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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"title: Fitting a Simple Additive Model in Python\n",
"tags: Statistics, Python\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Recently, I have been learning about [(generalized) additive models](https://en.wikipedia.org/wiki/Generalized_additive_model) by working through [Simon Wood's](http://people.bath.ac.uk/sw283/) [book](http://www.amazon.com/Generalized-Additive-Models-Introduction-Statistical/dp/1584884746). I have previously posted an IPython [notebook](http://nbviewer.ipython.org/gist/AustinRochford/bb19863446d46dbcdc83) implementing the models from Chapter 3 of the book. In this post, I will show how to fit a simple additive model in Python in a bit more detail.\n",
"\n",
"We will use a [LIDAR](https://en.wikipedia.org/wiki/Lidar) dataset that is available on the [website](http://www.stat.cmu.edu/~larry/all-of-nonpar/data.html) for Larry Wasserman's book [_All of Nonparametric Statistics_](http://www.stat.cmu.edu/~larry/all-of-nonpar/)."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from matplotlib import pyplot as plt\n",
"import numpy as np\n",
"import pandas as pd\n",
"import patsy\n",
"import scipy as sp\n",
"import seaborn as sns\n",
"from statsmodels import api as sm"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"df = pd.read_csv('http://www.stat.cmu.edu/~larry/all-of-nonpar/=data/lidar.dat',\n",
" sep=' *', engine='python')\n",
"df['std_range'] = (df.range - df.range.min()) / df.range.ptp()\n",
"\n",
"n = df.shape[0]"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>range</th>\n",
" <th>logratio</th>\n",
" <th>std_range</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
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],
"text/plain": [
" range logratio std_range\n",
"0 390 -0.050356 0.000000\n",
"1 391 -0.060097 0.003030\n",
"2 393 -0.041901 0.009091\n",
"3 394 -0.050985 0.012121\n",
"4 396 -0.059913 0.018182"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This data set is well-suited to additive modeling because the relationship between the variables is highly non-linear."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
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awtEsRBQ1bEv92gftXcdV+Ihs+JdARFElmEv9EkUTNukTERFpABM+ERGRBjDh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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f5e5c0881d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"blue = sns.color_palette()[0]\n",
"ax.scatter(df.std_range, df.logratio, c=blue, alpha=0.5);\n",
"\n",
"ax.set_xlim(-0.01, 1.01);\n",
"ax.set_xlabel('Scaled range');\n",
"\n",
"ax.set_ylabel('Log ratio');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"An additive model represents the relationship between explanatory variables $\\mathbf{x}$ and a response variable $y$ as a sum of smooth functions of the explanatory variables\n",
"\n",
"$$y = \\beta_0 + f_1(x_1) + f_2(x_2) + \\cdots + f_k(x_k) + \\varepsilon.$$\n",
"\n",
"The smooth functions $f_i$ can be estimated using a variety of nonparametric techniques. Following Chapter 3 of Wood's book, we will fit our additive model using penalized regression splines.\n",
"\n",
"Since our LIDAR data set has only one explanatory variable, our additive model takes the form\n",
"\n",
"$$y = \\beta_0 + f(x) + \\varepsilon.$$\n",
"\n",
"We fit this model by minimizing the penalized residual sum of squares\n",
"\n",
"$$PRSS = \\sum_{i = 1}^n \\left(y_i - \\beta_0 - f(x_i)\\right)^2 + \\lambda \\int_0^1 \\left(f''(x)\\right)^2\\ dx.$$\n",
"\n",
"The penalty term\n",
"\n",
"$$\\int_0^1 \\left(f''(x)\\right)^2\\ dx$$\n",
"\n",
"causes us to only choose less smooth functions if they fit the data much better. The smoothing parameter $\\lambda$ controls the rate at which decreased smoothness is traded for a better fit.\n",
"\n",
"In the penalized regression splines model, we must also choose basis functions $\\varphi_1, \\varphi_2, \\ldots, \\varphi_k$, which we then use to express the smooth function $f$ as\n",
"\n",
"$$f(x) = \\beta_1 \\varphi_1(x) + \\beta_2 \\varphi_2(x) + \\cdots + \\beta_k \\varphi_k(x).$$\n",
"\n",
"With these basis functions in place, if we define $\\mathbf{x}_i = [1\\ x_i\\ \\varphi_2(x_i)\\ \\cdots \\varphi_k(x_i)]$ and\n",
"\n",
"$$\\mathbf{X} = \\begin{bmatrix}\n",
" \\mathbf{x}_1 \\\\\n",
" \\vdots \\\\\n",
" \\mathbf{x}_n\n",
" \\end{bmatrix},$$\n",
" \n",
"the model $y_i = \\beta_0 + f(x_i) + \\varepsilon$ can be rewritten as $\\mathbf{y} = \\mathbf{X} \\beta + \\varepsilon$. It is tedious but not difficult to show that when $f$ is expressed as a linear combination of basis functions, there is always a [positive semidefinite](https://en.wikipedia.org/wiki/Positive-definite_matrix#Negative-definite.2C_semidefinite_and_indefinite_matrices) matrix $\\mathbf{S}$ such that\n",
"\n",
"$$\\int_0^1 \\left(f''(x)\\right)^2\\ dx = \\beta^{\\intercal} \\mathbf{S} \\beta.$$\n",
"\n",
"Since $\\mathbf{S}$ is positive semidefinite, it has a square root $\\mathbf{B}$ such that $\\mathbf{B}^{\\intercal} \\mathbf{B} = \\mathbf{S}$. The penalized residual sum of squares objective function can then be written as\n",
"\n",
"$$\n",
"\\begin{align*}\n",
" PRSS\n",
" & = (\\mathbf{y} - \\mathbf{X} \\beta)^{\\intercal} (\\mathbf{y} - \\mathbf{X} \\beta) + \\lambda \\beta^{\\intercal} \\mathbf{B}^{\\intercal} \\mathbf{B} \\beta\n",
" = (\\mathbf{\\tilde{y}} - \\mathbf{\\tilde{X}} \\beta)^{\\intercal} (\\mathbf{\\tilde{y}} - \\mathbf{\\tilde{X}} \\beta),\n",
"\\end{align*}\n",
"$$\n",
"\n",
"where\n",
"\n",
"$$\\mathbf{\\tilde{y}} = \\begin{bmatrix}\n",
" \\mathbf{y} \\\\\n",
" \\mathbf{0}_{k + 1}\n",
"\\end{bmatrix}\n",
"$$\n",
"\n",
"and\n",
"\n",
"$$\\mathbf{\\tilde{X}} = \\begin{bmatrix}\n",
" \\mathbf{X} \\\\\n",
" \\sqrt{\\lambda}\\ \\mathbf{B}\n",
"\\end{bmatrix}. \n",
"$$\n",
"\n",
"Therefore the augmented data matrices $\\mathbf{\\tilde{y}}$ and $\\mathbf{\\tilde{X}}$ allow us to express the penalized residual sum of squares for the original model as the residual sum of squares of the OLS model $\\mathbf{\\tilde{y}} = \\mathbf{\\tilde{X}} \\beta + \\tilde{\\varepsilon}$. This augmented model allows us to use widely available machinery for fitting OLS models to fit the additive model as well.\n",
"\n",
"The last step before we can fit the model in Python is to choose the basis functions $\\varphi_i$. Again, following Chapter 3 of Wood's book, we let\n",
"\n",
"$$R(x, z) = \\frac{1}{4} \\left(\\left(z - \\frac{1}{2}\\right)^2 - \\frac{1}{12}\\right) \\left(\\left(x - \\frac{1}{2}\\right)^2 - \\frac{1}{12}\\right) - \\frac{1}{24} \\left(\\left(\\left|x - z\\right| - \\frac{1}{2}\\right)^4 - \\frac{1}{2} \\left(\\left|x - z\\right| - \\frac{1}{2}\\right)^2 + \\frac{7}{240}\\right).$$"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def R(x, z):\n",
" return ((z - 0.5)**2 - 1 / 12) * ((x - 0.5)**2 - 1 / 12) / 4 - ((np.abs(x - z) - 0.5)**4 - 0.5 * (np.abs(x - z) - 0.5)**2 + 7 / 240) / 24\n",
"\n",
"R = np.frompyfunc(R, 2, 1)\n",
"\n",
"def R_(x):\n",
" return R.outer(x, knots).astype(np.float64)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Though this function is quite complicated, we will see that it has some very conveient properties. We must also choose a set of knots $z_i$ in $[0, 1]$, $i = 1, 2, \\ldots, q$."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"q = 20\n",
"\n",
"knots = df.std_range.quantile(np.linspace(0, 1, q))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we have used twenty knots situatied at percentiles of `std_range`.\n",
"\n",
"Now we define our basis functions as $\\varphi_1(x) = x$, $\\varphi_{i}(x) = R(x, z_{i - 1})$ for $i = 2, 3, \\ldots q + 1$.\n",
"\n",
"Our model matrices $\\mathbf{y}$ and $\\mathbf{X}$ are therefore"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"y, X = patsy.dmatrices('logratio ~ std_range + R_(std_range)', data=df)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that, by default, `patsy` always includes an intercept column in `X`.\n",
"\n",
"The advantage of the function $R$ is the the penalty matrix $\\mathbf{S}$ has the form\n",
"\n",
"$$S = \\begin{bmatrix}\n",
" \\mathbf{0}_{2 \\times 2} & \\mathbf{0}_{2 \\times q} \\\\\n",
" \\mathbf{0}_{q \\times 2} & \\mathbf{\\tilde{S}}\n",
"\\end{bmatrix},$$\n",
"\n",
"where $\\mathbf{\\tilde{S}}_{ij} = R(z_i, z_j)$. We now calculate $\\mathbf{S}$ and its square root $\\mathbf{B}$."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"S = np.zeros((q + 2, q + 2))\n",
"S[2:, 2:] = R_(knots)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"B = np.zeros_like(S)\n",
"B[2:, 2:] = np.real_if_close(sp.linalg.sqrtm(S[2:, 2:]), tol=10**8)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now have all the ingredients necessary to fit some additive models to the LIDAR data set."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def fit(y, X, B, lambda_=1.0):\n",
" # build the augmented matrices\n",
" y_ = np.vstack((y, np.zeros((q + 2, 1))))\n",
" X_ = np.vstack((X, np.sqrt(lambda_) * B))\n",
" \n",
" return sm.OLS(y_, X_).fit()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have not yet discussed how to choose the smoothing parameter $\\lambda$, so we will fit several models with different values of $\\lambda$ to see how it affects the results."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"data": {
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iY8TUJJ3hFDdqajlaeSj9mOv1HpLVo4TYXi7V9fL1H9Yt+ntFmZphYLeasJqNWMwGbGYD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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f5e36eb2110>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axes = plt.subplots(nrows=3, ncols=2, sharex=True, sharey=True, squeeze=True, figsize=(12, 13.5))\n",
"\n",
"plot_lambdas = np.array([1.0, 0.1, 0.01, 0.001, 0.0001, 0.00001])\n",
"\n",
"plot_x = np.linspace(0, 1, 100)\n",
"plot_X = patsy.dmatrix('std_range + R_(std_range)', {'std_range': plot_x})\n",
"\n",
"for lambda_, ax in zip(plot_lambdas, np.ravel(axes)):\n",
" ax.scatter(df.std_range, df.logratio, c=blue, alpha=0.5);\n",
" \n",
" results = fit(y, X, B, lambda_=lambda_)\n",
" ax.plot(plot_x, results.predict(plot_X));\n",
" \n",
" ax.set_xlim(-0.01, 1.01);\n",
" ax.set_xlabel('Scaled range');\n",
" \n",
" ax.set_ylabel('Log ratio');\n",
" \n",
" ax.set_title(r'$\\lambda = {}$'.format(lambda_));\n",
"\n",
"fig.tight_layout();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that as $\\lambda$ decreases, the model becomes less smooth. Visually, it seems that the optimal value of $\\lambda$ lies somewhere between $10^{-2}$ and $10^{-4}$. We need a rigorous way to choose the optimal value of $\\lambda$. As is often the case in such situations, we turn to [cross-validation](https://en.wikipedia.org/wiki/Cross-validation_(statistics)). Specifically, we will use [generalized cross-validation](http://www.stat.wisc.edu/~wahba/ftp1/oldie/golub.heath.wahba.pdf) to choose the optimal value of $\\lambda$. The GCV score is given by\n",
"\n",
"$$\\operatorname{GCV}(\\lambda) = \\frac{n \\sum_{i = 1}^n \\left(y_i - \\hat{y}_i\\right)^2}{\\left(n - \\operatorname{tr} \\mathbf{H}\\right)^2}.$$\n",
"\n",
"Here, $\\hat{y}_i$ is the $i$-th predicted value, and $\\mathbf{H}$ is upper left $n \\times n$ submatrix of the the [influence matrix](https://en.wikipedia.org/wiki/Hat_matrix) for the OLS model $\\mathbf{\\tilde{y}} = \\mathbf{\\tilde{X}} + \\varepsilon$."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def gcv_score(results):\n",
" X = results.model.exog[:-(q + 2), :]\n",
" n = X.shape[0]\n",
" y = results.model.endog[:n]\n",
" \n",
" y_hat = results.predict(X)\n",
" hat_matrix_trace = results.get_influence().hat_matrix_diag[:n].sum()\n",
" \n",
" return n * np.power(y - y_hat, 2).sum() / np.power(n - hat_matrix_trace, 2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we evaluate the GCV score of the model over a range of $\\lambda$ values."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"lambdas = np.logspace(0, 50, 100, base=1.5) * 1e-8"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"gcv_scores = np.array([gcv_score(fit(y, X, B, lambda_=lambda_)) for lambda_ in lambdas])"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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JUWaXgwsQGgAAAaX4oxOSpNzbMkyuBBcjNAAAAkb12VbtPnxa1w2PU+aIOLPL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\nITQAAACv/P8ujTOQa8xzRwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f5e42666650>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"ax.plot(lambdas, gcv_scores);\n",
"\n",
"ax.set_xscale('log');\n",
"ax.set_xlabel(r'$\\lambda$');\n",
"\n",
"ax.set_ylabel(r'$\\operatorname{GCV}(\\lambda)$');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The GCV-optimal value of $\\lambda$ is therefore"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.00063458365729550153"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lambda_best = lambdas[gcv_scores.argmin()]\n",
"\n",
"lambda_best"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This value of $\\lambda$ produces a visually reasonable fit."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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Mn5tCjK6IZbZYiItPJDYhHddg27QrYk1ey9xmHiAxLpouZzzhEVY0zeX1qlqj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\nAEP8DwU10IZraBorAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f5e36242390>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"ax.scatter(df.std_range, df.logratio, c=blue, alpha=0.5);\n",
"\n",
"results = fit(y, X, B, lambda_=lambda_best)\n",
"ax.plot(plot_x, results.predict(plot_X), label=r'$\\lambda = {}$'.format(lambda_best));\n",
"\n",
"ax.set_xlim(-0.01, 1.01);\n",
"\n",
"ax.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"We have only scratched the surface of additive models, fitting a simple model of one variable with penalized regression splines. In general, additive models are quite powerful and flexible, while remaining quite interpretable.\n",
"\n",
"This post is available as an [IPython](http://ipython.org/) notebook [here](http://nbviewer.ipython.org/gist/AustinRochford/c9c6862c6f7f7a28870a)."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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