{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# CS109B Data Science 2: Advanced Topics in Data Science \n", "## Lab 2 - Smoothers and Generalized Additive Models - Model Fitting\n", "\n", "
Spring 2020
\n", "\n", "**Harvard University**
\n", "**Spring 2020**
\n", "**Instructors:** Mark Glickman, Pavlos Protopapas, and Chris Tanner
\n", "**Lab Instructors:** Chris Tanner and Eleni Kaxiras
\n", "**Content:** Eleni Kaxiras and Will Claybaugh\n", "\n", "---" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "## RUN THIS CELL TO PROPERLY HIGHLIGHT THE EXERCISES\n", "import requests\n", "from IPython.core.display import HTML\n", "styles = requests.get(\"https://raw.githubusercontent.com/Harvard-IACS/2019-CS109B/master/content/styles/cs109.css\").text\n", "HTML(styles)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.interpolate import interp1d\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "\n", "%matplotlib inline " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Learning Goals\n", "\n", "By the end of this lab, you should be able to:\n", "* Understand how to implement GAMs with the Python package `pyGAM`\n", "* Learn about the practical aspects of Splines and how to use them.\n", "\n", "**This lab corresponds to lectures 1, 2, and 3 and maps to homework 1.**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Table of Contents\n", "\n", "* 1 - Overview - A Top View of LMs, GLMs, and GAMs to set the stage\n", "* 2 - A review of Linear Regression with `statsmodels`. What are those weird formulas?\n", "* 3 - Splines\n", "* 4 - Generative Additive Models with pyGAM\n", "* 5 - Smooting Splines using pyGAM" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "Linear Models (LM), Generalized Linear Models (GLMs), Generalized Additive Models (GAMs), Splines, Natural Splines, Smoothing Splines! So many definitions. Let's try and work through an example for each of them so we can better understand them. \n", "\n", "![](../images/GAM_venn.png)\n", "*image source: Dani Servén Marín (one of the developers of pyGAM)*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A - Linear Models\n", "\n", "First we have the **Linear Models** which you know from 109a. These models are linear in the coefficients. Very *interpretable* but suffer from high bias because let's face it, few relationships in life are linear. Simple Linear Regression (defined as a model with one predictor) as well as Multiple Linear Regression (more than one predictors) are examples of LMs. Polynomial Regression extends the linear model by adding terms that are still linear for the coefficients but non-linear when it somes to the predictiors which are now raised in a power or multiplied between them.\n", "\n", "![](../images/linear.png)\n", "\n", "$$\n", "\\begin{aligned}\n", "y = \\beta{_0} + \\beta{_1}{x_1} & \\mbox{(simple linear regression)}\\\\\n", "y = \\beta{_0} + \\beta{_1}{x_1} + \\beta{_2}{x_2} + \\beta{_3}{x_3} & \\mbox{(multiple linear regression)}\\\\\n", "y = \\beta{_0} + \\beta{_1}{x_1} + \\beta{_2}{x_1^2} + \\beta{_3}{x_3^3} & \\mbox{(polynomial regression)}\\\\\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Discussion
\n", "\n", " - What does it mean for a model to be **interpretable**?\n", " - Are linear regression models interpretable? Are random forests? What about Neural Networks such as FFNs and CNNs? \n", " - Do we always want interpretability? Describe cases where we do and cases where we do not care. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### B - Generalized Linear Models (GLMs)\n", "\n", "![](../images/GLM.png)\n", "\n", "$$\n", "\\begin{aligned}\n", "y = \\beta{_0} + \\beta{_1}{x_1} + \\beta{_2}{x_2} + \\beta{_3}{x_3}\n", "\\end{aligned}\n", "$$\n", "\n", "\n", "**Generalized Linear Models** is a term coined in the early 1970s by Nelder and Wedderburn for a class of models that includes both Linear Regression and Logistic Regression. A GLM fits one coefficient per feature (predictor). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### C - Generalized Additive Models (GAMs)\n", "\n", "Hastie and Tidshirani coined the term **Generalized Additive Models** in 1986 for a class of non-linear extensions to Generalized Linear Models.\n", "\n", "![](../images/GAM.png)\n", "\n", "$$\n", "\\begin{aligned}\n", "y = \\beta{_0} + f_1\\left(x_1\\right) + f_2\\left(x_2\\right) + f_3\\left(x_3\\right) \\\\\n", "y = \\beta{_0} + f_1\\left(x_1\\right) + f_2\\left(x_2, x_3\\right) + f_3\\left(x_3\\right) & \\mbox{(with interaction terms)}\n", "\\end{aligned}\n", "$$\n", "\n", "In practice we add splines and regularization via smoothing penalties to our GLMs. Decision Trees also fit in this category.\n", "\n", "*image source: Dani Servén Marín*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### D - Basis Functions\n", "\n", "In our models we can use various types of functions as \"basis\". \n", "- Monomials such as $x^2$, $x^4$ (**Polynomial Regression**)\n", "- Sigmoid functions (neural networks)\n", "- Fourier functions \n", "- Wavelets \n", "- **Regression splines** which we will look at shortly." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Discussion
\n", "\n", " - Where does polynomial regression fit in all this?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Answer: GLMs include Polynomial Regression so the graphic above should really include curved lines, not just straight..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation\n", "\n", "### 1 - Linear/Polynomial Regression\n", "\n", "We will use the `diabetes` dataset.\n", "\n", "Variables are:\n", "- subject: subject ID number\n", "- age: age diagnosed with diabetes\n", "- acidity: a measure of acidity called base deficit\n", "Response:\n", "- y: natural log of serum C-peptide concentration\n", "\n", "*Original source is Sockett et al. (1987) mentioned in Hastie and Tibshirani's book \n", "\"Generalized Additive Models\".*\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Reading data and (some) exploring in Pandas:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " subject age acidity y\n", "count 43.000000 43.000000 43.000000 43.000000\n", "mean 22.000000 9.032558 -8.148837 4.746512\n", "std 12.556539 4.022539 7.123080 0.720565\n", "min 1.000000 0.900000 -29.000000 3.000000\n", "25% 11.500000 5.500000 -12.700000 4.450000\n", "50% 22.000000 10.400000 -7.800000 4.900000\n", "75% 32.500000 11.850000 -2.000000 5.100000\n", "max 43.000000 15.600000 -0.200000 6.600000" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diab.describe()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting with matplotlib:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax0 = diab.plot.scatter(x='age',y='y',c='Red',title=\"Diabetes data\") #plotting direclty from pandas!\n", "ax0.set_xlabel(\"Age at Diagnosis\")\n", "ax0.set_ylabel(\"Log C-Peptide Concentration\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Linear/Polynomial regression with statsmodels. \n", "\n", "As you remember from 109a, we have two tools for Linear Regression:\n", "- `statsmodels` [https://www.statsmodels.org/stable/regression.html](https://www.statsmodels.org/stable/regression.html), and \n", "- `sklearn`[https://scikit-learn.org/stable/index.html](https://scikit-learn.org/stable/index.html)\n", "\n", "Previously, we worked from a vector of target values and a design matrix we built ourself (e.g. using `sklearn`'s PolynomialFeatures). `statsmodels` allows users to fit statistical models using R-style **formulas**. They build the target value and design matrix for you. \n", "\n", "```\n", "# our target variable is 'Lottery', while 'Region' is a categorical predictor\n", "df = dta.data[['Lottery', 'Literacy', 'Wealth', 'Region']]\n", "\n", "formula='Lottery ~ Literacy + Wealth + C(Region) + Literacy * Wealth'\n", "```\n", "\n", "For more on these formulas see:\n", "\n", "- https://www.statsmodels.org/stable/examples/notebooks/generated/formulas.html\n", "- https://patsy.readthedocs.io/en/latest/overview.html " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "import statsmodels.formula.api as sm\n", "\n", "model1 = sm.ols('y ~ age',data=diab)\n", "fit1_lm = model1.fit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's build a dataframe to predict values on (sometimes this is just the test or validation set). Very useful for making pretty plots of the model predictions - predict for TONS of values, not just whatever's in the training set." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " age\n", "0 0.000000\n", "1 0.161616\n", "2 0.323232\n", "3 0.484848\n", "4 0.646465" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x_pred = np.linspace(0,16,100)\n", "\n", "predict_df = pd.DataFrame(data={\"age\":x_pred})\n", "predict_df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use `get_prediction().summary_frame()` to get the model's prediction (and error bars!)" ] }, { "cell_type": "code", "execution_count": 9, "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
14.0094590.2409293.5228924.4960262.6168565.402063
24.0228870.2372803.5436914.5020842.6328425.412932
34.0363150.2336423.5644664.5081652.6487865.423845
44.0497430.2300163.5852164.5142702.6646875.434800
\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 4.009459 0.240929 3.522892 4.496026 2.616856 \n", "2 4.022887 0.237280 3.543691 4.502084 2.632842 \n", "3 4.036315 0.233642 3.564466 4.508165 2.648786 \n", "4 4.049743 0.230016 3.585216 4.514270 2.664687 \n", "\n", " obs_ci_upper \n", "0 5.391235 \n", "1 5.402063 \n", "2 5.412932 \n", "3 5.423845 \n", "4 5.434800 " ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "prediction_output = fit1_lm.get_prediction(predict_df).summary_frame()\n", "prediction_output.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the model and error bars" ] }, { "cell_type": "code", "execution_count": 10, "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(predict_df.age, prediction_output['mean'],color=\"green\")\n", "ax1.plot(predict_df.age, prediction_output['mean_ci_lower'], color=\"blue\",linestyle=\"dashed\")\n", "ax1.plot(predict_df.age, prediction_output['mean_ci_upper'], color=\"blue\",linestyle=\"dashed\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Exercise 1
\n", "\n", "- Fit a 3rd degree polynomial model and\n", "- plot the model+error bars.\n", "\n", "You can either take \n", "- **Route1**: Build a design df with a column for each of `age`, `age**2`, `age**3`, or \n", "- **Route2**: Just edit the formula" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "# your answer here\n" ] }, { "cell_type": "code", "execution_count": 12, "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
12.8462650.4728581.8898193.8027101.3074394.385090
22.9487510.4395582.0596613.8378411.4508604.446641
33.0479900.4083032.2221193.8738601.5867374.509242
43.1440310.3791042.3772213.9108411.7153284.572735
\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 2.846265 0.472858 1.889819 3.802710 1.307439 \n", "2 2.948751 0.439558 2.059661 3.837841 1.450860 \n", "3 3.047990 0.408303 2.222119 3.873860 1.586737 \n", "4 3.144031 0.379104 2.377221 3.910841 1.715328 \n", "\n", " obs_ci_upper \n", "0 4.324724 \n", "1 4.385090 \n", "2 4.446641 \n", "3 4.509242 \n", "4 4.572735 " ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# %load ../solutions/exercise1-1.py\n", "fit2_lm = sm.ols(formula=\"y ~ age + np.power(age, 2) + np.power(age, 3)\",data=diab).fit()\n", "\n", "poly_predictions = fit2_lm.get_prediction(predict_df).summary_frame()\n", "poly_predictions.head()\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# %load ../solutions/exercise1-2.py\n", "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", "ax2.plot(predict_df.age, poly_predictions['mean'],color=\"green\")\n", "ax2.plot(predict_df.age, poly_predictions['mean_ci_lower'], color=\"blue\",linestyle=\"dashed\")\n", "ax2.plot(predict_df.age, poly_predictions['mean_ci_upper'], color=\"blue\",linestyle=\"dashed\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Ed exercise
\n", "\n", "This example was similar with the Ed exercise. [Open it in Ed](https://us.edstem.org/courses/172/lessons/656/slides/2916) and let's go though it. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2 - Piecewise Polynomials a.k.a. Splines\n", "\n", "Splines are a type of piecewise polynomial interpolant. A spline of degree k is a piecewise polynomial that is continuously differentiable k − 1 times. \n", "\n", "Splines are the basis of CAD software and vector graphics including a lot of the fonts used in your computer. The name “spline” comes from a tool used by ship designers to draw smooth curves. Here is the letter $epsilon$ written with splines:\n", "\n", "![](../images/epsilon.png)\n", "\n", "*font idea inspired by David Knezevic (AM205)*\n", "\n", "If the degree is 1 then we have a Linear Spline. If it is 3 then we have a Cubic spline. It turns out that cubic splines because they have a continous 2nd derivative at the knots are very smoothly looking to the eye. We do not need higher order than that. The Cubic Splines are usually Natural Cubic Splines which means they have the added constrain of the end points' second derivative = 0.\n", "\n", "We will use the CubicSpline and the B-Spline as well as the Linear Spline.\n", "\n", "#### scipy.interpolate\n", "\n", "See all the different splines that scipy.interpolate has to offer: https://docs.scipy.org/doc/scipy/reference/interpolate.html\n", "\n", "Let's use the simplest form which is interpolate on a set of points and then find the points between them." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.interpolate import splrep, splev\n", "from scipy.interpolate import BSpline, CubicSpline\n", "from scipy.interpolate import interp1d\n", "\n", "# define the range of the function\n", "a = -1\n", "b = 1\n", "\n", "# define the number of knots \n", "num_knots = 10\n", "x = np.linspace(a,b,num_knots)\n", "\n", "# define the function we want to approximate\n", "y = 1/(1+25*(x**2))\n", "\n", "# make a linear spline\n", "linspline = interp1d(x, y)\n", "\n", "# sample at these points to plot\n", "xx = np.linspace(a,b,1000)\n", "yy = 1/(1+25*(xx**2))\n", "plt.plot(x,y,'*')\n", "plt.plot(xx, yy, label='true function')\n", "plt.plot(xx, linspline(xx), label='linear spline');\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Exercise 2
\n", "\n", "The Linear interpolation does not look very good. Fit a Cubic Spline and plot along the Linear to compare." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "# your answer here\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# %load ../solutions/exercise2.py\n", "# define the range of the function\n", "a = -1\n", "b = 1\n", "\n", "# define the knots \n", "num_knots = 10\n", "x = np.linspace(a,b,num_knots)\n", "\n", "# define the function we want to approximate\n", "y = 1/(1+25*(x**2))\n", "\n", "# make the Cubic spline\n", "cubspline = CubicSpline(x, y)\n", "\n", "# OR make a linear spline\n", "linspline = interp1d(x, y)\n", "\n", "# plot\n", "xx = np.linspace(a,b,1000)\n", "yy = 1/(1+25*(xx**2))\n", "plt.plot(xx, yy, label='true function')\n", "plt.plot(x,y,'*')\n", "plt.plot(xx, linspline(xx), label='linear');\n", "plt.plot(xx, cubspline(xx), label='cubic');\n", "plt.legend();\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Discussion
\n", "\n", "- Change the number of knots to 100 and see what happens. What would happen if we run a polynomial model of degree equal to the number of knots (a global one as in polynomial regression, not a spline)?\n", "- What makes a spline 'Natural'?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### B-Splines\n", "\n", "A B-splines (Basis Splines) is defined by a set of **control points** and a set of **basis functions** that intepolate (fit) the function between these points. By choosing to have no smoothing factor we forces the final B-spline to pass though all the points. If, on the other hand, we set a smothing factor, our function is more of an approximation with the control points as \"guidance\". The latter produced a smoother curve which is prefferable for drawing software. For more on Splines see: https://en.wikipedia.org/wiki/B-spline)\n", "\n", "![](../images/B-spline.png)\n", "\n", "We will use [`scipy.splrep`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.splrep.html#scipy.interpolate.splrep) to calulate the coefficients for the B-Spline and draw it. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### B-Spline with no smooting" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0. 0. 0. 0. 2.22222222 3.33333333\n", " 4.44444444 5.55555556 6.66666667 7.77777778 10. 10.\n", " 10. 10. ] [-4.94881722e-18 8.96543619e-01 1.39407154e+00 -2.36640266e-01\n", " -1.18324030e+00 -8.16301228e-01 4.57836125e-01 1.48720677e+00\n", " 1.64338775e-01 -5.44021111e-01 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00 0.00000000e+00] 3\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.interpolate import splev, splrep\n", "x = np.linspace(0, 10, 10)\n", "y = np.sin(x)\n", "\n", "t,c,k = splrep(x, y) # (tck) is a tuple containing the vector of knots, coefficients, degree of the spline\n", "print(t,c,k)\n", "# define the points to plot on (x2)\n", "x2 = np.linspace(0, 10, 200)\n", "y2 = BSpline(t, c, k)\n", "plt.plot(x, y, 'o', x2, y2(x2))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### B-Spline with smooting factor s" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.interpolate import splev, splrep\n", "x = np.linspace(0, 10, 10)\n", "y = np.sin(x)\n", "\n", "s = 0.5 # add smooting factor\n", "task = 0 # task needs to be set to 0, which represents:\n", "# we are specifying a smoothing factor and thus only want\n", "# splrep() to find the optimal t and c\n", "\n", "t,c,k = splrep(x, y, task=task, s=s)\n", "\n", "# define the points to plot on (x2)\n", "x2 = np.linspace(0, 10, 200)\n", "y2 = BSpline(t, c, k)\n", "plt.plot(x, y, 'o', x2, y2(x2))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### B-Spline with given knots" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[2.5 5. 7.5]\n" ] } ], "source": [ "x = np.linspace(0, 10, 100)\n", "y = np.sin(x)\n", "knots = np.quantile(x, [0.25, 0.5, 0.75])\n", "print(knots)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "# calculate the B-Spline\n", "t,c,k = splrep(x, y, t=knots)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "curve = BSpline(t,c,k)\n", "curve" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(x=x,y=y,c='grey', alpha=0.4)\n", "yknots = np.sin(knots)\n", "plt.scatter(knots, yknots, c='r')\n", "plt.plot(x,curve(x))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Ed exercise
\n", "\n", "This example was similar with the Ed exercise. [Open it in Ed](https://us.edstem.org/courses/172/lessons/656/slides/2917) and let's go though it. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3 - GAMs\n", "\n", "https://readthedocs.org/projects/pygam/downloads/pdf/latest/\n", "\n", "#### A - Classification in `pyGAM`\n", "\n", "Let's get our (multivariate!) data, the `kyphosis` dataset, and the `LogisticGAM` model from `pyGAM` to do binary classification.\n", "\n", "- kyphosis - wherther a particular deformation was present post-operation\n", "- age - patient's age in months\n", "- number - the number of vertebrae involved in the operation\n", "- start - the number of the topmost vertebrae operated on" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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KyphosisAgeNumberStart
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" ], "text/plain": [ " Kyphosis Age Number Start\n", "0 absent 71 3 5\n", "1 absent 158 3 14\n", "2 present 128 4 5\n", "3 absent 2 5 1\n", "4 absent 1 4 15" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
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" ], "text/plain": [ " Kyphosis Age Number Start\n", "count 81 81.000000 81.000000 81.000000\n", "unique 2 NaN NaN NaN\n", "top absent NaN NaN NaN\n", "freq 64 NaN NaN NaN\n", "mean NaN 83.654321 4.049383 11.493827\n", "std NaN 58.104251 1.619423 4.883962\n", "min NaN 1.000000 2.000000 1.000000\n", "25% NaN 26.000000 3.000000 9.000000\n", "50% NaN 87.000000 4.000000 13.000000\n", "75% NaN 130.000000 5.000000 16.000000\n", "max NaN 206.000000 10.000000 18.000000" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "Kyphosis object\n", "Age int64\n", "Number int64\n", "Start int64\n", "dtype: object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kyphosis = pd.read_csv(\"../data/kyphosis.csv\")\n", "\n", "display(kyphosis.head())\n", "display(kyphosis.describe(include='all'))\n", "display(kyphosis.dtypes)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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AgeNumberStartoutcome
count81.00000081.00000081.00000081.000000
mean83.6543214.04938311.4938270.209877
std58.1042511.6194234.8839620.409758
min1.0000002.0000001.0000000.000000
25%26.0000003.0000009.0000000.000000
50%87.0000004.00000013.0000000.000000
75%130.0000005.00000016.0000000.000000
max206.00000010.00000018.0000001.000000
\n", "
" ], "text/plain": [ " Age Number Start outcome\n", "count 81.000000 81.000000 81.000000 81.000000\n", "mean 83.654321 4.049383 11.493827 0.209877\n", "std 58.104251 1.619423 4.883962 0.409758\n", "min 1.000000 2.000000 1.000000 0.000000\n", "25% 26.000000 3.000000 9.000000 0.000000\n", "50% 87.000000 4.000000 13.000000 0.000000\n", "75% 130.000000 5.000000 16.000000 0.000000\n", "max 206.000000 10.000000 18.000000 1.000000" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# convert the outcome in a binary form, 1 or 0\n", "kyphosis = pd.read_csv(\"../data/kyphosis.csv\")\n", "kyphosis[\"outcome\"] = 1*(kyphosis[\"Kyphosis\"] == \"present\")\n", "kyphosis.describe()" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "from pygam import LogisticGAM, s, f, l\n", "\n", "X = kyphosis[[\"Age\",\"Number\",\"Start\"]]\n", "y = kyphosis[\"outcome\"]\n", "kyph_gam = LogisticGAM().fit(X,y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Outcome dependence on features\n", "\n", "To help us see how the outcome depends on each feature, `pyGAM` has the `partial_dependence()` function.\n", "```\n", " pdep, confi = kyph_gam.partial_dependence(term=i, X=XX, width=0.95)\n", "```\n", "For more on this see the : https://pygam.readthedocs.io/en/latest/api/logisticgam.html\n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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UxY5Dmew4mMm2g5nsTsui6CbHESK0bhBNh6Z1nY9Yzmhaj8Z1IxAfNSi2GT0DV98mAbaPu6zS+8vJK2DWur1MXbKbBVsP4QgRBnZswq29W9GjTfxJf69Ays4KtKBURm6urR4SgeuvtzPpDRxoG8TPO8/fpVMe4vesIRFpDXQDFrlY3VtEVgGp2KCwzsX7hwPDAVq2bOm9gvqAMYajx/M5nJnL4aw80jKPc/BoLgeOHWd/Rg57M3LYm55DanoOB44eP+G90eEOWsZH0ymxHld2TaRtQgynNY7llIQYv9epe7oRPDLMwZVdE7myayI7D2Xy8aJdTF2ymxlr9tChaV3uPK8NfzqzGeGhrtswAik7q7yB/QIiEISHFz9/+WXo2BFef932k+jb17ZJ9O/vt+Ip7/LJHYGI1AF+Ap4zxnxRal1doNAYc0xEBgETjDHl3pP6844gv6CQ9Ow8DmflkZGTR0Z2Hkdz8jl2PJ9jzp+Zx/PJzM0n83gBmcfzOepcd/R4HhnZ+RzNyaPQzcceGxlK03qRNKkXRdO6kTSvH0Xz+Cia14+mVYNoEur47gq/snxx1ZudW8BXK1N475ftbN5/jMZ1I/hznzbc1LMlsaX6KnR9arbbJIGVT/q2/4in75Z8IisLJk+2/SVuuw2ee87fJVLV5Lc7AhEJA6YBH5cOAgDGmIwSz78VkbdEpKEx5qC3y1biuBzOymNveg77Muxj/9Hj7D9qr8gPHcvlUGYuB48d52hO/kn3FxXmICYilDoR9mdsZCjN4iKpE1GHulFh1I0Mo25UKPWjw4mPCad+TDgJdSJIiI2ouXn18MfJ3pv14FHhDq7v0ZKh3Vvw46YDvPvzNsZ9t4E3523hll6t+HOfNiTERgDuU+z9EUcDJWW4UqKj4b774O67bXYSwLff2jaF55+3cz0QgG0fqtK8GgjEXrq+B6w3xrzsZpsmwD5jjBGRHtiB8A55ozzbD2ayZHsaKUeySTmSTeqRbPak57AnPZucvMIy29ePDiMhNoKGdSLolFiPBjHhxEWHUT/a/rQn9VBiI8OIjQz9I6e+RuXCe9jgbok+OQmICP3bN6J/+0asSU7nnZ+28vZPW3nvl+0M7d6C4X1Pcdv5raqd4qrDHynDJ1PhE3hERPHz33+Hd9+180O/8grTT+/Lo1+u/eP3KprUCNBgUIN4O2voXOBnYA02fRTg70BLAGPMOyIyErgHyAeygQeNMQvK229Vq4Y+XLiDMV+tQwQax0bSLC6SpnFRNKsXSdN6UTStF0mjupE0rhtBo9hIt3XPKjBtO3CMiT9t44sVyRhjO6y56ifhr6E8AunKuVrjb61cCXfdBYsXs6hdEvdfNII9dRNO2MRfn7EqX0BkDXlKVdNHx323gb0ZOTSrF8nfBp5eK0YNVWWlHslm0vxtfLxo5wknOgiwTB0/qvb4WwUF8PbbZD44imcvuIMpXQeesDqg2z6CmN+zhvypdCNmanpOlW5fS++nOrfBGlC8p1lcFGOv6MiI/qcyetpq5m7YjwEiQ0MY3vcU/ZzxwPhbDgeMHMlNKQmsLLQD6/XatZrfG51CRmSdwG77UGUERd2Hp+bk9dR+PDVZvCpfQmwE7w3rzooxF/PgxacRFe5gwg+bGTpxIfM27qcm3g0HmmHXnUtUeCiReTm8NX0cM/59H90PbKnxkzUFm6AIBJ7KJ/fUfjwVUFTFxEWHc++F7fh19AU88acz2JWWxZ//tYSBr/7MtGXJ5OaXTRSo7TyVUTW4WyLPD+lMg4T63H71GMLEMPXDUQz+eVrxGEkq4AVF1ZCnUvc8tZ9A6uhUJBiqqqLDQ7n93Dbc0qsV/1uVysT5W3no81WMm7mBW3u14saeLWlQJ+LkO6oF3J2jq3LuLs4UuwDS/mxHSb3vPjuhz7//feKoqyogBcUdwagB7QkrldIZFiKVvn311Ny+npos3lOCraoqPDSEq89uzqz7+/LvP3enQ9O6vDRnE73HzeXBz1aybOfhWl9tlOjmu+ZueYXFx8NXX8Gzz0JsrAaBGiJ4/kqlb3mrkOrvqQ5T/U9P4D+/7XK53B8CfvgDLxER+rVvRL/2jdi87ygfLNzB9BWpfLE8hdObxHJtUguu7NqMhrXwLsGr/RpE4LHHim8v1q2D9HQ7pacKSEGRPhpIg48FYnlq5PAHXnLseD5fr0xlyuJdrElJxxEinN4kltQj2RzOyiOxFlWb+aw68JJL7Cin//oX3HCD5/evKiyo00cDrU4+0MpTI4c/8JI6EaHc2LMlN/ZsyaZ9R3nhuw38sGH/H+tTjmTz4Gcr2ZOezd3ntw3YcZ8qwle9wJkyBYYMgRtvhE2bYMwYnWIzwARFG0Gg1ckHWnk81fZR25zWOJbluw6XWV5o4IWZG+n1/A+M/GQ57/+ynVW7j3A83/Vsb0GvQQM7R/Ntt9lRTP/yFzu7WinTV6TQZ9xc2oyeQZ9xc2ttG1UgCoo7gkAb5yXQylOlto/jxyEjo3iy9S++sHPsHj9up06MjIQ2bWy1AMDu3bYhMSbGy7+NZ5XXwap763iW7zzMN6v3ABAaIrRNqMPpTWM5NaEOrRvG0KZhDC3io6kbGVqj7x6qLSLCVg21aQNz59qeySWmx/RkZ01VeUHRRgDw+PQ1TFm0mwJjcIhwQ88WPDu488nf6CU1Ll3zvffg119h82bYvh1SU+Hcc23dL9iZrdavP/E9l10G33xjnzdrBnv22J+nnw4dOsCgQfYRwFqPnuF23Q5n+8me9GxW7DrCutR0Nuyxs8SlpuecsG1MuANHiJDhHL1WgE6JdbmyayJ1I8OoExlKVLiD6DAHUeEOwkNDiAi1P8McQlhICGGhIYSGCDNW7+Gl2RvZk55TM747peXl2SCQlmYnxGnSJODazWqroG4jmL4ihWnLUihwBr0CY5i2LIWkVvF++wfyWf1sRRUU2PrbZcvsY8UKOx794sV2/RdfwPLldk7biy+G1q1PnEx99mybJRIRYVMGc3LsMARFxo+HXbvsMdavhw8/tNsNGmRPDDfdBOefDwMGwKmn+vRXL09cVJjbOQ2KNK0XRdPOUQzq3PSPZVm5+XZGuYOZJB/OZtryZDbsPfrHegOsSclgTUoG1ZFyJJv7p67kya/XERcdVmIIdDv8eYOYcBrWiaBhbATN4qJoGR9NYlwU4aEh/rsYKboTuPlmOy3mrFkB124WbIIiEARreqRbhYX2yn75chg61M5PO2IETJxo10dFwZlnQlKS3TYkxA47XHIWq9KaNy//mDfdVLYMWVn2+e7dsGQJfP65fd2hg51c/fbboVWrqv2OHjL2io48OHUlJfsehziXlyc6PPSPaUMBxn23weV2IcBPf+vPseP5ZOcVkJ1rH7kFhRzPLyA3v5C8AkNeQSF5BYW8MXfLH3cVJeUVFNKleRw5eQVk5uZzOCuXXWlZHDp2vMz2IQINYiI4lHn8jwmS/FIVM3asvRDo04d+1z3FvJgWZTYJxoQFfwiKQKBXG8CqVfYqfNkyGwCOOq9Ok5LsJOU33wy9e8PZZ9uqm9IdgcoLAlUREgJ16tjnp5wC27bB1q3w3Xc26Dz3HFx4oQ0Eqal2+yZNPFuGCnI4hMISo5g6HJWv6y9wUwVbCLSIj67wfp7/1nVAyc4t4LUburlcdzy/gEPHckk5ks2uQ1nsTMti0vytZWbJy84r4Inpa2mbUIdOiXW936bRo4etbrzkEia9/zDDr3qMec3P/GO1Jiz4jmYN1RbGwN698MMP8NprMHw49OwJC5xTO2zbBm+9BdnZcMst8P77Nji0aWPXn3uuzero1Mk/vUFFbJXQ//2fbUzcs8eWCWDcOHvHMWSIXefDdq3xszaWGco6r8BUelwoh5uTqrvl7sRFh1VqOUBEqINmcVF0bx3P1Wc358GLT+O4i4mYAI4ez+fyN36h9/NzefKrtazY5eVe1u3bw4IFhJ3Shtd/nkzL2DAE2zagw4X7TlDcEXg1S8eY4pzooqvssDBbV+7JKypj4OBBe7JPTYWdO+3j4ouhXz97pd+9e/H28fHQpUvxFIOXXWazfMLcnzACSqNGxc9HjLDVVe+9Z+8WOnSAhx+2aYhe5qm7yRt6tnDZm/yGnmWrQ8rjqTGC3PUdaVI3kocHtGfO73uZsmQ3HyzcSZuGMVx9ViLXdW9Bo9jIyh2oIhITYf586hw6xPxTTz3xf0r5RFAEgmoNDZGfX3yF/MgjsHYtpKTYk3FGBlx0UXFmTIcOdh3YL3JkJFx3nR14C+y2+fl2LtjISHtSvvBCe/UOth49L89etWdnw7Fjtg7/gQfg0KETT45gG2Pr17eBoH17mDABOna0j8aNT/xn8nTVji+1bw8vvABPPQVTp8Ibb8DChcWB4MgRiIvzyqE91dmuKEOtuplr6S4arstb7o67i6PRl9oJm645uzkZOXnMXLOXL1Yk8+LsTbz6/WYGdGrCrb1a0aNNvGerjurXtw9j7BzJjRvbv7cGBJ8IikAAlcjSKSy01SmzZsGcOfZ1UebM77/bANCiha12qV/fpk0WGTPGBoeSJ/OSmTWxsXD4sL2yz8mx27VrV7x+yRJbFx4dbR9169r3gL3Cf+01W0/epImtO2/WrDhIxcbCvfdW70MKdJGRtvrq1lttfwWA334rDqYPPXTyRutK8uTdZFKreOZtOEDqkWya1IskqVV8pffhqcBUkYujupFhXNe9Bdd1b8G2A8f4ZNEuPl+WzIzVe+jSvB539j2FgR2bEOrwYA1zYaG9WHrmGfu/9s47OnCdD3i9H4GIDAQmAA7gXWPMuFLrxbl+EJAFDDPGLC9vn1Wds/ikJk+2VyEpKfaE3KOHrVJ5/HHPH0t5xrZt8PTT8J//2L/ZsGHw6KPFbR8e4Ik+KKU7TEHVps301H6qKievgGnLk3n35+1sP5hJqwbR9D6lAfM3HfBcvwZjbEbR00/brKLPPqtxHREDlbt+BF5tLBYRB/AmcClwBnCDiJxRarNLgXbOx3DgbW+W6QQFBbbOOT3dvg4Lg27d7Ngohw7Z6gcNAoHtlFNs1duWLXDHHfDBB/ZuLTfXI7t31welssMfeGoyoqKJYBLjovzSqBoZ5uCmnq34/sHzeefmsygsNHy6ZDep6Tl/DGH+wNSV1RseQsRekE2cCDNn2ouxGtjxtSbx6h2BiPQGxhpjBjhfPwpgjHm+xDYTgR+NMVOcrzcC/Ywxe9ztt9p3BPn58NFHNkVx61Zb5zxiRNX3pwJHSgqsWQMDB9pqhscegz//GU47rUq781SP10Ac4dUTHcra/X0GrhKQwkJg8z888HvNmGGDwJ/+VP19Kf/cEQCJwO4Sr5Odyyq7DSIyXESWisjSAwcOVK00xsC0abbe/i9/sQ2Mn38Od91Vtf2pwJOYaIMA2HHwJ0ywjfi33FJ2CIwK8FTWUKClMHtqMiI3WajkFcKynWnVL+hllxUHgYkTbbKA8jhvBwJXTf6lL4wqsg3GmEnGmCRjTFJCQhUncBGBt9+2P6dNs42z11yjjVG1VefOdlykBx+0Q2R07GizuA4dqvAuPHUC9+QIr54YpdMX82Zf/fZC7p2ywjMdNwsK4JNP4PrrbVKEh6r+lOXtQJAMlEyUbg6kVmEbz/nkE1t1MGSIpqYFg8aN7ThHO3faRuQtW6BePbtu376Tvt1TJ3BP1e176kreF73t/++CU5m1bi8XvPQjb87bQm6+m9uHinA4bBbf/ffD66/DeefZv6nyCG+3EYQCm4ALgRRgCXCjMWZdiW0uA0Zis4Z6Aq8ZY3qUt1+vZQ2p2q9o7KTsbJtZdNpptnPan/5kl7sQSCPFeqrNwlP7OdnorMmHs3j2m/XMXLeXtgkxPDO4E+e0bVjh/bs0bZqt2nU4bBtf/frV218Q8UsbgTEmH3uSnwWsBz4zxqwTkbtF5G7nZt8C24AtwGTgr94skwpyRSd7EXuHsHMnXHmlHV/p7bdtJ75SBndL5NfRF7B93GX8OvoCvw574KkreV9NRtS8fjTv3HI2/xrWndyCQm6cvIi//XcV6eXM83BSV18NK1faO72iIHC47ARCquK8PtaQMeZbY8xpxpi2xpjnnMveMca843xujDEjnOs7G2P0Ul95X9ZEcQQAAB2iSURBVGQk3HefvaKcMsVWF/31r3ZAPigemiPAeKrNwtdpqP1Pb8ScB87nnn5tmbY8hYtf+YlZ6/ZWfYdt2tjRacGOP5WYaDPEMqo3rHewCopB55RyKzTUNkAuXmwf551nl99/P5xzDkyaZIewCBCevJL3xJ2Ou1Y2V8sjwxw8MvB0vhrRhwZ1Irjro2Xc/+mKSg+PUcapp9q7hH/8wz5/7TXIzKzePoOMBgKlwFYVde9enEDQoYPtaHjXXXZIj8GDbeaRn/m7Q1lp57R1PUyGu+UAnRLr8fXIPtx/UTv+t3oPA1+dz69bDla9EC1b2n5BS5bYzLD77rPDq2sntAoLmqkqlao0Y+yorh9+aIPAoEH2DqGwEF580c6odvbZQZ1+3HHMTDJzy1ajxYQ7WPf0wJO+f9XuIzwwdSXbDmbSv30CG/cerf5QFQsW2I6F115rq/huvtn2Rxg8uHgOjCDlrrFYA4FSFVFYaKsbYmNhwwZ7xwB2cMDu3W010i23FC8PEhWZ0/lksnMLuP2DJSzYemL/Do+MobRtG1xwgU0KiIiAvn3hkktsdaCHByisCYJ6zmKlqi0kpHgk2NNPh/37bSPlggX2MX68neGtQweYP9+mpLZvb9NT27a1o8V262YDhzpBVLiDnYeyyiz3yHSyRbPfLVhg7+pmz4ZRo+ydXPPmdjyxzz+3f7eiv1ejRm5Tib3OGNtZLiLCvl61yt7dHD4MaWl2KHsvXGxoIFCqKhIS7FwRQ4fa19nZxSeP/HybhfTTT3ZU1CIrV9rJgj78EF56yZ5wGjSwj/h4O4x2XJwdCmPbNluNUaeODR4xMfbEFRISUBO3CC6GAcB9I7I77tJfXfV1qLSQEDvbXdGMd8nJxXN7rFlj04Zzcoq3Dw+3n39ioh35dNYsm6Zap479O8TE2LYjhwOWLrWdFMH+XQoK7N+maI7uGTPsMXJy7BzdWVn2JP/SS3b9Qw/ZWQUzMoofp55qh7wHGDkSfvmluGzvvquBQKmAFVUiffOCC+wD7D9+0WxyRXNPxMXZO4T9++3yQ4fsFV/RfBL/+Y/NgCktM9MGhQcesCevqCibBhsVZU9Oa9bYk9Drr9uTR2ysPVZ8vA1cd95p93P4sD2peWC2upt6tXQ589pNvVpWaj9x0WEcdtG3IDRE2J+RQ6O6HpwZrWSV0PDhdtTaXbtsld/mzScGiu3bbSBIS7PBvkjR+GTvvmvHQCopKqo4EHz6afHFQGSk/fsllrjDiY2134WiuUfq1bPznRR59VU7b0l8fPHkPV6gbQRKBYLCQnsSF7HzNe/ebTu3HTtWfCU5bJi9uv3mG3uiz8kpngCpoAA+/tju6/HH4b//tVOnHjli39ukid0v2A5033xjTzhFvau7d7cnxCrwxHwNXZ+azRE3aaSN60Yw8ZYkurbwzix0FVZQYD/rzEw7dAnYqWNLphc7HDZ5oGg+jKLgERHhv+qmErSxWKlglZNjg0LRYI1ff21TLbdvt1UgGzbY+vGFC+36oUNtQOrZ0/ar6NrV65lR5TU6N68fxf6jx3n+qs5cfXbwNfB6kjYWKxWsIiPto8gVV9hHEWNOHFojPNw2eBcN+Vynjq2Oevrp4u093EYh4jrtXwS+HnkuIz5ezkOfr2LD3gxGX9oBR0hgtJHUFv6/V1FK+ZdIcUYU2M5ZO3fauvIpU+wc0aeeatcdOmTruIcNs9k2Hup17a5iwhiIjwnnw9t7cGvvVkz+eTt3fbSMzOP5HjmusjQQKKVcS0y0+fZvvmmDAdg7h379bPXSddfZ6qYLL4QVK7xalDBHCE9f2YmnrujI3A37uOadhR4dMjvYaSBQSlVcq1Z2To/9+22D9UMP2UbounXt+lmz4Nlni9MfKyguynUGU+nlt53TmveHdSc5LYvBb/7K2pT0Kv0a6kQaCJRSlRcaCn36wLhx9qTftq1dPn8+PPGEHfOnUyd45hmbknkSY6/oSFipev+wEGHsFR3LbNuvfSP+e885hIYIQycuZN7G/R75lYKZBgKllOc895ztCfvGGzb3fcwYO+lPUSOAmykmB3dLZPy1XU4YTG/8tV3c9ipu3ySWL0f0oXXDGO74YClTFpfty6AqTtNHlVLek5xsA0PPnjaNtU0bO9bPiBHQo9yJCCvk2PF8Rn6ynB83HuC+C9tx/0XtkADpdR2I/DJDmVIqyDVvboMA2I5tV11lx/zp2dMGgs8+q9YkQHUiQpl8axLXnt2cCT9s5u9friG/oBpzIwcpvSNQSvlWRoZNUX39ddi40Q4I17t3tXZpjOGl2Zt4Y94W6pcarqJP23g+vrN6+68tfH5HICLjRWSDiKwWkS9FxGX/cBHZISJrRGSliOjZXanarm5dWzW0bh3MmVMcBF5+2aalVuHiVER4eEB7TmkYXWbMol+3pnHT5IWeKHmt5c2qoTlAJ2PMmcAm4NFytu1vjOnqKlIppWoph8MOqwx2YLUPPrDjIF1wAaxdW6VdbjtYdjhrsMFAuee1QGCMmW2MKer+9xugg4QopVwLC7NDOr/5pg0CZ51lh7TIq+Z8xqpCfNVY/BfgOzfrDDBbRJaJyHB3OxCR4SKyVESWHjhwwCuFVEr5UVgY/PWvdj6Ga66xHdOKxvpXXlWtQCAi34vIWhePK0ts8xiQD3zsZjd9jDFnAZcCI0Skr6uNjDGTjDFJxpikhKJRFJVStU/Dhrb38u+/F0/C4oHkkKU7tHrInWoFAmPMRcaYTi4eXwGIyG3An4CbjJv0JGNMqvPnfuBLoPrJxUqpmq9ooLvvvrPzJdx7r9sOaUViwh0ulwtw83uL+GmT1ia44s2soYHAI8AVxhiXLTgiEiMisUXPgUuAqrUSKaVqp4suggcftOmml15q51Zw46qzXPdEHnJWIm0a1uGOD5bw3Zo93ippjeXNNoI3gFhgjjM19B0AEWkmIt86t2kM/CIiq4DFwAxjzEwvlkkpVdOEhdk5fj/4wM4DfeGFcPCgy03nbXB9xf/btjQ+vbMXnRPrMeKT5fx3WbI3S1zjeG1iGmPMqW6WpwKDnM+3AV28VQalVC1y6612zt6hQ2HePLj22jKbuBuaOvVINvWiw/jo9p7c9dEyHv58FVm5+dzau7WXC10z6BATSqma4/LLbSZRURAo1fTYLC7K5duKlsdEhPLesCQuPqMxY75ax9s/bvVqcWsKDQRKqZqlWTP7c84cO6dyiVnSRg1oT1TYiQ3GUWEORg1o/8friFAHb910Fld0acYLMzfw4qyN1MShdjxJ5yxWStVMhYWweLGdf3nmTIiO/mPY6vGzNpJ6JJtmcVGMGtC+zHDWYY4QXhnalehwB2/M20J2XgGPX9YhaEcu1UCglKqZBgywg9fdcAPceKMd1TQkhMHdEt3OY1CSI0R4fkhnIsMcvPfLdnLyCnjmyk6EhARfMNBAoJSquYYOtdNm3nsvjB1rh6WoBBHhycvPICrcwds/biU7r4B/Xn0moY7gqjXXQKCUqtlGjoSVK+0EOMZAJat3RIS/OdsWXp6zieP5hbw6tCthQRQMNBAopWo2EZg40Y5mWsU6fhHh3gvbERkWwj++3cDxvEK2HzzK1gPFfWHbNYphzoP9PFTowBI8IU8pVXuFhtogsH697X2ckVGl3Qzv25anr+zI9+v3nRAEADbvz+Til3/0QGEDjwYCpVTtkZYGs2fDPfdUaYIboNxOZpv3Z1axYIFNA4FSqvbo08c2Gn/yic0oUhWigUApVbv8/e/Qt6+dDnPzZn+XpkbQQKCUql0cDvj4YwgPh+ef93dpagTNGlJK1T7Nm8P8+XDaaR7f9f6jOTSKjfT4fv1J7wiUUrVTx452COvDh2Hbtkq9tXFsuMvlAgyd+Bt70l2PclpTaSBQStVextj5C669FvLyKvy2RY9dXCYYNI4N5/O7e3Pg6HGum7iQ3Wku59uqkaQmjrqXlJRklnpgDlOlVBCYNg2uuQaefRYee6zau1u5+wi3vreI2MgwPr6jJ60bxnigkL4hIsuMMUmll+sdgVKqdrv6arjuOnjqKdiwodq769oijk/u7EVWbj5DJy1ky/5jHiikf2kgUErVfq+9BjExcPfdVe5oVlKnxHp8Orw3BYVw/aSFbNzrfh7lmsCbk9ePFZEU53zFK0VkkJvtBorIRhHZIiKjvVUepVQQa9wYXnjBBoOjnjlpt28Sy6fDe+EIEa6ftJC1Keke2a8/eK2NQETGAseMMS+Ws40D2ARcDCQDS4AbjDG/l7dvbSNQSlVa0bnOw5PP7DyUyY2TF3E0J48Pb+9J1xZxHt2/JwVqG0EPYIsxZpsxJhf4FLjSz2VSStVGIvaxfTu8/rrHdtuqQQxT7+pFvegwbn53Ect2pnls377i7UAwUkRWi8j7IlLfxfpEYHeJ18nOZWWIyHARWSoiSw8cOOCNsiqlgsG779qJbH791WO7bF4/ms/u6k1CbAS3vLeY37Yd8ti+faFagUBEvheRtS4eVwJvA22BrsAe4CVXu3CxzGVdlTFmkjEmyRiTlJCQUJ1iK6WC2d//bnsejxwJBQUe223TelFMHd6LxLgohv1rMT9vrjkXrNUKBMaYi4wxnVw8vjLG7DPGFBhjCoHJ2Gqg0pKBFiVeNwdSq1MmpZQqV0wMvPiindVs8mSP7rpR3Ug+Hd6L1g1iuP2DpczbsN+j+/cWbzYWNzXG7HE+fwDoaYy5vtQ2odjG4guBFGxj8Y3GmHXl7Vsbi5VS1WIMXHABrF4NmzZBgwYe3f3hzFxufX8xa0plEvl7ljN/NBb/U0TWiMhqoD/wgLMgzUTkWwBjTD4wEpgFrAc+O1kQUEqpahOxfQtuvNGOVuph9WPCyTxedkiLQJ3lzGujjxpjbnGzPBUYVOL1t8C33iqHUkq51LmzR7OHStt20PVYRIE4y5m/00eVUsq/fvnFZhHVwHHXPEUDgVIquK1YYe8M/vc/f5fEbzQQKKWC2913w+mnw8MPQ26ux3bbrpH7UUnf+2W7x47jCRoIlFLBLSwMXnrJzm/81lse2+2cB/uVCQanJkRzaacmPPPN77z941aPHau6dD4CpZQyBgYOhMWLYcsWj6eTlpRfUMgDn63if6tSeeCi07jvonZeO1Zp7tJHdc5ipZQSsXcF338Pdep49VChjhBeHdqVMIfwyvebyCso5KFLTkM8PBhepcrktyMrpVQg6dTJPnzAESK8eE0Xwh0hvDFvC8fzC/j7oA5+CwYaCJRSqqRPPoElS+CVV7x6mJAQ4R9XdSY8NITJP28nN7+QJy/vSEiI74OBNhYrpVRJ69fDq6/aYOBlISHCU1d05I5z2/DBwp08Nn0NhYW+b7fVQKCUUiX97W+QkACjRvmkk5mI8NhlHRjRvy1TFu9m1H9XU+DjYKCBQCmlSoqNhbFj4aefYMYMnxxSRHj4kvY8cNFpTFuezP1TV5JXUOiTY4MGAqWUKuvOO6FdOxg92qNzFpRHRLjvonY8MvB0/rcqlf/7ZAW5+b4JBtpYrJRSpYWF2WEnsrMhxLfXy/f0a0uYQ3h2xnr++vEy3rzpLCJCPT9CakkaCJRSypUBA/x26DvOO4WI0BCe+Godd364jEm3nE1kmPeCgQYCpZRyp6AAnnkGGjeGe+7x6aFv6d2a8NAQRn+xhstf/4Vjx/PZm55Ds7goRg1oz+BuLqd3rxJtI1BKKXccDli4EB5/HNLTT769hw3t3pIbe7Rk8/5j7EnPwQApR7J59Is1TF+R4rHjaCBQSqnyjBsHaWkwfrxfDv/jxgNllmXnFTB+1kaPHUMDgVJKladbNxg61HYy27fP54dPPZJdqeVV4bVAICJTRWSl87FDRFa62W6Hc27jlSKiQ4oqpQLPM89ATg4895zPD90sLqpSy6vCm3MWDy16LiIvAeVVsPU3xhz0VlmUUqpa2rWDCROgd2+fH3rUgPY8+sUasvOK+zNEhTkYNaC9x47h9awhscPpXQdc4O1jKaWU14wY4ZfDFmUHjZ+1kdQj2V7JGvJF+uh5wD5jzGY36w0wW0QMMNEYM8nVRiIyHBgO0LJlS68UVCmlyrVvHzzyiB2HqGNHnx12cLdEj574S6tWIBCR74EmLlY9Zoz5yvn8BmBKObvpY4xJFZFGwBwR2WCMmV96I2eAmAR2hrLqlFsppaokNBS+/BKOHoVp0/xdGo+pViAwxlxU3noRCQWGAGeXs49U58/9IvIl0AMoEwiUUsrvGjSABx+0g9ItXQpJZWZ9rJG8nT56EbDBGJPsaqWIxIhIbNFz4BJgrZfLpJRSVffAAzYgPP64v0viMd4OBNdTqlpIRJqJyLfOl42BX0RkFbAYmGGMmenlMimlVNXVrWtHJZ01C+bXjsoLrzYWG2OGuViWCgxyPt8GdPFmGZRSyuNGjIC9e6FtW3+XxCN00DmllKqsqCh48UV/l8JjdIgJpZSqqiVLYORIn0xp6U0aCJRSqqrWroU334Svv/Z3SapFA4FSSlXVLbfY4SeeeAIKfTfHsKdpIFBKqaoKDYWnnoI1a+Dzz/1dmirTQKCUUtUxdKgdbuLJJyE/39+lqRLNGlJKqeoICYEXXoDVq+3UlqE177Ra80qslFKB5rLL7KOG0qohpZTyBGPg00/hiy/8XZJK0zsCpZTylFdfhT177N1BRIS/S1NhekeglFKeIAJPPw27dsF77/m7NJWigUAppTzl4ovh3HPt3MbZnptc3ts0ECillKeI2InuU1Nh4kR/l6bCNBAopZQn9esHd9wBNWhKXW0sVkopT5s82d8lqBS9I1BKKW/IzIRXXoFjx/xdkpPSQKCUUt6wdq2d3/jNN/1dkpPSQKCUUt7QsycMGgT//CdkZPi7NOWqViAQkWtFZJ2IFIpIUql1j4rIFhHZKCID3Lw/XkTmiMhm58/61SmPUkoFlKeegrQ0eP11f5ekXNW9I1gLDAFOmMFZRM7ATlzfERgIvCUiDhfvHw38YIxpB/zgfK2UUrVDUhJcfjm89BKkp/u7NG5VKxAYY9YbYza6WHUl8Kkx5rgxZjuwBejhZrsPnM8/AAZXpzxKKRVwxo6FLl3g0CF/l8Qtb6WPJgK/lXid7FxWWmNjzB4AY8weEWnkbociMhwYDtCyBuXnKqWC3Flnwbx5/i5FuU56RyAi34vIWhePK8t7m4tl1Zrd2RgzyRiTZIxJSkhIqM6ulFLK91JT4bvv/F0Kl056R2CMuagK+00GWpR43RxIdbHdPhFp6rwbaArsr8KxlFIq8D3wAMycCTt2QP3AyovxVvro18D1IhIhIm2AdsBiN9vd5nx+G/CVl8qjlFL+9dhjNo305Zf9XZIyqps+epWIJAO9gRkiMgvAGLMO+Az4HZgJjDDGFDjf826JVNNxwMUishm42PlaKaVqnzPPhGuugQkTbEppABFjqlV17xdJSUlm6dKl/i6GUkpVztq10LmzvTt49lmfH15Elhljkkov157FSinlK506wfXXB9wdgY4+qpRSvvTxxxASWNfggVUapZSq7YqCwKpVAdPJTAOBUkr5WnKy7Wj24ov+LgmggUAppXyveXO47jo7GN3Bg/4ujQYCpZTyizFjICvLDkjnZxoIlFLKHzp0sBlEAXBXoIFAKaX85YknwOEAP/eL0vRRpZTylw4d7GB0MTF+LYbeESillD/FxIAxsGmT34qggUAppfxtzBibTnrggF8Or4FAKaX87aab/JpBpIFAKaX87fTT4YYb4I03/JJBpIFAKaUCweOP++2uQAOBUkoFgqJ+BdOnQ0GBTw+t6aNKKRUoJkyAunVt3wIf0kCglFKBIiHB/szNtY86dXxyWK0aUkqpQJKZCe3bw3PP+eyQ1Z2z+FoRWScihSXmIUZELhaRZSKyxvnzAjfvHysiKSKy0vkYVJ3yKKVUjRcTA716+TSDqLp3BGuBIcD8UssPApcbYzoDtwEflbOPV4wxXZ2Pb6tZHqWUqvmeeMLeGbz8sk8OV61AYIxZb4zZ6GL5CmNMqvPlOiBSRCKqcyyllAoaZ5xRPF+BD2Yx80UbwdXACmPMcTfrR4rIahF5X0Tqu9uJiAwXkaUisvSAn7phK6WUzxTdFfznP14/1EkDgYh8LyJrXTyurMB7OwIvAHe52eRtoC3QFdgDuO1JYYyZZIxJMsYkJRS1rCulVG3VsSMsWgT33uv1Q500fdQYc1FVdiwizYEvgVuNMVvd7Htfie0nA99U5VhKKVUrde9uf+blQViY1w7jlaohEYkDZgCPGmN+LWe7piVeXoVtfFZKKVVk6lRo0wbS0rx2iOqmj14lIslAb2CGiMxyrhoJnAo8USI1tJHzPe+WSDX9pzPFdDXQH3igOuVRSqla54wzICUFXn3Va4cQY4zXdu4tSUlJZqmfp3ZTSimfueYamDMHduyA+m5zak5KRJYZY5JKL9eexUopFejGjIGMDK/dFWggUEqpQHfmmTBkCMyaZae19DAddE4ppWqCyZOhXj0Q8fiuNRAopVRNEB/vtV1r1ZBSSgU5DQRKKRXkNBAopVSQ00CglFJBTgOBUkoFOQ0ESikV5DQQKKVUkNNAoJRSQa5GDjonIgeAnf4uRwU0xM7fXJNomb2vppUXtMy+4IvytjLGlJnZq0YGgppCRJa6GukvkGmZva+mlRe0zL7gz/Jq1ZBSSgU5DQRKKRXkNBB41yR/F6AKtMzeV9PKC1pmX/BbebWNQCmlgpzeESilVJDTQKCUUkFOA0E1iUgLEZknIutFZJ2I3Odim34iki4iK52PMf4oa6ky7RCRNc7yLHWxXkTkNRHZIiKrReQsf5TTWZb2JT67lSKSISL3l9rG75+xiLwvIvtFZG2JZfEiMkdENjt/upx5XEQGishG5+c92s9lHi8iG5x/9y9FJM7Ne8v9Dvm4zGNFJKXE33+Qm/f6/HN2U96pJcq6Q0RWunmvbz5jY4w+qvEAmgJnOZ/HApuAM0pt0w/4xt9lLVWmHUDDctYPAr4DBOgFLPJ3mZ3lcgB7sR1jAuozBvoCZwFrSyz7JzDa+Xw08IKb32krcAoQDqwq/R3ycZkvAUKdz19wVeaKfId8XOaxwMMV+O74/HN2Vd5S618CxvjzM9Y7gmoyxuwxxix3Pj8KrAcS/Vsqj7gS+NBYvwFxItLU34UCLgS2GmMCrme5MWY+kFZq8ZXAB87nHwCDXby1B7DFGLPNGJMLfOp8n9e5KrMxZrYxJt/58jeguS/KUlFuPueK8MvnXF55RUSA64Ap3i5HeTQQeJCItAa6AYtcrO4tIqtE5DsR6ejTgrlmgNkiskxEhrtYnwjsLvE6mcAIcNfj/p8m0D5jgMbGmD1gLxqARi62CdTPGuAv2DtDV072HfK1kc7qrPfdVMEF4ud8HrDPGLPZzXqffMYaCDxEROoA04D7jTEZpVYvx1ZldAFeB6b7unwu9DHGnAVcCowQkb6l1ouL9/g111hEwoErgM9drA7Ez7iiAu6zBhCRx4B84GM3m5zsO+RLbwNtga7AHmx1S2mB+DnfQPl3Az75jDUQeICIhGGDwMfGmC9KrzfGZBhjjjmffwuEiUhDHxezdJlSnT/3A19ib5tLSgZalHjdHEj1TencuhRYbozZV3pFIH7GTvuKqtScP/e72CbgPmsRuQ34E3CTcVZWl1aB75DPGGP2GWMKjDGFwGQ3ZQmoz1lEQoEhwFR32/jqM9ZAUE3OOr73gPXGmJfdbNPEuR0i0gP7uR/yXSnLlCdGRGKLnmMbB9eW2uxr4FZn9lAvIL2oisOP3F49BdpnXMLXwG3O57cBX7nYZgnQTkTaOO96rne+zy9EZCDwCHCFMSbLzTYV+Q75TKn2q6vclCWgPmfgImCDMSbZ1Uqffsbebo2u7Q/gXOzt5WpgpfMxCLgbuNu5zUhgHTZL4TfgHD+X+RRnWVY5y/WYc3nJMgvwJjbLYg2Q5OcyR2NP7PVKLAuozxgbpPYAedirz9uBBsAPwGbnz3jnts2Ab0u8dxA242xr0d/Dj2Xegq1LL/o+v1O6zO6+Q34s80fO7+lq7Mm9aaB8zq7K61z+76Lvb4lt/fIZ6xATSikV5LRqSCmlgpwGAqWUCnIaCJRSKshpIFBKqSCngUAppYKcBgKllApyGgiUUirI/T/b2f78pAxkLwAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "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.scatter(X.iloc[:,term.feature], pdep2 + res)\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": [ "Notice that we did not specify the basis functions in the .fit(). Cool. `pyGAM` figures them out for us by using $s()$ (splines) for numerical variables and $f()$ for categorical features. If this is not what we want we can manually specify the basis functions, as follows: " ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "kyph_gam = LogisticGAM(s(0)+s(1)+s(2)).fit(X,y)" ] }, { "cell_type": "code", "execution_count": 28, "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": [ "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.scatter(X.iloc[:,term.feature], pdep2 + res)\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": [ "#### B - Regression in `pyGAM`\n", "\n", "For regression problems, we can use a `linearGAM` model. For this part we will use the `wages` dataset.\n", "\n", "https://pygam.readthedocs.io/en/latest/api/lineargam.html" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### The `wages` dataset\n", "\n", "Let's inspect another dataset that is included in `pyGAM` that notes the wages of people based on their age, year of employment and education." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100% (11 of 11) |########################| Elapsed Time: 0:00:00 Time: 0:00:00\n" ] }, { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# from the pyGAM documentation\n", "from pygam import LinearGAM, s, f\n", "from pygam.datasets import wage\n", "\n", "X, y = wage(return_X_y=True)\n", "\n", "## model\n", "gam = LinearGAM(s(0) + s(1) + f(2))\n", "gam.gridsearch(X, y)\n", "\n", "\n", "## plotting\n", "plt.figure();\n", "fig, axs = plt.subplots(1,3);\n", "\n", "titles = ['year', 'age', 'education']\n", "for i, ax in enumerate(axs):\n", " XX = gam.generate_X_grid(term=i)\n", " ax.plot(XX[:, i], gam.partial_dependence(term=i, X=XX))\n", " ax.plot(XX[:, i], gam.partial_dependence(term=i, X=XX, width=.95)[1], c='r', ls='--')\n", " if i == 0:\n", " ax.set_ylim(-30,30)\n", " ax.set_title(titles[i]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Discussion
\n", "\n", "What are your observations from the plots above?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4 - Smoothing Splines using pyGAM\n", "\n", "For clarity: this is the fancy spline model that minimizes $MSE - \\lambda\\cdot\\text{wiggle penalty}$ $=$ $\\sum_{i=1}^N \\left(y_i - f(x_i)\\right)^2 - \\lambda \\int \\left(f''(x)\\right)^2$, across all possible functions $f$. The winner will always be a continuous, cubic polynomial with a knot at each data point." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see how this smoothing works in `pyGAM`. We start by creating some arbitrary data and fitting them with a GAM." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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UgLnQLE0Eme80fxvjp4l975V4eRbyjvCxlQsLBBW2xo/LcgWuZoLK6p5nwSQ+PrDJR+eT5gVUZddG66vEHdvW2CoBZluz1FWgNNnB5GW2sDF+miS3eq2Ke2+tturLl4i6sqk3C3lHuNrK6bbuJhqura1k3As0UCljRbkvc21xGXGt91b3l7HjMzdg5fJlbZ+l3U2YChFdd6qBStnp2IBdzTJQGCYjsemy6+jbbGFrfFlfVx3BDi8wF84JgcMnG13X55WFvCNcbOVkW/eh50+h9vjLuGnXUSMNd+sGOy0W4+zxH0w3cXGq6cRGG2eDFwI4fLLRJqAuN+dTj5dEiOzZvrFjB1EuEfbetdH52DY1S5XCIESnE9e32cLX+L7NVKawkHeEixonsoeqOS9awtQEWQnXNMT5OmX1zR89ZKebvarlW8DkdNPqy5dYiERPPkMqSpKxbWqWqh2ErNibr3o+LsZPUqLbt5nKFA6hdIgqDCxtuJeNh8fWA5gmxXxOCCsx1royCjrSnnsw171HJlq7gxVluX4k81U050Xq8MkkMeM247YH+su4OCW/x7Lj+U7ztzF+0hBUX5m5SWEhnzMjY4221maByQWIF3xJi3KpjpGVkbGGNDbdBBvx4jKhG1Apl7Ci3CcVUFnP/crsVZPPxammVAC40O5MBZjNsXW31nXwgK/ckqSLZN41otJSSHNNnl2RkrL3yIRU0zNpbBFXvzsOmzVc0gj4gMbkdOZ7Uq9VMb7nDnxzx+aObfqdn7pO+jfr/kl6IW9qf/XphLQ5tm6npjpe1vcubby7rfc96SLp20xlSuE0+bgtVx6agqyOyuRUE9cPVDo0zwDV52GiW/dVlbL27wYiY9s41ywx6mFspcbLtFyV7f2vfn4BI2MNp1EuPrU7m2Ordo0EeSiojWxb1UK698iEcf2YLFm+qnNeVVEHGfg2U5lQOCEfp3G5rsMhq6MSkNXUAnQ+VOt2HVX+7t67Nnpr1rG6v4ybr/sNvPrzC9Lvbab5Rxdu1XUWkNuTTTC1vyax39vGZs0X2YJBAB7cstaZPyDO2evaDzG0bX2bKTXg0sxsauWgGyickNdpXKoH4tFDZjZxE9Jquqr46jhKGtu4i1oppn6B/uXL8OY/2k/zjwr0rRvW4PDJRtvCTbDf3Dqplmxivzclye7TlmaZdMGw4Q/QPVuqZ9mmH6Jeq2LfSxMd/pyggTgL+S5BFRVw/UBFeeOTRH3EvXBpHq5yibBne7o4ap1tvDE5jdv2v2LVJGUa2WJyHZLaimVb82dPnEsUsZjWNu4rysVnHfskC0YaU0eUoW3r8cjwuPQ71fNkO8JlUhFR1G1hkUkolONVV0+lsVitUIVJHLWJYyjpw7VyeQkHvnxL6hc2LmY8iN65+T/9b6zbdRTrdh1F7fGXUzungoQbfc7pwnXQXYs0tuIkzbsB+82tTTMibWqXvZJwM7RtPcp9nU9FYOowQZcxrHqWbCdC+c7edUGhhHxcPZW4iJC4l9DkhUsaAaNr0GyC6uUK05wXmGq2mw+GXkiWmBSOYHjutbe1wjV4yVTXIm2JgSRCsjpQwcHFyBtgwawV3Ks0C1xw/ut2HcUnHvs+1mkiOWwKil5JuKnXqvjQik7DQGDqMGXP9o2JhLbtCJc0i0Y3R/MBBTPXZH3w415CkxcuvK03sV1ncQaGx1Ntc1UksTOqmmHIkHVBshXNpIv4CM8oeCmDcbKaO5I2A8kjyqUbNUsbpo40zmObES5Jx/fdFtKEQgj53SOnY7XLKJVyKfFLaPLChW32OqdomMbkNG7adTS1EKzXqomFPGD+8pk6k2Xt/Wy+gKqIDwEoW+3ZsI8nbQbiOsqlGxNuAHsLUtpnxlZ4dJLxe6E7VM8L+d0jp/HMiXOJ/iYQBEkfCN0LNzLW6MjATJIwFLbxA/loAaYvn8liIBM8LroFAVd3SWENfk6IDg1eN/ck2mWaZiC+olxskebe+VyQfGnUvWBO63kh/9xrbyu/G6iUcWlmttXnE2jfyqfRmIHOFw6AUcSJCUm1gOBlTEq5RMYvn0pDKxFhXgipEHD10gV/++ihUx2LqOza2dAu48JGdceysdDlnXCT9t75WpCCMX1o1L1gTut5Ia/Tlsf33JH5JZP9fdQkcdv+V6wI+ABTLUDWLd6ElctLePJL5s4plYamc3DpchJG37qA42fOp7oncWUVXGSg6sJGdcfqBXutjCwC01cGqC+NeuuGNVJLgq2S3jbo+egaVQMJ2eeXrsxi30sTxl5w01oaaR+klcvlUTimWoDOVqyKt1ndX04k4IF0EQy6nIRnTpxL3Y8zzj8gy0DNGn0RPgZw9dmKO1avhD9G6QUTRBRfoY+q0t22SnrboOc1+Qc+e4N0JX3gszfElhiIq2ljqtGkrQ5ZLvWhUkZqLVP10hGAgzs2S23XabMvk2poSa5Jkm21TtCorp0N7TLNMXpRWAK9YYKI4ssf0Av3uOc1+Sfqm/DQlrUdmvvxM+ex76UJrdYXjpuWaewqIRVEw2ze9zJqj7/cEqRJ+WC6mUnL1GkvQeJOdaAibeDxyPB45sQoHUnzBeJeiiAWWWWcKxF1XQXAXk2s8d3pKQ224+VN6YV73POaPLAg6AdvvBZDL5xqOVlNtcjG5LQ0/HC6OacNgRRo3xmkKbwbCGPdg6jzKWzdsKYjrd+0yXJAkBgF2LUT6xykMuKclzrfQ5x/wBcm96cb8elATUvwnjQWQ5cbi7WqALf+Dxs7CNeVcQsh5AFg30sTbVE0NpgTAuUSWTluqY8wN98Z5aND5rjbOTyOR4bHW5FD4ZkR0NHT08Rs0pwTVou0BciSkWTEXQudHV6WfGWbNC9h0Iov7v50y3yj+HKgpiFpsppNsi6IeTjnCyPkVa3KMiMWnJWTU+Z9VGX0Afjw4nHCD4LuhdTVapHVkRfodPiYFhSz1ZovSjS2PdgdqZKXZOgWKdMXKq3gS/sSqu6da4ecbL6PDI9j30sT2LPdfunpbiBpspqKtM9IlgUxj9BP5zZ5IvoCEZ0lojeIaJfr8WwTNMq+fqCSuhxwcJzLzblWNcwDx85i98hpbfROGudN9G8CW6UqCimMq8iPeq3aqrETbjJd7qPYF2lkrKH1d5jMN23HoeD4aSJkfDnkVAIvcLh3W10VG6RJVouS5RnJQh7PiVMhT0QlAH8M4IsAbgbwABHd7GKsfseNGRqT0/gg425hujnf9hA9e+KcVoCkcd7I/qZeq+Kp+2+JLWQGuBNCqraHOw+Na1+kA8fOandQcaaokbEGHj10KnUoY9qX0JdDTjevXgjfTEPcNTW55r7CXfN4Tlxr8p8B8IYQ4hdCiBkA3wFwt+1BRsYa1u3xMubjfyURcY0tkkaoqFqzAQuC/sB9t2Agpr63KyGkalMoBLQaU5wwJUD5t0kTp2SkfQlV924qQendNKQtstfL6N4TUyeoSllwfb3yiGRyLeSrAMJ1B95Z/KwFET1MRKNENHr+fDp7ZVyJ4V5DYCGLFkBbEk6cHi6gthMH9sYPppuoDlTw0Ja1HQ8X4WqjEZkgclVSVacxxQmtoIqnjKSJUzK2bliTqi59YCaLLqqmZpO01zpOMeim0D5bpE1WC9CZBF1frzxCP107XmXXrk0aCyGeBvA0AAwODqaS1FlX23DD61WVMmZm59rqrydldX8ZM7PzuGRQK17Vqi6wCX7jnk2tMgrhMDEZqgYiMmfcMyfOob/ch9WLnbTC85A5F7M69FYrOnYFhO9htBF6XIRTGpOKaXRTlgiZeq2KA8fOduxi4hxrqqiq0bcu4In6ptgxAXQUywPyLRaWd/hlVuen7OnS7Yxt4jqSybUm/w6AG0I/fxzAu7YHybraTk43cbk5j4M7NmPvXRtxZTbbrqB/+TI8+aVNsaaWSrmEB7esVQrnqIYbJDg9tGVtIu1SpdFONedxuTmP1f1lacLU3iMTLW1SZtcGzDXTPds3olxS70WCexh1gE1ON1sRTnF/a/o5EYy0JRsRMmkWINW4z544Z6TR12tVjO+5A99cbJqSZ3KQLwdmFlT3Qrcz7iVcC/kfA/gkEd1ERMsBfAXAEduDJLVdywiEms6Ga8q7k9PSbdhDiwI9+PneW6s4fua81nkYfQDTaJdxzjiVhj053Wy9rLprYuqgWrlcvnEML1AyAdecFxACUsexrpqmqmuWEMDoWxdi52sj8mEgYTs73fEFFjR0UwKlIK5doU16sV6P6l7EtdbsFZyaa4QQs0T0BwCOASgB+JYQwvwpNSSakJBWRKucg2H6CJgXajMLcNWmLqtYGWBaQTL6AKbRLtPW1kmCTvDJzjW4ftE4edVxVPdm5fJlSuFVr1Wx76UJ6SL27IlzGLzxWq3gy1rDRdVzOK7Ms+5+TU43MTLW6Lrkr4BeqOUSxXcdfNemLedx8kKI7wsh/rkQ4hNCiCddjRPWWlyuwIGA/2cfXan9vbhtqmm3pamZ2ZbzbfeIup6O7iWysdOJQyf4VAtT0EkqmqGbhA9iFmZVSzqdwzYgrdM1QBUQoFuYgIX7lTU3IC1ZzS29UMslig3nZxpHeV6mrZ4vUCbDtVATAH72/qXY39NtU00164uLmbaBs1SF7iVSRXpEKRG1HvIkiV9xDqok2p0qpEw1nywx0nG7j6xlCVTHj1uY6rUqHtyyNvFxbSAr6pfE3NKLxc2AbKattMI6L9NWIYV8NKQqTYVIW8heyLgsTiDZnE26PIWdcSrmhWg95Hu2bzRKngLiHVQqQdtH1PEiqLSqPds3phIeOq04ze7je6fe045ncnwTrfaJ+qbUC1taRsYaSv+M6cLiqxqkT7o9K7owtWuiBGFJt+1/xbk9WofshYzL4qwmtKHHbf/DBGF9cbZmnT1bNl8dqvo5qno5upCypPbLeq2K0bcuJK4GqfMNmNrEVY3HTbsG3fmp61JXsUxj69UJpSQLS9qQQB+hlzbIkhWdR93+QmryYXw6fFQvpG5Ob+6/M3HrsLjtfxTVlnrrhjVtdkUTAZ8kMUhWPyfJ9jTtlvqJ+iYcTBhOuEpj2koy33tvrbbtJASAwycbRslQac1FMvPBzuFx7B45rf27OL+OS3ox9DLAZla0C9NW4YW8T4ePSpCoBEhgM9c1J5eR9BxlNnqCwPCP3257yVSEbfemW/F6rYr5DOUFspJ0gdDVc0sy3+NnzktzEOIWiiwx+mnj7FXP0UCl7Fyj7sXQy4C0wjov01ZhzTUBpqV24whCJ02pLjYEkaESIMHnSeL0s6z8V2avZvWaZvhmadCh2p6GQ067pda6KioHSLaopt3KZ7HX6uLsdZm2qlDCvXdtjB0zK7oubN1OlpryedTtL5yQl73E37hnU9tnWzeswXOvvW0kTAPnl8p0USn3YToiIOMEr0qATE41E21Ps7S8Mw3htDUeoF9w82jwkKQ2vGpBSprqnsbuOjLWQJ+iK5nJAqOLs9ctElkbYGRB1YXNpER2N9DNTVYKJeRVL3G4/kvA4I3XYuj5U7GFzfqXL9M2zP7pf/5iYoeR6iVcVSm3hE4cBOCp+29J/WClMZHMC5HpQY42EIliu1lClCQNGlRO0we3rE00v6SJNrrKmaa7tqFt67FzeFzq3I9bJHwJK5XClTX73ARfDt+8xi2UTT6JXa9eq+JDK+LXuOAGyAg+T2rvVdnwiGCsXWetq2GrVn1Sgmul0s9c2ueTmEBk9tKDOzbHFggzOY5uN6TaYSXZRQVx9lkSufJGFaGlKyVtA18O3zzHLZQmn9SOqbO7BgQrrM20Z9W2eKekobiKuMSmOFSmk5XLS7g0M9dRtsG2gFDtZoLYeRcaTVLTiS2tNslxVM9q0l1U0Nw+bcvDvDVb1e4jzo8QJenc82i/53vcQgn5pC9xXE2XsP31mmV9rZuyur+cuV9m+MUPHswkG9OspkpV/Pi8QCthyuWLniR23pbQ8VmjxBSbsdNpFimbjaWT3Ld6rYpHFEqO6e4uzdxVx/ZV68nFTrZQ5pqkoUxx5Q8C4ffYi6fbCmT9+vIs9r00YaV5RnjblgSTXUgcqvC+Rw+dau0qDu7Y3PJn2GwYYho7v3vkNHYOj1vZ1vZCNqbvsgC2QhnT3DeVycZ0gUszd0H5u3wAABUpSURBVGU5arg1E+VZ46dQQj7pS6wTNFj8e1Xp23BNmSy2tDRRLsCCkzar0FVpDXNCtJ2brOH4I8PjqD3+cqYXIS52fmSs0bHTALLFT8f5T1x1v0oyv2gOwwrH/YvD2NAw0963rAtcmrmryl6YFLDLQp6LeaHMNUDyLWrwu6ptvImdPIstLe327NLMbGt3kXZLbVKCeLo5pww3DRqGJB0XiDdRXb+4wMb1wbWJTVNFVsI5DFmuc1JsmIvS3resIZxp5m7DTBSQ1DwF5BOuWihNPi26HYDpw51W6KTdnkXb4SXVbkfGGrh0pbPWuQwbDUOiY+tMVMECq7umLra1qu1+kkYdLueRR/anDQ1TpziYhHCmrQaZdu5ZzUTAwjM99MKptt3u0AuntDvBLOeaBBbyi6guuGnZ4rRCR9W9KA1JHVTRRhyqacQlpCRd4HQmqnB9Fp291MW2VleULK7uSx7zSKNIJDU/ZfVb6Cqsuu6ZmnbuNha2fS9NdChezTmBfS/lqyDIKJy5xjbRbdWqShmXZmbbbmjWcEpdtUdZKOOKcp/097M4qADgwyvKuDI732G2uvfWKg6fbCgFc9IFTieswvVZbCUkBUQbhAfN24Otss58ZdJJygZZs12jx0rTfD1L6KjOVKO6bzZDNtPM3YbpRPX+mhT5cw0LeQOiD47tOGJVpAxhIbolOhag9iGYoNNYByplrCj3tYTf1g1rcPzMeUw3O2Pnk44bEOcLCL6zabeMCrzwLiawvd97a1XZmCVpvHYabGS7hlEt5i5t/LoFXJZI1i1+kG4uS5AVFvIpsP1A6BxGurFsO6iABeFXKZdwcMfmjjj64P8rl5cwNTOXWuiaFI2rPf5yS9u0ca3jopimm3M4fua8thCd62qZNrJdw8Q1cHexaKmeLZXd21cykm0GKmVpH+KsSYs2YCHfBaRJ0ski/OKEbOBs/GC6Kd16T83M4eCOzZm21ACw98iEskG3bW3TtHqjLiHNddlqW9muAXE7JheLVtJGKb3Y+FvG3rs2dtTCKvdRLhU842DHaxeQd5JOeDwVkwoBD9iJIa7XFtoR6ggWGxtx66bVG3U1VFwnJNlOkIkLGnCxaNVryRql9GLjbxn1WhUH7rul7R0+cJ++gGBeORks5LuEeq3acv69OzmNA8fOOk3ECaKJ0m4nbWlaca0DJ6ebVrJd4wReIMRlv5fF2Zt1jlmd+qoG7i6zaHWZ1NF75zvD1yZJQiK5QNkSxJcDKm0NnKyaVuC8bkxOSx26KtLaa3UmIpkQd5WkonPau0iQCcx6eRYd02VSR5/pPJOCugkuULYE8eWASlMDJ6umFV3QklYMT7uLMBV4riIt4hZyV4I476qSOl+A7JkucmSLCi5QtgTx5YBKqpHb8BeookgGKuU2m2bQlStKll1EnMBzaSfd99KEciFP23w7Dh/10uNMY73mVHVBnr4I1uS7BJslZpMwtG29snZHGALwy/13WhlT9ZJ/MN1sc8buHjndUegqyy7CRJN2ZTIbGWsoE2Mak9N49NCpjvj4oPl2liSsJDtEWxp/8DeycwJ6z6nqgjzLXrMm3yX4ckDVa1WlxhzG5otposWMjDVw+GSjTcCHSx6kIa4mjMuaMXHHUNUHyhrJZLpDTFN7RUe9VsVT999SGKeqbfKMqGMh3yXkHUYZZs/2jdrtte0XU7Wdn5qZbQkVmWkjXPIgDXECz6XJLMsxsvytqVnARe0Vn890L5BXgTI213QRvhxQsvo80bouNuelinQJEqBG37qgNG1kFXg6k5hLk5lJWWfd36bF1CzgqvbKUnSqdhusyTMA2rWKvXdtRP9yt+t/vVbFyms6xwjq16vIKvB05gOXJjPTaqZRso7P2jTDmjzTRtTZ6TJeXxdPrSKrwAPUMdkuY7Zlu6VfXW521Mnpo4WuXzZ3UdHQ0Z3D4zhw7Gzbsbu59kpSfDQi72ZYyDMt4tq25VXMSsVApWxF4AFXhW3g1AwL+jwEwsprlqE5N49LM+1+h3kBCGEvkikgLnKom2uvJMF3VctuXGDYXMO0yLvdXhITRqVcsiJwZHHjNvrVxiFrbB0V8AEumpTERQ6lqb3SjSTt7mUzL2JkrIGh5yMRSs+nj1CyBWvyTIu82+3FxVMHVC1qRD5qrKt2SDpsNykxiRwqgpNUV0J7ZKzRkfhmU+vfe2SibScEAM15gb1HJrxeV9bkmRZ5t9sDFl6m+RgBbzO8zKTGum10OyQVNip9hilKtcc4dK0qo9dTl4GcBlXZbNXnecFCnmnhqwJjnotLnFBrTE5bL2egW1h0BeJsmsiKVO1Rh25HGL6eugzkopVdcCbkiWgvETWIaHzxv3/taizGDrJwu4M7Nkvbttkkz8XFxA9gu76LbmHRyCTrWvY1y66+7qv7y22hlHnVNneNrnR1+HrqtPW0112VOW6SUe4S1zb5g0KIP3I8BmMRH3bZcMRLY3IapcVG1sfPnO+wo9oaS9eVCrjqrLMxtkm7wyg2teyo7RkALjfnW99Fr4WvPqs2GNq2viNKCADKJWq7njptPe1137N9I4ZeONWWOVwuEfZs9xuhxI5XpisIhEke4W/RuPEkzrq04wFXwzZBeg0eyFajJ4oq4mTn8DiWlaijnEHwvY2wWdOQQtvF0cIL1+r+cqtfcIAqfDdLmG631sYnEfe0pT0w0V4A/wbArwCMAnhUCHFR9zeDg4NidHTUyXyY7ue2/a8om0C/uut26+PFCXkXY4+MNYyqftoc96ZdRxM7foHslUdlO4hKudSRcWv6e2nnIBO6Lsf0ARGdFEIMyr7LZJMnor8kotcl/90N4E8BfALAZgDvAXhKcYyHiWiUiEbPn09ffIrpffKsqR+Ol08zp7So4rVdjjuQ0iac1SdgWtXTVfVPXS193+Ue8vSBZDLXCCE+b/J7RPTfAXxPcYynATwNLGjyWebD9DZ51tRXxcu7Hts0nM7WuCNjDfz68mziv7PhEzBdtF0t7nG19H3lBeSdlesyuua60I9fAvC6q7GYYjC0bT3Kfe0xheU+chLmZyJAfIUYRp2EWThw7GyHEzKOPrLjEzCNzXcVw++r21ocLvsWyHAZJ/9fiOg0Ef0EwFYAOx2OxRSFaNx4ykbjcZgIEBfb97hwutX9ZRz4sr1yAmkE2rwADp9sZDYhmMbmu4rhV5mpfCeAqUyEaUtRx+FMyAshfk8IsUkI8SkhxF1CiPdcjcUUgwPHzkobV7jQcOLi5W0UQ5OxZ/tGlEudK9dDW9bizf13Yuzrd1gdN61As6FZmtq9XdjHVWaq6C7JR36AKitXl62bBQ6hZLqGPLfXunh5l9UX67UqRt+60FHL5vDJhtVaNQGqpiGfXrsKr/78gvZvbVz3sN07XOpYVubZ5rmrzFQrly9rm4+PipWqrFxdtm4WWMgzXUPezczD8fJhYf+hFW5fi+NnzudWzlnV9euvfn4BlXIfrszOd9S0D7B53WUCdefwOB4ZHseAg05kumbxAUmanNukqnjOddm6WeDaNUzX4LO+ypXZ+da/g4qUrrbueTsEg65fB3dsxpXZeVycakIAmG7O45plJTy0Za3T6z4y1sCjh05Je/YCCxFHwZxslZQwceb6cszm/ZyzkGe6hrBtFliwUQaalUtbad7RDioBtKpSdmofVp3n8TPnncWMBxp8ElOEjWtvIkh9VebMO0afzTVMV5FneYOAvDU6mZ283Ee4NDPbMhm5OGfdebqKGTfNR5DNKQsmJQZMm5ynIa5MQ54x+izkma4jb1upD18A0C6ApmZmO0rf2j7nvM8TSB8WaGNOcYLUVa0Z3y0Io7CQZ7qOvMsbXLrSGWrn2hcQFUA37Toq/T3bNeWjmisB2LphjbUxogQVRZPgsklNFBcatS+HrgoW8kzXkZfGKStSBcirFromj3OWhW8KAMN/8zaO/uQ9q9EtAWnCAgV6r8RxmG7LtGXHK9N15BV9oLIX94diqfMir3OWhW8254X16JaANGGBtkIJfTVC6bZWiyzkma4jr+iDbtK4fJ9zGJuRRSaduMLYdHyqKlC6pttaLbK5hulK8og+8OGI1OHznKPYWuiizs0+jY2+atFU5NMu3m3NQ1jIM0sWlyF03YppK0LbvoBAwKkczARYbc5iskuz1Y1Khq8yxjJYyDNLlm7TuPJAVubg0sxsW2E4lwtdXrunuHF8hjm6XFxkOGv/lwZu/8cw+ZOn0MkroimuvV/erSYDdo+c7ihOZ6PtoK79H2vyDLPEydO0oKr+GdQLCv+O7XFWlK/Gmbh0uuv6ykYFPODeV8BCnmGY3AgEoKwNogthFy08F1S+VCVpZTUb6cxAB46dVTZUdxnRxUKeYZhckJkqotgUdrIIm2BsmYC34YvQRfXooppcRnSxkGcYxjkqU0UUVcu+NJgsGCUizAvhvI79u5PT2hIPLiO6WMgzzBIj7+gOQG+qCGMzDsQkJ2BeCPxy/53Ox4ybi8vrzxmvDLOE8JUJamqG+UBiq0+LSbatbTOJLttVVa7BVUeoABbyDLOEyLtBSoCpMLWdhPWNezZpG2TbrsCpK0/hq9wBm2sYZgnhs+XdzuFxrcnGhcCTNaEJ46KBejQkNSiUFiSfrSj3Oan4qYI1eYZZQqg0ZQE4rdRYr1W1An51f9lZC7x6rYp7b5Uf1/UuJmoem5xu4nJzHgd3bMaru27PJT+BhTzDLCF0dmrX9nmd7flyc175nQ2Onzmv/M7lLsaXeSwMC3mGWUIEWq3KSu1SAOkWGNeCTyfIV1XshW2ajptnOWsW8gyzxJA1DgnjSgAFTsm8xwX0Dt1LM7POdi/d0ECEhTzDLDHihKlLAVSvVZVmG5fj6nYRzTmR6+4l73LWLOQZZomhE6Z5CCAfgs/XLiKvjl86OISSYZYYqsYheTUw91XHv16rKmvIuN69+OxRwEKeYZYY3dAsxZfgG9q2HkPPn0Jzvt0rYTspqptgIc8wSxDf2qVPZEXChn/8tvWkKB81gmRwZyiGYQpPIHB1RcJsdoVSlVVeubyEqZk560KfO0MxDLNkUbUcjGLL+aorq3xpJv+eshxdwzBModn30kSsgAfsOV9NyyrnlfnKQp5hmMIyMtbAxan48sXlElkL4UyyI8gj85WFPMMwhcVEU17dX8aBL99izWySZEeQR+Yr2+QZhiksOk35mzs2O7GHq/IQopT77O0edGTS5InoPiKaIKJ5IhqMfPcYEb1BRGeJaFu2aTIMwyRHpSkPVMrOHJ5BlutAXOEzdS8Tq2Q117wO4B4APwp/SEQ3A/gKgI0AvgDgT4hI34eLYRjGMqoSCnvv2uh03HqtipXX6A0lLmvmhMlkrhFC/BQAqLO91t0AviOEuALgl0T0BoDPAPjrLOMxDMMkwWd2r4lTNQ/HqyubfBXAidDP7yx+1gERPQzgYQBYu3ato+kwDLNU8ZXde/1ARZt8FfyOa2LNNUT0l0T0uuS/u3V/JvlMGjoqhHhaCDEohBhcs6a49SMYhlla6MobA/mVHI7V5IUQn09x3HcA3BD6+eMA3k1xHIZhmJ4kbCpqTE6DcFXTzaviJ+AuTv4IgK8Q0TVEdBOATwL4G0djMQzDdCX1WrWl0YdNGa572obJGkL5JSJ6B8BvAThKRMcAQAgxAeAQgL8D8AMAXxNCxOcVMwzDFAzfzbyzRtd8F8B3Fd89CeDJLMdnGIbpdXw38+ayBgzDMA7x3cybhTzDMIxDfDfz5to1DMMwDvHdbpGFPMMwjGN8tltkcw3DMEyBYSHPMAxTYFjIMwzDFBgW8gzDMAWGHa8MwzAOGRlreIusAVjIMwzDOGNkrNHWCrAxOY3HXjwNALkJejbXMAzDOMJ33RqAhTzDMIwzfNetAVjIMwzDOMN33RqAhTzDMIwzfNetAdjxyjAM4wzfdWsAFvIMwzBO8Vm3BmBzDcMwTKFhIc8wDFNgWMgzDMMUGBbyDMMwBYaFPMMwTIEhIYTvObQgovMA3spwiI8A+AdL0+kVlto5L7XzBficlwpZzvlGIcQa2RddJeSzQkSjQohB3/PIk6V2zkvtfAE+56WCq3Nmcw3DMEyBYSHPMAxTYIom5J/2PQEPLLVzXmrnC/A5LxWcnHOhbPIMwzBMO0XT5BmGYZgQLOQZhmEKTCGEPBF9gYjOEtEbRLTL93xcQ0Q3ENFxIvopEU0Q0R/6nlNeEFGJiMaI6Hu+55IHRDRARC8Q0ZnF+/1bvufkEiLaufhMv05EzxHRCt9zsg0RfYuI3iei10OfXUtE/4eIfrb4/9W2xut5IU9EJQB/DOCLAG4G8AAR3ex3Vs6ZBfCoEOJfANgC4GtL4JwD/hDAT31PIkf+G4AfCCE2ALgFBT53IqoC+PcABoUQvwmgBOArfmflhD8H8IXIZ7sA/FAI8UkAP1z82Qo9L+QBfAbAG0KIXwghZgB8B8DdnufkFCHEe0KIv1389//Dwovvr2B1ThDRxwHcCeDPfM8lD4jowwB+G8D/AAAhxIwQYtLvrJyzDECFiJYB6Afwruf5WEcI8SMAFyIf3w3g24v//jaAuq3xiiDkqwDeDv38DpaAwAsgonUAagBe8zuTXPgmgP8AYN73RHLinwI4D+B/Lpqo/oyIVvqelCuEEA0AfwTgHID3AHwghHjZ76xy42NCiPeABSUOwEdtHbgIQp4kny2JuFAi+hCAwwAeEUL8yvd8XEJEvwvgfSHESd9zyZFlAD4N4E+FEDUAl2BxG99tLNqh7wZwE4DrAawkoof8zqr3KYKQfwfADaGfP44CbvGiEFEZCwL+WSHEi77nkwO3AbiLiN7EgknudiJ6xu+UnPMOgHeEEMEu7QUsCP2i8nkAvxRCnBdCNAG8COBfep5TXvw9EV0HAIv/f9/WgYsg5H8M4JNEdBMRLceCo+aI5zk5hYgIC3banwoh/qvv+eSBEOIxIcTHhRDrsHCPXxFCFFrLE0L8XwBvE9H6xY8+B+DvPE7JNecAbCGi/sVn/HMosKM5whEAX13891cB/IWtA/d8I28hxCwR/QGAY1jwxn9LCDHheVquuQ3A7wE4TUTji5/9RyHE9z3OiXHDvwPw7KIC8wsA/9bzfJwhhHiNiF4A8LdYiCAbQwHLGxDRcwD+FYCPENE7APYA2A/gEBH9PhYWu/usjcdlDRiGYYpLEcw1DMMwjAIW8gzDMAWGhTzDMEyBYSHPMAxTYFjIMwzDFBgW8gzDMAWGhTzDMEyB+f8/KdpcyYandAAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X = np.linspace(0,10,500)\n", "y = np.sin(X*2*np.pi)*X + np.random.randn(len(X))\n", "\n", "plt.scatter(X,y);" ] }, { "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": [ "# let's try a large lambda first and lots of splines\n", "gam = LinearGAM(lam=1e6, n_splines=50). fit(X,y)\n", "XX = gam.generate_X_grid(term=0)\n", "plt.scatter(X,y,alpha=0.3);\n", "plt.plot(XX, gam.predict(XX));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the large $\\lambda$ forces a straight line, no flexibility. Let's see now what happens if we make it smaller." ] }, { "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": [ "# let's try a smaller lambda \n", "gam = LinearGAM(lam=1e2, n_splines=50). fit(X,y)\n", "XX = gam.generate_X_grid(term=0)\n", "plt.scatter(X,y,alpha=0.3);\n", "plt.plot(XX, gam.predict(XX));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is some curvature there but still not a good fit. Let's try no penalty. That should have the line fit exactly." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# no penalty, let's try a 0 lambda \n", "gam = LinearGAM(lam=0, n_splines=50). fit(X,y)\n", "XX = gam.generate_X_grid(term=0)\n", "plt.scatter(X,y,alpha=0.3)\n", "plt.plot(XX, gam.predict(XX))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Yes, that is good. Now let's see what happens if we lessen the number of splines. The fit should not be as good." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# no penalty, let's try a 0 lambda \n", "gam = LinearGAM(lam=0, n_splines=10). fit(X,y)\n", "XX = gam.generate_X_grid(term=0)\n", "plt.scatter(X,y,alpha=0.3);\n", "plt.plot(XX, gam.predict(XX));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Indeed." ] } ], "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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 4 }