW7Ys/vzzz7TexX9FR0dneB/FyMgIUVFR2TqnIAiZyCg75PfX99gjIOVr/3t7e3PIkCEcOnQoz507l2t7AMhkMl679pLDh5+mkdEfBLyoojKf1apt4I8/nuT69XcYtP00U7t1J4sUkc/7b9aMPHyYTEmhj48Py5cvz+jo6LQ23717RyMjIz58+DDd+VJSUmhpacmDBw+mld2/f5+lS5ems7MzV65cmemzAQ8fPuS+ffu+qCd0/PhxVqlShQmf7Efw9u1bGhgY8OnTp9luRxAKM4jVRwumhw/fc9q0S6xQYTUBL2poLGTHjge4b1+QfAmHlBRy716yfn35H3exYuSwYWRgoEI7v/zyS4Z7/A4YMIBLly7N8Nz/7q3cqVMnduzYkSoqKrS2tuZff/3FVq1asWrVqnz//n3a8YmJiezevTuNjY3ZunVrli5dmi1btlRIPplJTU1l586d6eDgwJUrV3LhwoUsV64cp02b9oXvmCAUXpklAvFA2Xfo7dtYLFt2E05OW2BltRbTp1+GubkO1q51x5s3Q7BzZxu0a2IKnU1rgEqVAE9PICQEWLgQCA0Fli2Tl39CW1sbERER6c714cMHFCtWLMM46tati6CgILi5ucHb2xvz58/H/fv3MWDAABw8eBD29vYKzwTMnj0b4eHhCA4OxsGDBxEcHAx9fX2MGzcuy2tWUVHBli1bMHHiRFy+fBkBAQFYs2YNpk6d+mVvniAI6WWUHfL7qzD2CGJiErlly302b76bqqrzCXixWrUNnDfvGkNCov5/4Lt35JQppL6+vAfg6Eju2kV+ZqE4Ur6JjIGBgcJa/j4+PtTX1+eHDx8+WzcoKIjm5ubphrl8fHz46Z+VhYUFb926pXDMq1evWKxYMbFwmiB8AxA3i7/Mo0eP8OeffyIoKAi2trYYOnQozM3Nv2kMKSkynDnzHJs338fevQ8RG5uMMmWKY9y4WujWrTJsbY3+f/Dz58D8+fKnf+PjgbZtgXHjgLp1gWwswWxpaYlly5ahfv36qFu3LpKSkuDn54etW7d+du8CANDS0kJMTAySk5MVHvD6b28iKioKRkZGCnX19fWRmJiIlJQUqKqqZu+N+Y5FR0dj0qRJ2LJlC+Lj49GyZUvMnTsX5cqVU3ZoQiEmhoYycO3aNdStWxfa2toYPHgwUlNTUatWLdy7dy/Pz00SN268xqhRZ2FmthLu7rtx6NBjdO1qjfPnOyM4eCBmz3b5fxIICgL69gXKlwdWrAC6dAHu3wf27wecnbOVBP7VtWtXBAcHo2/fvhg2bBieP38Od3f3LOuVLl0a9vb2mDt3rvzGE+Qf+jNnzkTPnj3TjmvatCk2bNigUHfLli1wdnaGRgZ7ERc0JOHh4YGIiAj4+fnhxYsXsLe3R4MGDdL2GBAEpciom5DfX3k9NOTi4sKNGzcqlC1evJjt2rXLs3M+fvyBM2deZqVKawl4sUiRhfTw2M89ex4wISGDYZ2AAPKHH0gVFVJTkxw+nHz+PM/iy0pISAirVatGOzs7dujQgQYGBhw6dGjaiqWkfLaQqakpBwwYwG3btnHUqFE0MjJS2BKzILt69SrLly+fbhisa9eu6fagFoS8gPy4H4EkSR0BTANQGUBtktlaNyIvl5hISUmBpqYm4uPjFbZ+DA8Ph6WlZa7OWQ8Li8OuXUHYvPk+Ll9+CQBwcTFDjx42aN++IvT0NNNXevAAmDED2LYNKFoUGDoUGDMGyAfbFZKEj48PXrx4AUdHR1haWqY75s2bN1i9ejVu374NKysrDBo06JsPuSnLhg0bcObMGWzcuFGhfMWKFfD398eqVauUFJlQWOTXJSbuAvAEkG/+BaiqqqJYsWJ4/fo1ypQpk1YeGhqaK5uAxMcn4+DBx9iyJQDHjj1FSooMVaoYYM6c+ujatTLMzXXw4MEDeHnNwIcPH9CoUSO0a9cOaiEh8gSwcaM8Afz8szwB/GfMXZkkSUL9+vU/e0zJkiUxefLkbxRR/mJtbY1Zs2ZBJpPJl/T+6NKlS6hZM/1eIYLwrSj1HgHJAJIPlBnDf0mShH79+mHkyJFp+/NGR0dj7Nix6N+/f47aJImLF0PRp88xlCy5Al26HIav7xuMHFkD/v49cedOb4wf7whzcx3s2LED9evXh0wmQ+XKlbF21iwcLVcOrFQJsq1bcbZaNfRp0ABz9fTwvhDcXC1IHB0dYWZmhn79+uHFixeIiorCvHnzcO7cOfTq1UvZ4QmFWUbjRd/6BeAcgJpZHDMQwA0AN8zNzXN34Ow/4uPj2bVrVxoaGtLV1ZV6enrs37//Z/fqzYhMJuPx409Yr95WAl7U0VnCvn2P0dv7GVNSUtMdHxsbSwMDA/r5+ZFRUeTUqZRpazMF4CU7O9rp63PKlCncuXMne/bsyXLlyvHly5cKbTx69IhDhw6ls7Mze/TowevXr3/NWyHkssjISA4ZMoQ6OjosUqQIPTw8MnxyWxDyApT1ZDGA05APAf331faTY7JMBJ++vtVzBE+fPuWpU6cYEhLyxXVTU2Vs1mwXAS+ama3ksmW+jI1N+myd06dPs16dOuTq1WTJkvI/no4decDLi8WKFeOJEycUjh85ciR/+umntJ/v3r1LY2NjTp48mefPn+eiRYtobGzMY8eOfXH8Qt7LreVFBCG7lJYIsvPKr4kgpyIiIujp+TsBL1pZ/cjNm7dn6x/9naVLGaipKf9jqVuX/Lif8O+//05NTc10bfj5+bFy5cppP3fs2JELFixQOObo0aO0tbUVHzqCIIglJvKCj48PGjZsCHV1dZQtWxbz5s1DdHQ06tdvhGPHAGtrLcyY4YK5c3/HpEmTMm/o+XOgUyfYjhgB7ZQUXBoxAvDxARwdERYWhnXr1kFFRQVxcXEK1V6/fq3wsNfFixfRsWNHhWOaNWuG4OBgREZG5ualC4JQgCg1EUiS5CFJUiiAOgCOSJJ0QpnxfAl/f394eHhg4MCBiIqKwqFDh3Do0CF06NABiYl1EB9fBGvXtkWXLl1w9uxZrFy5Ei9evFBsJCkJmD0bqFwZOHQImD4d4RcvosvevWjQsCG6du2KihUrolatWrC2tsaQIUOQmpoKQP7U7pQpU9C3b9+05kqWLIknT54onOLVq1dQVVXNdOtHQRAEpQ8L5eSVH4aGunfvzoULFyqUvXr1impqBlRX92KnTgcVfte6dWvu2bPn/wU+PmSVKvJhIE9PMjg47VeJiYk8ePAg58yZwzJlytDZ2ZkdO3akuro6ixUrxqZNm1JPT4+jR49WGPJZsWIFHRwc0m4gR0VF0cPDQ+E+giAIhRfy8z2CL33lh0Tg4ODAa9eupSsvUqQHVVTm8cmTD2llMpmMNjY29PHxISMjyUGD5G+9uTl56FCG7ctkMjo4OHD58uVpZVFRUbSxseHo0aP54sWLDOtMnjyZJUqUoL29PfX09Ni7d2/Gx8d//QULgvDdyywRiHsEOWRtbY1Lly4plJ08eR9JSVWhofEPXr8OACB/UnnMmDH48OED3m3ejNTKlYHVq4HRo+VrArVqlWH7QUFBePPmDQYNGpRWVrx4cUyfPh337t2DqalpujqSJGHmzJkIDg7GX3/9hYCAAKxfvx6amhk8oSwIgvCRsp8s/m6NGTMG7u7uMDExgaenJ+7evYt27bZAVVUP7u5q8PDwgJ6eHkJDQ6GWkID9lpZosHIlHqio4Pn06WiSxdO1CQkJ0NbWVngCFZAng4SEhM/W1dXVzfaTqjKZDAcPHsTRo0ehpaWFbt26KWwyLwhCwSd6BDlkb2+P3bt3Y/ny5dDU1ISjYz/Ex5vAw0MLFSqYISUlBe7u7nDR0ECYmRkaPHoEjB+P5GvX0GnBArx///6z7dva2iIhIQFnzpxJK5PJZFixYgVaZdKL+FIymQxdunTBjBkzYGdnB0NDQ7Rr1w5Lly7NlfYFQfhOZDRelN9f+eEewaeWLPmDRYtOp43NWiYny58Yvnb5MqerqzNFksiyZckLF9KO9/T0TLe6aUZOnDhBQ0NDjhgxgosXL2b9+vXp7OzM2NjYXIn74MGDrF69usI+wM+ePaOuri7fvHmTK+cQBCH/gLhHkHdWrryN+HgtLFjgCjU1FeDtW9SeMgVTkpNxvVw54NYt4JPF2CRJkt+pz0LTpk3h6+sLAwMDBAUFYciQIThz5kyuTQU9cuQIevfurbAXgLm5Odzc3HD69OlcOYcgCPmfuEfwlcLD4/HokSVsbdXRrJklcPEi0KUL+P49xunpYWtsLO6kpODfdUsDAgLg7e2NlStXZqt9c3NzTJkyJU9iz2yf4oiICGhra+fJOQVByH9Ej+ArzZhxBampaoiP34XYhQsBNzdASwuHJ03C0VKl0KdvX9jZ2WHMmDEYPHgw6tWrh2XLlsHQ0FDZoaN79+5YtWoVnj59mlZ2/Phx3Lt3L1s7kwmCUDCIHsFXePDgPZYv98fAvjbo4bsV2mPGwM/UFBMNDRGwejUOHz4MOzs7dOnSBQcPHoSpqSn8/f0V9jlQJnt7e0yePBn29vZo2LAhIiIiEBgYiD179ogpp4JQiCh1h7KcyssdyjLy7Nkz/PHHH7hz5w4qVqyIoUOHolKlSmjbdh98zwThsf1xaFw8h4gBA3CwTh3oGxnB3d1dYYez/CwsLAze3t7Q0tJCkyZNRBIQhAIqv+5Qlu/du3cPbm5u6NWrF0aMGIFr166hXr16mDJlI/456Ad/k+3QuBoMbNgA3V690DPLFvMfQ0NDdO7cWdlhCIKgJCIRZGHy5Mn45Zdf8NNPPwEAWrRogQoVrDB/0GFcU9sJ46h44PBhoGlTJUcqCIKQMyIRZOHs2bNYvXq1QlnRx5o4Ff83dIoXgeR9FhBP4gqC8B0Ts4ayoK+vj5CQkLSfY2/cQoMZfZAMQP2qj0gCgiB890QiyMKAAQMwduxYREVFAYGBkDV0RQolLGjRFao2NsoOTxAE4auJoaEsjBs3DiEhIXApUwan4hORmqyO7qY/4MieJcoOTRAEIVeIHkEW1NTUsPz333HD2BgaVEVz9R+x7vI8McVSEIQCQySCrCQmAp6eUHn2HK1SeqH52NYoW7aEsqMSBEHINWJo6HNIYMAA4Nw5/FZxCB5EVMHhCbWVHZUgCEKuEj2Cz1m8GNi0Cfe6/ISpQZaYOdMZOjoaWVYTBEH4nogeQWZu3ADGj0dqm7Zoc80GtrZF0LevnbKjytSDBw8QEBAAa2trWFtbKzscQRC+I6JHkJGoKKBLF6BUKaxwGIYnT6OwYEFD+V4D+Ux8fDw6dOiAhg0bYt26dXBzc4Onpyfi4+OVHZogCN+J/PfJpmwkMGgQEByMiBXrMXlhAFq0sETTphbKjixD06ZNA0kEBwfj4MGDCA4OhpqaGn799VdlhyYIwndCrD76X1u3At26Ab//jmEva2Plylu4fbsXbGyUv39ARoyNjXHlyhWUL18+rSw4OBgODg4IDw9XYmSCIOQ3YvXRTKSkpOD06dN49eoVnG1tUXH0aKB2bQS06Y+V1Tdh0KBq+TYJAEBUVBSMjIwUyoyMjBAVFQWSkCRJSZEJgvC9KNSJ4MmTJ2jevDl0dXVRqVIlJA0bhgpxceCBAxg3wQfFihXBtGl1lR3mZzVt2hTr169PWx0VANavXw93d3eRBARByJZCnQh69+6NQYMGYfTo0cCdO+DWrThgbIzz231x5EgcvLwawMgodzaKzytz5syBm5sbgoKCUK9ePVy+fBm7du0Sm88LgpBthfZm8fPnzxEYGIgRI0bIbxAPGwapRAloLFiE1atfo1y5Ehg+3F7ZYWbJxsYGfn5+MDIywv79+6Gvr4+bN2/C1tZW2aEJgvCdKLQ9gvj4eBQtWhSqqqrArl3AhQvAqlU4c6sIYmN1MG9eA2hofB9vj4mJCaZNm6bsMARB+E4V2h6BlZUVNDU1cezoUWDOHKBSJUR17I5lyx7C3DwVnp5Wyg5REAThm1BqIpAkyUuSpEBJkm5LkrRPkiTdb3VuFRUVrFq1Cn/98APg54cz9vaoaj8aiYnq+PvvDuJGqyAIhYayewSnANiSrAogCMDEvDrRhw8fsHbtWixatAj37t0DADRs2BDbatZErLY2Nkt6ePmyArp2rYSGDctn0ZogCELBodREQPIkyZSPP14FYJYX5/H29oaVlRVOnDiBR48eoXHjxhg7dix47x6KnjkD7Z9/RgJaQFVVDXPnNsiLEARBEPKt/HQ3tC+AHZn9UpKkgQAGAoC5uXm2G01ISMAPP/yAPXv2oEED+Yf877//DicnJ4y8exdmmprwre2JbVOPY/JkJ5Qpo/N1VyEIgvCdyfMegSRJpyVJupvBq+0nx0wCkAJgS2btkPyLZE2SNf/7JO3nnDt3DpUqVUpLAgCgq6uLsT16oOSpU2CvXhg+4zZKldLG+PFirwFBEAqfPO8RkGz8ud9LktQLQCsAjZgHCx+lpqZCTS39Zdr98w/UZTIctW6LK6vuYe1adxQrViS3Ty8IgpDvKXvWUDMA4wG0IRmXF+dwdXXF7du34evrm1YWFxcHzdOnEW5lhaFLQlCtmhF69aqSF6cXBEHI95R9j+APABoATn2crnmV5ODcPIGWlhbWrFmDpk2bokOHDjAyMsKJLVtwLS4Ol8s2QPDpKJw+3RGqqsqeQCUIgqAcyp41VIFkGZLVP75yNQn8q127drh16xYqVKgASZKwuWdPqAD49YoOWrcuj0aNyubFaQVBEL4Lyu4RfDNmZmYYN26c/Ifu3RGtWQKXEkxwx0tMFxUEoXArNIkgjUyGlKPHcSChPH4cUQOVKul/UfWEhATs3LkTN27cgIWFBXr06JFuPwBBEITvSeEbGL9xA2ofwnFOyw5TptT5oqrv37+Ho6MjNm/eDEtLS9y5cwd2dnbw8/PLo2AFQRDyXqHrETxaugWWkBBWwwjjxg2Fq6srOnXqBA0NjSzrzpo1C46Ojli1alXaWkQbNmzAkCFDcOXKlbwOXRAEIU8Uqh5BSooM0bv24zpMYe1cBI6Ojli3bh2aNGmC+Pj4LOsfPHgQw4YNU1iQrnv37ggICMC7d+/yMnRBEIQ8U6gSwQYvb1RLCkFKUzfMmfM7Bg0aBG9vbxQvXhxr1qzJsr6Ghgbi4hQfd0hKSkJqairU1dXzKmxBEIQ8VagSgca5Q1AB4fzb8LQyFRUVDBgwAEePHs2yfteuXTFz5kwkJyenlXl5eaFBgwbQ1dXNi5AFQRDyXKG6R9CyyFOEqarCoEYNhfIPHz6gWLFiWdYfM2YMbty4ASsrKzRp0gS3bt1CXFwcjh8/nlchC4Ig5LlC1SPQ270b/cuXx+q1a9PKwsLCMG/ePPTo0SPL+hoaGti7dy92794NBwcHzJgxA7du3YKZWZ6sni0IgvBNSHmwzlueq1mzJm/cuJGjuoGBgWjVqhX09PRQtmxZnDlzBkOHDsWMGTPErmSCIBRokiT5kqz53/JCNTQEANbW1njw4AHOnj2LsLAwLF68WHyjFwShUCt0iQAAVFVV0bjxZ1fHFgRBKDQK1T0CQRAEIT2RCARBEAq5Qjk0lJmwsDBs3LgRwcHBqFGjBjp37oyiRYsqOyxBEIQ8JXoEH/n7+8PW1ha3b9+GpaUltm3bhtq1ayM8PFzZoQmCIOSpQjd9NDPOzs4YMGAAevfuDQAgiR9//BFaWlpYuHBhrp5LEARBGTKbPip6BADCw8Nx9+5ddO/ePa1MkiQMGzYMBw8eVGJkgiAIeU8kAgBqamqQyWRISkpSKI+NjYWmpqaSohIEQfg2RCIAUKJECbi6umLu3LlpZcnJyZg5cya6du2qxMgEQRDynkgEH61YsQJ79+5FrVq10L9/f1SsWBFqamoYO3asskMTBEHIU2L66EelS5eGv78/Tp8+jWfPnmHw4MGoWTPdPRVBEIQCRySCT6iqqsLd3V3ZYQiCIHxTYmhIEAShkBOJQBAEoZATiUAQBKGQE4lAEAShkBOJQBAEoZD7LtcakiTpHYBnX1DFEEBYHoWTn4nrLlzEdRc+X3rtZUka/bfwu0wEX0qSpBsZLbRU0InrLlzEdRc+uXXtYmhIEAShkBOJQBAEoZArLIngL2UHoCTiugsXcd2FT65ce6G4RyAIgiBkrrD0CARBEIRMiEQgCIJQyBX4RCBJUjNJkh5IkvRIkqQJyo7nW5AkqYwkSWclSQqQJOmeJEk/KTumb0mSJFVJkvwkSTqs7Fi+FUmSdCVJ2i1JUuDHP/c6yo7pW5AkadTHv+N3JUnaJklSgdxSUJKkdZIkvZUk6e4nZfqSJJ2SJOnhx//q5bT9Ap0IJElSBfAngOYAbAB0lSTJRrlRfRMpAMaQrAzACcDQQnLd//oJQICyg/jGlgA4TtIaQDUUguuXJKk0gBEAapK0BaAKoItyo8ozGwA0+0/ZBADeJK0AeH/8OUcKdCIAUBvAI5JPSCYB2A6grZJjynMkX5G8+fH/oyH/UCit3Ki+DUmSzAC0BLBG2bF8K5Ik6QBwAbAWAEgmkYxQalDfjhqAopIkqQHQAvBSyfHkCZIXALz/T3FbAH9//P+/AbTLafsFPRGUBhDyyc+hKCQfiP+SJMkCgD2Aa0oO5VtZDOBnADIlx/EtlQPwDsD6j0NiayRJ0lZ2UHmN5AsA8wE8B/AKQCTJk8qN6psqSfIVIP/yB8A4pw0V9EQgZVBWaObLSpJUDMAeACNJRik7nrwmSVIrAG9J+io7lm9MDUANACtI2gOIxVcME3wvPo6JtwVgCcAUgLYkSd2VG9X3qaAnglAAZT752QwFtOv4X5IkqUOeBLaQ3KvseL4RZwBtJEkKhnwY0E2SpM3KDembCAUQSvLfXt9uyBNDQdcYwFOS70gmA9gLoK6SY/qW3kiSZAIAH//7NqcNFfREcB2AlSRJlpIkFYH8RtJBJceU5yRJkiAfLw4guVDZ8XwrJCeSNCNpAfmf9RmSBf4bIsnXAEIkSar0sagRgPtKDOlbeQ7ASZIkrY9/5xuhENwk/8RBAL0+/n8vAAdy2lCB3ryeZIokScMAnIB8RsE6kveUHNa34AygB4A7kiT5fyz7heRR5YUk5LHhALZ8/MLzBEAfJceT50hekyRpN4CbkM+U80MBXW5CkqRtABoCMJQkKRTAVABzAOyUJKkf5EmxY47bF0tMCIIgFG4FfWhIEARByIJIBIIgCIWcSASCIAiFnEgEgiAIhZxIBIIgCIWcSASCIAiFnEgEgiAIhZxIBIKQCz7u/9Dk4///JknSUmXHJAjZVaCfLBaEb2gqgBmSJBlDvtprGyXHIwjZJp4sFoRcIknSeQDFADT8uA+EIHwXxNCQIOQCSZLsAJgASBRJQPjeiEQgCF/p4xLAWyBfGz9WkiR3JYckCF9EJAJB+AqSJGlBvg7+GJIBAGYCmKbUoAThC4l7BIIgCIWc6BEIgiAUciIRCIIgFHIiEQiCIBRyIhEIgiAUciIRCIIgFHIiEQiCIBRyIhEIgiAUcv8DV2sGsh79Eb0AAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fitted_spline_model = sm.ols('y~x+h(x,1,1)+h(x,2,1)+h(x,3,1)+h(x,4,1)+h(x,5,1)+h(x,6,1)+h(x,7,1)+h(x,8,1)+h(x,9,1)',\n", " data={'x':x,'y':y}).fit()\n", "\n", "plt.scatter(x,y,facecolors='none', edgecolors='black')\n", "plt.title(\"9 knots\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$\")\n", "plt.plot(x, fitted_spline_model.predict(),color=\"darkblue\", label=\"Linear Spline with 9 knots\")\n", "plt.plot(x, norm.ppf(x/10), color=\"red\", label=\"Truth\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using code to write out the formula this time. Comments provided for those who are new to python" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'y ~ x + h(x,0.0,1) + h(x,0.4166666666666667,1) + h(x,0.8333333333333334,1) + h(x,1.25,1) + h(x,1.6666666666666667,1) + h(x,2.0833333333333335,1) + h(x,2.5,1) + h(x,2.916666666666667,1) + h(x,3.3333333333333335,1) + h(x,3.75,1) + h(x,4.166666666666667,1) + h(x,4.583333333333334,1) + h(x,5.0,1) + h(x,5.416666666666667,1) + h(x,5.833333333333334,1) + h(x,6.25,1) + h(x,6.666666666666667,1) + h(x,7.083333333333334,1) + h(x,7.5,1) + h(x,7.916666666666667,1) + h(x,8.333333333333334,1) + h(x,8.75,1) + h(x,9.166666666666668,1) + h(x,9.583333333333334,1) + h(x,10.0,1)'" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n_knots = 25\n", "\n", "# make a list of strings that each look like 'h(x,?,1)' where ? takes the values in np.linspace(0,10,n_knots)\n", "components = ['h(x,{},1)'.format(x) for x in np.linspace(0,10,n_knots)]\n", "# glue all the strings in 'components' together with \" + \" between each\n", "formula = ' + '.join(components)\n", "# paste a 'y ~ x + ' in front of the above. Now we've got a full formula!\n", "final_formula = 'y ~ x + ' + formula\n", "\n", "final_formula" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fitted_spline_model = sm.ols(final_formula,data={'x':x,'y':y}).fit()\n", "\n", "plt.scatter(x,y,facecolors='none', edgecolors='black')\n", "plt.title(\"25 knots\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$\")\n", "plt.plot(x, fitted_spline_model.predict(),color=\"darkblue\", label=\"Linear Spline with 25 knots\")\n", "plt.plot(x, norm.ppf(x/10), color=\"red\", label=\"Truth\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Cubic splines, instead of linear. Still using code to write the formula. [Knots at 2,5,8, each one cubic; starting intercept, slope, acceleration, and jerk]" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "components = ['h(x,{},3)'.format(x) for x in [2,5,8]]\n", "formula = ' + '.join(components)\n", "final_formula = 'y~x + np.power(x,2) + np.power(x,3) + ' + formula\n", "\n", "fitted_spline_model = sm.ols(final_formula,data={'x':x,'y':y}).fit()\n", "\n", "plt.scatter(x,y,facecolors='none', edgecolors='black')\n", "plt.title(\"3 knots\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$\")\n", "plt.plot(x, fitted_spline_model.predict(),color=\"darkblue\", label=\"Cubic Spline with 3 knots\")\n", "plt.plot(x, norm.ppf(x/10), color=\"red\", label=\"Truth\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As above, but with more knots (a more flexible fit)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "components = ['h(x,{},3)'.format(x) for x in [1,2,3.5,5,6.5,8]]\n", "formula = ' + '.join(components)\n", "final_formula = 'y~x + np.power(x,2) + np.power(x,3) + ' + formula\n", "\n", "fitted_spline_model = sm.ols(final_formula,data={'x':x,'y':y}).fit()\n", "\n", "plt.scatter(x,y,facecolors='none', edgecolors='black')\n", "plt.title(\"6 knots\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$\")\n", "plt.plot(x, fitted_spline_model.predict(),color=\"darkblue\", label=\"Cubic Spline with 3 knots\")\n", "plt.plot(x, norm.ppf(x/10), color=\"red\", label=\"Truth\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "More knots" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n_knots = 9\n", "components = ['h(x,{},3)'.format(x) for x in np.linspace(0,10,n_knots)]\n", "formula = ' + '.join(components)\n", "final_formula = 'y~x + np.power(x,2) + np.power(x,3) + ' + formula\n", "\n", "fitted_spline_model = sm.ols(final_formula,data={'x':x,'y':y}).fit()\n", "\n", "plt.scatter(x,y,facecolors='none', edgecolors='black')\n", "plt.title(\"9 knots\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$\")\n", "plt.plot(x, fitted_spline_model.predict(),color=\"darkblue\", label=\"Cubic Spline with 9 knots\")\n", "plt.plot(x, norm.ppf(x/10), color=\"red\", label=\"Truth\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Even more knots. As with the linear splines, this looks like it is overfitting a lot." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n_knots = 25\n", "components = ['h(x,{},3)'.format(x) for x in np.linspace(0,10,n_knots)]\n", "formula = ' + '.join(components)\n", "final_formula = 'y~x + np.power(x,2) + np.power(x,3) + ' + formula\n", "\n", "fitted_spline_model = sm.ols(final_formula,data={'x':x,'y':y}).fit()\n", "\n", "plt.scatter(x,y,facecolors='none', edgecolors='black')\n", "plt.title(\"25 knots\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$\")\n", "plt.plot(x, fitted_spline_model.predict(),color=\"darkblue\", label=\"Cubic Spline with 25 knots\")\n", "plt.plot(x, norm.ppf(x/10), color=\"red\", label=\"Truth\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It turns out that the *number* of knots matters far more than *where* they are placed. You can play with the code above to verify if you wish." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Smoothing splines\n", "Smoothing splines, as described in class, minimize the sum of squared errors subject to a penalty that depends on the wiggliness of the function. The resulting solution is a cubic spline with knots at every data value that is regularized according to a smoothing parameter.\n", "\n", "We use the csaps library to implement smoothing splines. The smoothing parameter takes on values between 0 and 1, and is the weight attached to the error sum of squares of the weighted average between the error sum of squares and the wiggliness penalty. A smoothing parameter of 0 correspondends to a least-squares fit, and a parameter of 1 corresponds to connecting-the-dots." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "from csaps import csaps" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Read in csaps to carry out smoothing splines." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for cur_smoothing in [0, 0.2, 0.4, 0.6, 0.8, 0.95]:\n", " diab_sort = diab\n", " diab_sort['age'] = diab_sort['age']+np.random.normal(0,0.001, len(diab_sort)) \n", " # ties not allowed (and the data is already sorted)\n", " diab_sort = diab.sort_values(['age']) # need to re-sort\n", "\n", " x = diab_sort['age']\n", " y = diab_sort['y']\n", " xs = np.linspace(min(x), max(x), len(x))\n", " ys = csaps(diab_sort['age'], diab_sort['y'], xs, smooth=cur_smoothing)\n", "\n", " plt.plot(x, y, 'o', xs, ys, '-')\n", " plt.title(\"Smoothing spline, smoothing parameter = {}\".format(cur_smoothing))\n", " plt.xlabel(\"Age\")\n", " plt.ylabel(\"y\")\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can select the smoothing parameter by CV." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([3.82575939, 3.56948936, 3.84662234, 4.16899586, 4.6888201 ,\n", " 5.70534349])" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.model_selection import KFold\n", "\n", "candidate_smoothings = [0, 0.2, 0.4, 0.6, 0.8, 0.95]\n", "\n", "kf = KFold(n_splits=5, random_state=47, shuffle=True)\n", "scores = np.zeros((5,len(candidate_smoothings)))\n", "\n", "for i, (train_index, test_index) in enumerate(kf.split(diab_sort)):\n", " train_df = diab_sort.iloc[train_index,:]\n", " test_df = diab_sort.iloc[test_index,:]\n", " for j,cur_smoothing in enumerate(candidate_smoothings):\n", " train_df_sort = train_df.sort_values(['age'])\n", " test_df_sort = test_df.sort_values(['age'])\n", " x = train_df_sort['age']\n", " y = train_df_sort['y']\n", " xs = test_df_sort['age']\n", " ys = csaps(x,y,xs,smooth=cur_smoothing)\n", " scores[i,j] = sum((test_df['y']-ys)**2)\n", " \n", "np.mean(scores, axis=0)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "best_s = candidate_smoothings[np.argmin(np.mean(scores, axis=0))]\n", "x = diab_sort['age']\n", "y = diab_sort['y']\n", "xs = np.linspace(min(x), max(x), len(x))\n", "ys = csaps(diab_sort['age'], diab_sort['y'], xs, smooth=best_s)\n", "\n", "plt.plot(x, y, 'o', xs, ys, '-')\n", "plt.title(\"Smoothing spline, optimal smoothing parameter = {}\".format(best_s))\n", "plt.xlabel(\"Age\")\n", "plt.ylabel(\"y\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## B-Splines\n", "Back to the diabetes data. First, let's see the data" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "diab_sort = diab\n", "diab_sort['age'] = diab_sort['age']+np.random.normal(0,0.001,len(diab_sort)) # again, ties not allowed\n", "diab_sort = diab_sort.sort_values(['age'])\n", "\n", "ax = diab_sort.plot.scatter(x='age',y='y',c='Red',title=\"Diabetes data with least-squares cubic fit\")\n", "ax.set_xlabel(\"Age at Diagnosis\")\n", "ax.set_ylabel(\"Log C-Peptide Concentration\")\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Get quartiles" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "quarts = diab_sort['age'].quantile([0.25, 0.5, 0.75]).values.reshape(-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Build a Bspline model. Call `splrep` (spline representation) to find the knots and coefficients that smooth the given data, then call BSpline to build something that can predict on given values. Notice that when we're done `b_spline_model` can be called like a function" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array(4.99125149)" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.interpolate import splrep\n", "from scipy.interpolate import BSpline\n", "\n", "t,c,k = splrep(diab_sort['age'].values, diab_sort['y'].values, t=quarts)\n", "b_spline_model = BSpline(t,c,k)\n", "b_spline_model(7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`LSQUnivariateSpline` fits splines to data, using user-specified knots" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "from scipy.interpolate import LSQUnivariateSpline\n", "\n", "natural_spline_model = LSQUnivariateSpline(diab_sort['age'].values, diab_sort['y'].values, quarts)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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"text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = diab_sort.plot.scatter(x='age',y='y',c='grey',title=\"Diabetes data\")\n", "ax.plot(diab_sort['age'], b_spline_model(diab_sort['age']), label=\"B-spline, knots at quartiles\")\n", "plt.legend()\n", "plt.show()\n", "\n", "ax = diab_sort.plot.scatter(x='age',y='y',c='grey',title=\"Diabetes data\")\n", "ax.plot(diab_sort['age'], natural_spline_model(diab_sort['age']), label=\"Natural Spline, knots at quartiles\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## GAMs\n", "Generalized Aditive Models essentially provide spline-like fits when there are multiple input variables. We use the PyGam library, which relies on B-splines (really penalized B-splines, a.k.a. P-splines) as the smoother of choice.\n", "\n", "Here we work with Kyphosis data, on 81 children who received a corrective spinal surgery. Each row records the child's age, the number of vertebrae operated on, the first vertebrae involved in the operation, and whether the operation was a success or experienced complications." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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AgeNumberStartoutcome
count64.00000064.00000064.00000064.000000
mean77.1093754.14062511.2812500.203125
std58.1208691.6984324.9263420.405505
min1.0000002.0000001.0000000.000000
25%19.2500003.0000008.7500000.000000
50%75.5000004.00000013.0000000.000000
75%128.5000005.00000016.0000000.000000
max206.00000010.00000017.0000001.000000
\n", "
" ], "text/plain": [ " Age Number Start outcome\n", "count 64.000000 64.000000 64.000000 64.000000\n", "mean 77.109375 4.140625 11.281250 0.203125\n", "std 58.120869 1.698432 4.926342 0.405505\n", "min 1.000000 2.000000 1.000000 0.000000\n", "25% 19.250000 3.000000 8.750000 0.000000\n", "50% 75.500000 4.000000 13.000000 0.000000\n", "75% 128.500000 5.000000 16.000000 0.000000\n", "max 206.000000 10.000000 17.000000 1.000000" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.model_selection import train_test_split\n", "\n", "kyphosis = pd.read_csv(\"data/kyphosis.csv\")\n", "kyphosis[\"outcome\"] = 1*(kyphosis[\"Kyphosis\"] == \"present\")\n", "\n", "kyph_train, kyph_test = train_test_split(kyphosis, test_size=.2, stratify=kyphosis['outcome'])\n", "\n", "kyph_train.describe()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using pygam is a lot like using the formula interface for statsmodels, but with raw code instead of with strings. Instead of `'s(Age)+s(Number)+s(Start)'` we have `s(0)+s(1)+s(2)` (the corresponding column indices). `s` is for 'smooth'. Each smooth accepts a `lam` parameter specifying the degree of smoothing. As before, larger lambdas mean smoother curves" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "from pygam import LogisticGAM, s\n", "\n", "X = kyph_train[[\"Age\",\"Number\",\"Start\"]]\n", "y = kyph_train[\"outcome\"]\n", "kyph_gam = LogisticGAM(s(0)+s(1, lam=0.5)+s(2)).fit(X,y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Correct classification rate is pretty good!" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.921875" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kyph_gam.accuracy(X,y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Summary of GAM fit on training data:" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "LogisticGAM \n", "=============================================== ==========================================================\n", "Distribution: BinomialDist Effective DoF: 13.6787\n", "Link Function: LogitLink Log Likelihood: -12.3667\n", "Number of Samples: 64 AIC: 52.0909\n", " AICc: 61.6165\n", " UBRE: 2.9849\n", " Scale: 1.0\n", " Pseudo R-Squared: 0.6171\n", "==========================================================================================================\n", "Feature Function Lambda Rank EDoF P > x Sig. Code \n", "================================= ==================== ============ ============ ============ ============\n", "s(0) [0.6] 20 8.1 2.46e-01 \n", "s(1) [0.5] 20 4.3 1.59e-01 \n", "s(2) [0.6] 20 1.2 6.99e-02 . \n", "intercept 1 0.0 1.86e-02 * \n", "==========================================================================================================\n", "Significance codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n", "\n", "WARNING: Fitting splines and a linear function to a feature introduces a model identifiability problem\n", " which can cause p-values to appear significant when they are not.\n", "\n", "WARNING: p-values calculated in this manner behave correctly for un-penalized models or models with\n", " known smoothing parameters, but when smoothing parameters have been estimated, the p-values\n", " are typically lower than they should be, meaning that the tests reject the null too readily.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/chris/anaconda3/envs/cs109a/lib/python3.7/site-packages/ipykernel_launcher.py:1: UserWarning: KNOWN BUG: p-values computed in this summary are likely much smaller than they should be. \n", " \n", "Please do not make inferences based on these values! \n", "\n", "Collaborate on a solution, and stay up to date at: \n", "github.com/dswah/pyGAM/issues/163 \n", "\n", " \"\"\"Entry point for launching an IPython kernel.\n" ] } ], "source": [ "kyph_gam.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "GAMs provide plots of the effect of increasing each variable (conditional on / adjusted for the other variables)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "res = kyph_gam.deviance_residuals(X,y)\n", "for i, term in enumerate(kyph_gam.terms):\n", " if term.isintercept:\n", " continue\n", "\n", " XX = kyph_gam.generate_X_grid(term=i)\n", " pdep, confi = kyph_gam.partial_dependence(term=i, X=XX, width=0.95)\n", " pdep2, _ = kyph_gam.partial_dependence(term=i, X=X, width=0.95)\n", " plt.figure()\n", " plt.plot(XX[:, term.feature], pdep)\n", " plt.plot(XX[:, term.feature], confi, c='r', ls='--')\n", " plt.title(X.columns.values[term.feature])\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Above, we see that as age ranges from 1 to 200 the chance of success first increases and then decreases, though with wide error bars. Moreover, we see that the Number of the vertebrae appears to have no effect or a mild effect until it reaches 12, and then drastically lowers." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below, we try a model with only \"Age\" and \"Start\". In just a moment we'll compare the two models via cross-validation." ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X = kyph_train[[\"Age\",\"Number\",\"Start\"]]\n", "y = kyph_train[\"outcome\"]\n", "small_kyph_gam = LogisticGAM(s(0)+s(2)).fit(X,y)\n", "\n", "\n", "res = small_kyph_gam.deviance_residuals(X,y)\n", "for i, term in enumerate(small_kyph_gam.terms):\n", " if term.isintercept:\n", " continue\n", "\n", " XX = small_kyph_gam.generate_X_grid(term=i)\n", " pdep, confi = small_kyph_gam.partial_dependence(term=i, X=XX, width=0.95)\n", " pdep2, _ = small_kyph_gam.partial_dependence(term=i, X=X, width=0.95)\n", " plt.figure()\n", " plt.plot(XX[:, term.feature], pdep)\n", " plt.plot(XX[:, term.feature], confi, c='r', ls='--')\n", " plt.title(X.columns.values[term.feature])\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Test Accuracy m1: 0.82, m2: 0.76\n" ] } ], "source": [ "from sklearn.metrics import accuracy_score\n", "\n", "X_test = kyph_test[[\"Age\",\"Number\",\"Start\"]]\n", "y_test = kyph_test[\"outcome\"]\n", "\n", "acc = accuracy_score(y_test, kyph_gam.predict(X_test))\n", "acc_small = accuracy_score(y_test, small_kyph_gam.predict(X_test))\n", "\n", "print(\"Test Accuracy m1: {:0.2f}, m2: {:0.2f}\".format(acc, acc_small))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We find that the richer model has a higher accuracy on the test set (it gets rid of one false positive present in the smaller model). Depending on taste, this may or may not be enough to declare the larger model the better.\n", "\n", "A cross-validation (below) would make better use of the small data than a simple train-test split. (We again stratify on the outcome to ensure all test sets have a representative number of kyphosis cases)" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Average accuracy [0.71617647 0.74044118]\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.model_selection import StratifiedKFold\n", "\n", "kf = StratifiedKFold(n_splits=5, random_state=47, shuffle=True)\n", "scores = np.zeros((5,2))\n", "\n", "for i, (train_index, test_index) in enumerate(kf.split(kyphosis, kyphosis['outcome'])):\n", " train_df = kyphosis.iloc[train_index,:]\n", " test_df = kyphosis.iloc[test_index,:]\n", " \n", " # with all three (inserting lower smoothing on 'number' to prevent errors while fitting)\n", " cur_model_all = LogisticGAM(s(0)+s(1, lam=.5)+s(2)).fit(train_df[['Age', 'Number', 'Start']], train_df['outcome'])\n", " scores[i,0] = accuracy_score(test_df['outcome'], cur_model_all.predict(test_df[['Age', 'Number', 'Start']]))\n", " \n", " # dropping 'number'\n", " cur_model_some = LogisticGAM(s(0)+s(1)).fit(train_df[['Age', 'Number', 'Start']], train_df['outcome'])\n", " scores[i,1] = accuracy_score(test_df['outcome'], cur_model_some.predict(test_df[['Age', 'Number', 'Start']]))\n", " \n", "print(\"Average accuracy\", np.mean(scores, axis=0))\n", "plt.scatter([0]*5, scores[:,0])\n", "plt.scatter([1]*5, scores[:,1])\n", "plt.xlabel(\"Model\")\n", "plt.ylabel(\"CV Accuracy\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a naive average, it appears that the second model (without 'Number') is has the better accuracy. However, plotting the various CV scores shows that the two models aren't particularly different. As the test is inconclusive, one might choose the model without 'number' as it does not appear to be noticeably weaker, or one might stick with the richer model as it does not noticeably overfit." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }