Morten Hjorth-Jensen
5080 lines
1.4 MiB
Plaintext
5080 lines
1.4 MiB
Plaintext
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"# Resampling Methods"
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]
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"## Introduction\n",
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"\n",
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"Resampling methods are an indispensable tool in modern\n",
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"statistics. They involve repeatedly drawing samples from a training\n",
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"set and refitting a model of interest on each sample in order to\n",
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"obtain additional information about the fitted model. For example, in\n",
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"order to estimate the variability of a linear regression fit, we can\n",
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"repeatedly draw different samples from the training data, fit a linear\n",
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"regression to each new sample, and then examine the extent to which\n",
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"the resulting fits differ. Such an approach may allow us to obtain\n",
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"information that would not be available from fitting the model only\n",
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"once using the original training sample.\n",
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"\n",
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"Two resampling methods are often used in Machine Learning analyses,\n",
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"1. The **bootstrap method**\n",
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"\n",
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"2. and **Cross-Validation**\n",
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"\n",
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"In addition there are several other methods such as the Jackknife and the Blocking methods. We will discuss in particular\n",
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"cross-validation and the bootstrap method. \n",
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"\n",
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"Resampling approaches can be computationally expensive, because they\n",
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"involve fitting the same statistical method multiple times using\n",
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"different subsets of the training data. However, due to recent\n",
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"advances in computing power, the computational requirements of\n",
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"resampling methods generally are not prohibitive. In this chapter, we\n",
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"discuss two of the most commonly used resampling methods,\n",
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"cross-validation and the bootstrap. Both methods are important tools\n",
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"in the practical application of many statistical learning\n",
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"procedures. For example, cross-validation can be used to estimate the\n",
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"test error associated with a given statistical learning method in\n",
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"order to evaluate its performance, or to select the appropriate level\n",
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"of flexibility. The process of evaluating a model’s performance is\n",
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"known as model assessment, whereas the process of selecting the proper\n",
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"level of flexibility for a model is known as model selection. The\n",
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"bootstrap is widely used.\n",
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"\n",
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"* Our simulations can be treated as *computer experiments*. This is particularly the case for Monte Carlo methods\n",
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"\n",
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"* The results can be analysed with the same statistical tools as we would use analysing experimental data.\n",
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"\n",
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"* As in all experiments, we are looking for expectation values and an estimate of how accurate they are, i.e., possible sources for errors."
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"source": [
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"## Reminder on Statistics\n",
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"\n",
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"* As in other experiments, many numerical experiments have two classes of errors:\n",
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"\n",
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" * Statistical errors\n",
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"\n",
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" * Systematical errors\n",
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"\n",
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"* Statistical errors can be estimated using standard tools from statistics\n",
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"\n",
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"* Systematical errors are method specific and must be treated differently from case to case. \n",
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"\n",
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"The\n",
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"advantage of doing linear regression is that we actually end up with\n",
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"analytical expressions for several statistical quantities. \n",
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"Standard least squares and Ridge regression allow us to\n",
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"derive quantities like the variance and other expectation values in a\n",
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"rather straightforward way.\n",
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"\n",
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"It is assumed that $\\varepsilon_i\n",
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"\\sim \\mathcal{N}(0, \\sigma^2)$ and the $\\varepsilon_{i}$ are\n",
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"independent, i.e.:"
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"source": [
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"$$\n",
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"\\begin{align*} \n",
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"\\mbox{Cov}(\\varepsilon_{i_1},\n",
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"\\varepsilon_{i_2}) & = \\left\\{ \\begin{array}{lcc} \\sigma^2 & \\mbox{if}\n",
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"& i_1 = i_2, \\\\ 0 & \\mbox{if} & i_1 \\not= i_2. \\end{array} \\right.\n",
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"\\end{align*}\n",
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"$$"
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"source": [
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"The randomness of $\\varepsilon_i$ implies that\n",
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"$\\mathbf{y}_i$ is also a random variable. In particular,\n",
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"$\\mathbf{y}_i$ is normally distributed, because $\\varepsilon_i \\sim\n",
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"\\mathcal{N}(0, \\sigma^2)$ and $\\mathbf{X}_{i,\\ast} \\, \\boldsymbol{\\beta}$ is a\n",
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"non-random scalar. To specify the parameters of the distribution of\n",
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"$\\mathbf{y}_i$ we need to calculate its first two moments. \n",
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"\n",
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"Recall that $\\boldsymbol{X}$ is a matrix of dimensionality $n\\times p$. The\n",
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"notation above $\\mathbf{X}_{i,\\ast}$ means that we are looking at the\n",
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"row number $i$ and perform a sum over all values $p$.\n",
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"\n",
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"The assumption we have made here can be summarized as (and this is going to be useful when we discuss the bias-variance trade off)\n",
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"that there exists a function $f(\\boldsymbol{x})$ and a normal distributed error $\\boldsymbol{\\varepsilon}\\sim \\mathcal{N}(0, \\sigma^2)$\n",
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"which describe our data"
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"source": [
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"$$\n",
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"\\boldsymbol{y} = f(\\boldsymbol{x})+\\boldsymbol{\\varepsilon}\n",
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"$$"
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"source": [
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"We approximate this function with our model from the solution of the linear regression equations, that is our\n",
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"function $f$ is approximated by $\\boldsymbol{\\tilde{y}}$ where we want to minimize $(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2$, our MSE, with"
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"source": [
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"$$\n",
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"\\boldsymbol{\\tilde{y}} = \\boldsymbol{X}\\boldsymbol{\\beta}.\n",
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"$$"
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"source": [
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"We can calculate the expectation value of $\\boldsymbol{y}$ for a given element $i$"
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]
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"source": [
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"$$\n",
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"\\begin{align*} \n",
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"\\mathbb{E}(y_i) & =\n",
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"\\mathbb{E}(\\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta}) + \\mathbb{E}(\\varepsilon_i)\n",
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"\\, \\, \\, = \\, \\, \\, \\mathbf{X}_{i, \\ast} \\, \\beta, \n",
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"\\end{align*}\n",
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"$$"
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"source": [
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"while\n",
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"its variance is"
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"source": [
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"$$\n",
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"\\begin{align*} \\mbox{Var}(y_i) & = \\mathbb{E} \\{ [y_i\n",
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"- \\mathbb{E}(y_i)]^2 \\} \\, \\, \\, = \\, \\, \\, \\mathbb{E} ( y_i^2 ) -\n",
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"[\\mathbb{E}(y_i)]^2 \\\\ & = \\mathbb{E} [ ( \\mathbf{X}_{i, \\ast} \\,\n",
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"\\beta + \\varepsilon_i )^2] - ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta})^2 \\\\ &\n",
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"= \\mathbb{E} [ ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta})^2 + 2 \\varepsilon_i\n",
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"\\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta} + \\varepsilon_i^2 ] - ( \\mathbf{X}_{i,\n",
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"\\ast} \\, \\beta)^2 \\\\ & = ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta})^2 + 2\n",
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"\\mathbb{E}(\\varepsilon_i) \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta} +\n",
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"\\mathbb{E}(\\varepsilon_i^2 ) - ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta})^2 \n",
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"\\\\ & = \\mathbb{E}(\\varepsilon_i^2 ) \\, \\, \\, = \\, \\, \\,\n",
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"\\mbox{Var}(\\varepsilon_i) \\, \\, \\, = \\, \\, \\, \\sigma^2. \n",
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"\\end{align*}\n",
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"$$"
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"source": [
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"Hence, $y_i \\sim \\mathcal{N}( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta}, \\sigma^2)$, that is $\\boldsymbol{y}$ follows a normal distribution with \n",
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"mean value $\\boldsymbol{X}\\boldsymbol{\\beta}$ and variance $\\sigma^2$ (not be confused with the singular values of the SVD). \n",
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"\n",
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"With the OLS expressions for the parameters $\\boldsymbol{\\beta}$ we can evaluate the expectation value"
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"source": [
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"$$\n",
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"\\mathbb{E}(\\boldsymbol{\\beta}) = \\mathbb{E}[ (\\mathbf{X}^{\\top} \\mathbf{X})^{-1}\\mathbf{X}^{T} \\mathbf{Y}]=(\\mathbf{X}^{T} \\mathbf{X})^{-1}\\mathbf{X}^{T} \\mathbb{E}[ \\mathbf{Y}]=(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\mathbf{X}^{T}\\mathbf{X}\\boldsymbol{\\beta}=\\boldsymbol{\\beta}.\n",
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"$$"
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"source": [
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"This means that the estimator of the regression parameters is unbiased.\n",
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"\n",
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"We can also calculate the variance\n",
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"\n",
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"The variance of $\\boldsymbol{\\beta}$ is"
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]
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"source": [
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"$$\n",
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"\\begin{eqnarray*}\n",
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"\\mbox{Var}(\\boldsymbol{\\beta}) & = & \\mathbb{E} \\{ [\\boldsymbol{\\beta} - \\mathbb{E}(\\boldsymbol{\\beta})] [\\boldsymbol{\\beta} - \\mathbb{E}(\\boldsymbol{\\beta})]^{T} \\}\n",
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"\\\\\n",
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"& = & \\mathbb{E} \\{ [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y} - \\boldsymbol{\\beta}] \\, [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y} - \\boldsymbol{\\beta}]^{T} \\}\n",
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"\\\\\n",
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"% & = & \\mathbb{E} \\{ [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y}] \\, [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y}]^{T} \\} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n",
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"% \\\\\n",
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"% & = & \\mathbb{E} \\{ (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y} \\, \\mathbf{Y}^{T} \\, \\mathbf{X} \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n",
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"% \\\\\n",
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"& = & (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\, \\mathbb{E} \\{ \\mathbf{Y} \\, \\mathbf{Y}^{T} \\} \\, \\mathbf{X} \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n",
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"\\\\\n",
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"& = & (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\, \\{ \\mathbf{X} \\, \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T} \\, \\mathbf{X}^{T} + \\sigma^2 \\} \\, \\mathbf{X} \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n",
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"% \\\\\n",
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"% & = & (\\mathbf{X}^T \\mathbf{X})^{-1} \\, \\mathbf{X}^T \\, \\mathbf{X} \\, \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^T \\, \\mathbf{X}^T \\, \\mathbf{X} \\, (\\mathbf{X}^T % \\mathbf{X})^{-1}\n",
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"% \\\\\n",
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"% & & + \\, \\, \\sigma^2 \\, (\\mathbf{X}^T \\mathbf{X})^{-1} \\, \\mathbf{X}^T \\, \\mathbf{X} \\, (\\mathbf{X}^T \\mathbf{X})^{-1} - \\boldsymbol{\\beta} \\boldsymbol{\\beta}^T\n",
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"\\\\\n",
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"& = & \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T} + \\sigma^2 \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n",
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"\\, \\, \\, = \\, \\, \\, \\sigma^2 \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1},\n",
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"\\end{eqnarray*}\n",
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"$$"
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"source": [
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"where we have used that $\\mathbb{E} (\\mathbf{Y} \\mathbf{Y}^{T}) =\n",
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"\\mathbf{X} \\, \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T} \\, \\mathbf{X}^{T} +\n",
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"\\sigma^2 \\, \\mathbf{I}_{nn}$. From $\\mbox{Var}(\\boldsymbol{\\beta}) = \\sigma^2\n",
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"\\, (\\mathbf{X}^{T} \\mathbf{X})^{-1}$, one obtains an estimate of the\n",
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"variance of the estimate of the $j$-th regression coefficient:\n",
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"$\\boldsymbol{\\sigma}^2 (\\boldsymbol{\\beta}_j ) = \\boldsymbol{\\sigma}^2 \\sqrt{\n",
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"[(\\mathbf{X}^{T} \\mathbf{X})^{-1}]_{jj} }$. This may be used to\n",
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"construct a confidence interval for the estimates.\n",
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"\n",
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"In a similar way, we can obtain analytical expressions for say the\n",
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"expectation values of the parameters $\\boldsymbol{\\beta}$ and their variance\n",
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"when we employ Ridge regression, allowing us again to define a confidence interval. \n",
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"\n",
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"It is rather straightforward to show that"
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"source": [
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"$$\n",
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"\\mathbb{E} \\big[ \\boldsymbol{\\beta}^{\\mathrm{Ridge}} \\big]=(\\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I}_{pp})^{-1} (\\mathbf{X}^{\\top} \\mathbf{X})\\boldsymbol{\\beta}^{\\mathrm{OLS}}.\n",
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||
"$$"
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]
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"cell_type": "markdown",
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"source": [
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"We see clearly that \n",
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"$\\mathbb{E} \\big[ \\boldsymbol{\\beta}^{\\mathrm{Ridge}} \\big] \\not= \\boldsymbol{\\beta}^{\\mathrm{OLS}}$ for any $\\lambda > 0$. We say then that the ridge estimator is biased.\n",
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"\n",
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"We can also compute the variance as"
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"source": [
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"$$\n",
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"\\mbox{Var}[\\boldsymbol{\\beta}^{\\mathrm{Ridge}}]=\\sigma^2[ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1} \\mathbf{X}^{T} \\mathbf{X} \\{ [ \\mathbf{X}^{\\top} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}\\}^{T},\n",
|
||
"$$"
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]
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"cell_type": "markdown",
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"metadata": {
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"source": [
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"and it is easy to see that if the parameter $\\lambda$ goes to infinity then the variance of Ridge parameters $\\boldsymbol{\\beta}$ goes to zero. \n",
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||
"\n",
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"With this, we can compute the difference"
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"source": [
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"$$\n",
|
||
"\\mbox{Var}[\\boldsymbol{\\beta}^{\\mathrm{OLS}}]-\\mbox{Var}(\\boldsymbol{\\beta}^{\\mathrm{Ridge}})=\\sigma^2 [ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}[ 2\\lambda\\mathbf{I} + \\lambda^2 (\\mathbf{X}^{T} \\mathbf{X})^{-1} ] \\{ [ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}\\}^{T}.\n",
|
||
"$$"
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"cell_type": "markdown",
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"source": [
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||
"The difference is non-negative definite since each component of the\n",
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||
"matrix product is non-negative definite. \n",
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||
"This means the variance we obtain with the standard OLS will always for $\\lambda > 0$ be larger than the variance of $\\boldsymbol{\\beta}$ obtained with the Ridge estimator. This has interesting consequences when we discuss the so-called bias-variance trade-off below."
|
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]
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"metadata": {
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"source": [
|
||
"## Resampling methods\n",
|
||
"\n",
|
||
"With all these analytical equations for both the OLS and Ridge\n",
|
||
"regression, we will now outline how to assess a given model. This will\n",
|
||
"lead us to a discussion of the so-called bias-variance tradeoff (see\n",
|
||
"below) and so-called resampling methods.\n",
|
||
"\n",
|
||
"One of the quantities we have discussed as a way to measure errors is\n",
|
||
"the mean-squared error (MSE), mainly used for fitting of continuous\n",
|
||
"functions. Another choice is the absolute error.\n",
|
||
"\n",
|
||
"In the discussions below we will focus on the MSE and in particular since we will split the data into test and training data,\n",
|
||
"we discuss the\n",
|
||
"1. prediction error or simply the **test error** $\\mathrm{Err_{Test}}$, where we have a fixed training set and the test error is the MSE arising from the data reserved for testing. We discuss also the \n",
|
||
"\n",
|
||
"2. training error $\\mathrm{Err_{Train}}$, which is the average loss over the training data.\n",
|
||
"\n",
|
||
"As our model becomes more and more complex, more of the training data tends to be used. The training may thence adapt to more complicated structures in the data. This may lead to a decrease in the bias (see below for code example) and a slight increase of the variance for the test error.\n",
|
||
"For a certain level of complexity the test error will reach minimum, before starting to increase again. The\n",
|
||
"training error reaches a saturation.\n",
|
||
"\n",
|
||
"Two famous\n",
|
||
"resampling methods are the **independent bootstrap** and **the jackknife**. \n",
|
||
"\n",
|
||
"The jackknife is a special case of the independent bootstrap. Still, the jackknife was made\n",
|
||
"popular prior to the independent bootstrap. And as the popularity of\n",
|
||
"the independent bootstrap soared, new variants, such as **the dependent bootstrap**.\n",
|
||
"\n",
|
||
"The Jackknife and independent bootstrap work for\n",
|
||
"independent, identically distributed random variables.\n",
|
||
"If these conditions are not\n",
|
||
"satisfied, the methods will fail. Yet, it should be said that if the data are\n",
|
||
"independent, identically distributed, and we only want to estimate the\n",
|
||
"variance of $\\overline{X}$ (which often is the case), then there is no\n",
|
||
"need for bootstrapping. \n",
|
||
"\n",
|
||
"The Jackknife works by making many replicas of the estimator $\\widehat{\\beta}$. \n",
|
||
"The jackknife is a resampling method where we systematically leave out one observation from the vector of observed values $\\boldsymbol{x} = (x_1,x_2,\\cdots,X_n)$. \n",
|
||
"Let $\\boldsymbol{x}_i$ denote the vector"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3925f435",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}_i = (x_1,x_2,\\cdots,x_{i-1},x_{i+1},\\cdots,x_n),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "cc6328ee",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which equals the vector $\\boldsymbol{x}$ with the exception that observation\n",
|
||
"number $i$ is left out. Using this notation, define\n",
|
||
"$\\widehat{\\beta}_i$ to be the estimator\n",
|
||
"$\\widehat{\\beta}$ computed using $\\vec{X}_i$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 1,
|
||
"id": "b751a941",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Runtime: 0.147161 sec\n",
|
||
"Jackknife Statistics :\n",
|
||
"original bias std. error\n",
|
||
" 100.113 100.103 0.15078\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"from numpy import *\n",
|
||
"from numpy.random import randint, randn\n",
|
||
"from time import time\n",
|
||
"\n",
|
||
"def jackknife(data, stat):\n",
|
||
" n = len(data);t = zeros(n); inds = arange(n); t0 = time()\n",
|
||
" ## 'jackknifing' by leaving out an observation for each i \n",
|
||
" for i in range(n):\n",
|
||
" t[i] = stat(delete(data,i) )\n",
|
||
"\n",
|
||
" # analysis \n",
|
||
" print(\"Runtime: %g sec\" % (time()-t0)); print(\"Jackknife Statistics :\")\n",
|
||
" print(\"original bias std. error\")\n",
|
||
" print(\"%8g %14g %15g\" % (stat(data),(n-1)*mean(t)/n, (n*var(t))**.5))\n",
|
||
"\n",
|
||
" return t\n",
|
||
"\n",
|
||
"\n",
|
||
"# Returns mean of data samples \n",
|
||
"def stat(data):\n",
|
||
" return mean(data)\n",
|
||
"\n",
|
||
"\n",
|
||
"mu, sigma = 100, 15\n",
|
||
"datapoints = 10000\n",
|
||
"x = mu + sigma*random.randn(datapoints)\n",
|
||
"# jackknife returns the data sample \n",
|
||
"t = jackknife(x, stat)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "25ff562a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"### Bootstrap\n",
|
||
"\n",
|
||
"Bootstrapping is a nonparametric approach to statistical inference\n",
|
||
"that substitutes computation for more traditional distributional\n",
|
||
"assumptions and asymptotic results. Bootstrapping offers a number of\n",
|
||
"advantages: \n",
|
||
"1. The bootstrap is quite general, although there are some cases in which it fails. \n",
|
||
"\n",
|
||
"2. Because it does not require distributional assumptions (such as normally distributed errors), the bootstrap can provide more accurate inferences when the data are not well behaved or when the sample size is small. \n",
|
||
"\n",
|
||
"3. It is possible to apply the bootstrap to statistics with sampling distributions that are difficult to derive, even asymptotically. \n",
|
||
"\n",
|
||
"4. It is relatively simple to apply the bootstrap to complex data-collection plans (such as stratified and clustered samples).\n",
|
||
"\n",
|
||
"Since $\\widehat{\\beta} = \\widehat{\\beta}(\\boldsymbol{X})$ is a function of random variables,\n",
|
||
"$\\widehat{\\beta}$ itself must be a random variable. Thus it has\n",
|
||
"a pdf, call this function $p(\\boldsymbol{t})$. The aim of the bootstrap is to\n",
|
||
"estimate $p(\\boldsymbol{t})$ by the relative frequency of\n",
|
||
"$\\widehat{\\beta}$. You can think of this as using a histogram\n",
|
||
"in the place of $p(\\boldsymbol{t})$. If the relative frequency closely\n",
|
||
"resembles $p(\\vec{t})$, then using numerics, it is straight forward to\n",
|
||
"estimate all the interesting parameters of $p(\\boldsymbol{t})$ using point\n",
|
||
"estimators. \n",
|
||
"\n",
|
||
"In the case that $\\widehat{\\beta}$ has\n",
|
||
"more than one component, and the components are independent, we use the\n",
|
||
"same estimator on each component separately. If the probability\n",
|
||
"density function of $X_i$, $p(x)$, had been known, then it would have\n",
|
||
"been straight forward to do this by: \n",
|
||
"1. Drawing lots of numbers from $p(x)$, suppose we call one such set of numbers $(X_1^*, X_2^*, \\cdots, X_n^*)$. \n",
|
||
"\n",
|
||
"2. Then using these numbers, we could compute a replica of $\\widehat{\\beta}$ called $\\widehat{\\beta}^*$. \n",
|
||
"\n",
|
||
"By repeated use of (1) and (2), many\n",
|
||
"estimates of $\\widehat{\\beta}$ could have been obtained. The\n",
|
||
"idea is to use the relative frequency of $\\widehat{\\beta}^*$\n",
|
||
"(think of a histogram) as an estimate of $p(\\boldsymbol{t})$.\n",
|
||
"\n",
|
||
"But\n",
|
||
"unless there is enough information available about the process that\n",
|
||
"generated $X_1,X_2,\\cdots,X_n$, $p(x)$ is in general\n",
|
||
"unknown. Therefore, [Efron in 1979](https://projecteuclid.org/euclid.aos/1176344552) asked the\n",
|
||
"question: What if we replace $p(x)$ by the relative frequency\n",
|
||
"of the observation $X_i$; if we draw observations in accordance with\n",
|
||
"the relative frequency of the observations, will we obtain the same\n",
|
||
"result in some asymptotic sense? The answer is yes.\n",
|
||
"\n",
|
||
"Instead of generating the histogram for the relative\n",
|
||
"frequency of the observation $X_i$, just draw the values\n",
|
||
"$(X_1^*,X_2^*,\\cdots,X_n^*)$ with replacement from the vector\n",
|
||
"$\\boldsymbol{X}$. \n",
|
||
"\n",
|
||
"The independent bootstrap works like this: \n",
|
||
"\n",
|
||
"1. Draw with replacement $n$ numbers for the observed variables $\\boldsymbol{x} = (x_1,x_2,\\cdots,x_n)$. \n",
|
||
"\n",
|
||
"2. Define a vector $\\boldsymbol{x}^*$ containing the values which were drawn from $\\boldsymbol{x}$. \n",
|
||
"\n",
|
||
"3. Using the vector $\\boldsymbol{x}^*$ compute $\\widehat{\\beta}^*$ by evaluating $\\widehat \\beta$ under the observations $\\boldsymbol{x}^*$. \n",
|
||
"\n",
|
||
"4. Repeat this process $k$ times. \n",
|
||
"\n",
|
||
"When you are done, you can draw a histogram of the relative frequency\n",
|
||
"of $\\widehat \\beta^*$. This is your estimate of the probability\n",
|
||
"distribution $p(t)$. Using this probability distribution you can\n",
|
||
"estimate any statistics thereof. In principle you never draw the\n",
|
||
"histogram of the relative frequency of $\\widehat{\\beta}^*$. Instead\n",
|
||
"you use the estimators corresponding to the statistic of interest. For\n",
|
||
"example, if you are interested in estimating the variance of $\\widehat\n",
|
||
"\\beta$, apply the estimator $\\widehat \\sigma^2$ to the values\n",
|
||
"$\\widehat \\beta^*$.\n",
|
||
"\n",
|
||
"Before we proceed however, we need to remind ourselves about a central\n",
|
||
"theorem in statistics, namely the so-called **central limit theorem**.\n",
|
||
"This theorem plays a central role in understanding why the Bootstrap\n",
|
||
"(and other resampling methods) work so well on independent and\n",
|
||
"identically distributed variables.\n",
|
||
"\n",
|
||
"Suppose we have a PDF $p(x)$ from which we generate a series $N$\n",
|
||
"of averages $\\langle x_i \\rangle$. Each mean value $\\langle x_i \\rangle$\n",
|
||
"is viewed as the average of a specific measurement, e.g., throwing \n",
|
||
"dice 100 times and then taking the average value, or producing a certain\n",
|
||
"amount of random numbers. \n",
|
||
"For notational ease, we set $\\langle x_i \\rangle=x_i$ in the discussion\n",
|
||
"which follows. \n",
|
||
"\n",
|
||
"If we compute the mean $z$ of $m$ such mean values $x_i$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fa55ab5a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"z=\\frac{x_1+x_2+\\dots+x_m}{m},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "697c0c94",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"the question we pose is which is the PDF of the new variable $z$.\n",
|
||
"\n",
|
||
"The probability of obtaining an average value $z$ is the product of the \n",
|
||
"probabilities of obtaining arbitrary individual mean values $x_i$,\n",
|
||
"but with the constraint that the average is $z$. We can express this through\n",
|
||
"the following expression"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bd26bbd1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\tilde{p}(z)=\\int dx_1p(x_1)\\int dx_2p(x_2)\\dots\\int dx_mp(x_m)\n",
|
||
" \\delta(z-\\frac{x_1+x_2+\\dots+x_m}{m}),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "68664e4f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where the $\\delta$-function enbodies the constraint that the mean is $z$.\n",
|
||
"All measurements that lead to each individual $x_i$ are expected to\n",
|
||
"be independent, which in turn means that we can express $\\tilde{p}$ as the \n",
|
||
"product of individual $p(x_i)$. The independence assumption is important in the derivation of the central limit theorem.\n",
|
||
"\n",
|
||
"If we use the integral expression for the $\\delta$-function"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "742a107a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\delta(z-\\frac{x_1+x_2+\\dots+x_m}{m})=\\frac{1}{2\\pi}\\int_{-\\infty}^{\\infty}\n",
|
||
" dq\\exp{\\left(iq(z-\\frac{x_1+x_2+\\dots+x_m}{m})\\right)},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b6d624c1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and inserting $e^{i\\mu q-i\\mu q}$ where $\\mu$ is the mean value\n",
|
||
"we arrive at"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "46458586",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\tilde{p}(z)=\\frac{1}{2\\pi}\\int_{-\\infty}^{\\infty}\n",
|
||
" dq\\exp{\\left(iq(z-\\mu)\\right)}\\left[\\int_{-\\infty}^{\\infty}\n",
|
||
" dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}\\right]^m,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ca119461",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"with the integral over $x$ resulting in"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f75b40fc",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\int_{-\\infty}^{\\infty}dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}=\n",
|
||
" \\int_{-\\infty}^{\\infty}dxp(x)\n",
|
||
" \\left[1+\\frac{iq(\\mu-x)}{m}-\\frac{q^2(\\mu-x)^2}{2m^2}+\\dots\\right].\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a4b64e20",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The second term on the rhs disappears since this is just the mean and \n",
|
||
"employing the definition of $\\sigma^2$ we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fc76951f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\int_{-\\infty}^{\\infty}dxp(x)e^{\\left(iq(\\mu-x)/m\\right)}=\n",
|
||
" 1-\\frac{q^2\\sigma^2}{2m^2}+\\dots,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "76979572",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"resulting in"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3edff7d2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\left[\\int_{-\\infty}^{\\infty}dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}\\right]^m\\approx\n",
|
||
" \\left[1-\\frac{q^2\\sigma^2}{2m^2}+\\dots \\right]^m,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "73a9341f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and in the limit $m\\rightarrow \\infty$ we obtain"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "88f1cc30",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\tilde{p}(z)=\\frac{1}{\\sqrt{2\\pi}(\\sigma/\\sqrt{m})}\n",
|
||
" \\exp{\\left(-\\frac{(z-\\mu)^2}{2(\\sigma/\\sqrt{m})^2}\\right)},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1aec913e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which is the normal distribution with variance\n",
|
||
"$\\sigma^2_m=\\sigma^2/m$, where $\\sigma$ is the variance of the PDF $p(x)$\n",
|
||
"and $\\mu$ is also the mean of the PDF $p(x)$. \n",
|
||
"\n",
|
||
"Thus, the central limit theorem states that the PDF $\\tilde{p}(z)$ of\n",
|
||
"the average of $m$ random values corresponding to a PDF $p(x)$ \n",
|
||
"is a normal distribution whose mean is the \n",
|
||
"mean value of the PDF $p(x)$ and whose variance is the variance\n",
|
||
"of the PDF $p(x)$ divided by $m$, the number of values used to compute $z$.\n",
|
||
"\n",
|
||
"The central limit theorem leads to the well-known expression for the\n",
|
||
"standard deviation, given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "42b317e7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sigma_m=\n",
|
||
"\\frac{\\sigma}{\\sqrt{m}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e5baf71d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The latter is true only if the average value is known exactly. This is obtained in the limit\n",
|
||
"$m\\rightarrow \\infty$ only. Because the mean and the variance are measured quantities we obtain \n",
|
||
"the familiar expression in statistics"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8e2b39e5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sigma_m\\approx \n",
|
||
"\\frac{\\sigma}{\\sqrt{m-1}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "472e7c2c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"In many cases however the above estimate for the standard deviation,\n",
|
||
"in particular if correlations are strong, may be too simplistic. Keep\n",
|
||
"in mind that we have assumed that the variables $x$ are independent\n",
|
||
"and identically distributed. This is obviously not always the\n",
|
||
"case. For example, the random numbers (or better pseudorandom numbers)\n",
|
||
"we generate in various calculations do always exhibit some\n",
|
||
"correlations.\n",
|
||
"\n",
|
||
"The theorem is satisfied by a large class of PDFs. Note however that for a\n",
|
||
"finite $m$, it is not always possible to find a closed form /analytic expression for\n",
|
||
"$\\tilde{p}(x)$.\n",
|
||
"\n",
|
||
"The following code starts with a Gaussian distribution with mean value\n",
|
||
"$\\mu =100$ and variance $\\sigma=15$. We use this to generate the data\n",
|
||
"used in the bootstrap analysis. The bootstrap analysis returns a data\n",
|
||
"set after a given number of bootstrap operations (as many as we have\n",
|
||
"data points). This data set consists of estimated mean values for each\n",
|
||
"bootstrap operation. The histogram generated by the bootstrap method\n",
|
||
"shows that the distribution for these mean values is also a Gaussian,\n",
|
||
"centered around the mean value $\\mu=100$ but with standard deviation\n",
|
||
"$\\sigma/\\sqrt{n}$, where $n$ is the number of bootstrap samples (in\n",
|
||
"this case the same as the number of original data points). The value\n",
|
||
"of the standard deviation is what we expect from the central limit\n",
|
||
"theorem."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"id": "0ff7b796",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Bootstrap Statistics :\n",
|
||
"original bias std. error\n",
|
||
" 99.966 14.8724 99.9645 0.146212\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"%matplotlib inline\n",
|
||
"\n",
|
||
"import numpy as np\n",
|
||
"from time import time\n",
|
||
"from scipy.stats import norm\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"# Returns mean of bootstrap samples \n",
|
||
"# Bootstrap algorithm\n",
|
||
"def bootstrap(data, datapoints):\n",
|
||
" t = np.zeros(datapoints)\n",
|
||
" n = len(data)\n",
|
||
" # non-parametric bootstrap \n",
|
||
" for i in range(datapoints):\n",
|
||
" t[i] = np.mean(data[np.random.randint(0,n,n)])\n",
|
||
" # analysis \n",
|
||
" print(\"Bootstrap Statistics :\")\n",
|
||
" print(\"original bias std. error\")\n",
|
||
" print(\"%8g %8g %14g %15g\" % (np.mean(data), np.std(data),np.mean(t),np.std(t)))\n",
|
||
" return t\n",
|
||
"\n",
|
||
"# We set the mean value to 100 and the standard deviation to 15\n",
|
||
"mu, sigma = 100, 15\n",
|
||
"datapoints = 10000\n",
|
||
"# We generate random numbers according to the normal distribution\n",
|
||
"x = mu + sigma*np.random.randn(datapoints)\n",
|
||
"# bootstrap returns the data sample \n",
|
||
"t = bootstrap(x, datapoints)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "22680159",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We see that our new variance and from that the standard deviation, agrees with the central limit theorem.\n",
|
||
"\n",
|
||
"We plot then the histogram together with a best fit for the data set."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"id": "fe018bb3",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
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"metadata": {
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"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_51_0.png"
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||
}
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||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# the histogram of the bootstrapped data (normalized data if density = True)\n",
|
||
"n, binsboot, patches = plt.hist(t, 50, density=True, facecolor='red', alpha=0.75)\n",
|
||
"# add a 'best fit' line \n",
|
||
"y = norm.pdf(binsboot, np.mean(t), np.std(t))\n",
|
||
"lt = plt.plot(binsboot, y, 'b', linewidth=1)\n",
|
||
"plt.xlabel('x')\n",
|
||
"plt.ylabel('Probability')\n",
|
||
"plt.grid(True)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
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||
"id": "5bbd613c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The bias-variance tradeoff\n",
|
||
"\n",
|
||
"We will discuss the bias-variance tradeoff in the context of\n",
|
||
"continuous predictions such as regression. However, many of the\n",
|
||
"intuitions and ideas discussed here also carry over to classification\n",
|
||
"tasks. Consider a dataset $\\mathcal{L}$ consisting of the data\n",
|
||
"$\\mathbf{X}_\\mathcal{L}=\\{(y_j, \\boldsymbol{x}_j), j=0\\ldots n-1\\}$. \n",
|
||
"\n",
|
||
"Let us assume that the true data is generated from a noisy model"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
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||
"id": "ca3fde4a",
|
||
"metadata": {
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||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{y}=f(\\boldsymbol{x}) + \\boldsymbol{\\epsilon}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
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||
"id": "8e11f84b",
|
||
"metadata": {
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"editable": true
|
||
},
|
||
"source": [
|
||
"where $\\epsilon$ is normally distributed with mean zero and standard deviation $\\sigma^2$.\n",
|
||
"\n",
|
||
"In our derivation of the ordinary least squares method we defined then\n",
|
||
"an approximation to the function $f$ in terms of the parameters\n",
|
||
"$\\boldsymbol{\\beta}$ and the design matrix $\\boldsymbol{X}$ which embody our model,\n",
|
||
"that is $\\boldsymbol{\\tilde{y}}=\\boldsymbol{X}\\boldsymbol{\\beta}$. \n",
|
||
"\n",
|
||
"Thereafter we found the parameters $\\boldsymbol{\\beta}$ by optimizing the means squared error via the so-called cost function"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
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||
"id": "026a65c8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\boldsymbol{X},\\boldsymbol{\\beta}) =\\frac{1}{n}\\sum_{i=0}^{n-1}(y_i-\\tilde{y}_i)^2=\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right].\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e59918c7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We can rewrite this as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2fd3f73c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\frac{1}{n}\\sum_i(f_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\frac{1}{n}\\sum_i(\\tilde{y}_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\sigma^2.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7daf46c9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The first term represents the square of the bias of the learning\n",
|
||
"method, which can be thought of as the error caused by the simplifying\n",
|
||
"assumptions built into the method. The second term represents the\n",
|
||
"variance of the chosen model and finally the last terms is variance of\n",
|
||
"the error $\\boldsymbol{\\epsilon}$.\n",
|
||
"\n",
|
||
"To derive this equation, we need to recall that the variance of $\\boldsymbol{y}$ and $\\boldsymbol{\\epsilon}$ are both equal to $\\sigma^2$. The mean value of $\\boldsymbol{\\epsilon}$ is by definition equal to zero. Furthermore, the function $f$ is not a stochastic variable, idem for $\\boldsymbol{\\tilde{y}}$.\n",
|
||
"We use a more compact notation in terms of the expectation value"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6094266b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{f}+\\boldsymbol{\\epsilon}-\\boldsymbol{\\tilde{y}})^2\\right],\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "643e0047",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and adding and subtracting $\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]$ we get"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1319bde5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{f}+\\boldsymbol{\\epsilon}-\\boldsymbol{\\tilde{y}}+\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2\\right],\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9c6d6da1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which, using the abovementioned expectation values can be rewritten as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "855756ef",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{y}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2\\right]+\\mathrm{Var}\\left[\\boldsymbol{\\tilde{y}}\\right]+\\sigma^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "34d24717",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"that is the rewriting in terms of the so-called bias, the variance of the model $\\boldsymbol{\\tilde{y}}$ and the variance of $\\boldsymbol{\\epsilon}$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"id": "d51b6100",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Error: 0.013121574015585152\n",
|
||
"Bias^2: 0.012073649446193166\n",
|
||
"Var: 0.0010479245693919886\n",
|
||
"0.013121574015585152 >= 0.012073649446193166 + 0.0010479245693919886 = 0.013121574015585155\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_65_1.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.linear_model import LinearRegression, Ridge, Lasso\n",
|
||
"from sklearn.preprocessing import PolynomialFeatures\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.pipeline import make_pipeline\n",
|
||
"from sklearn.utils import resample\n",
|
||
"\n",
|
||
"np.random.seed(2018)\n",
|
||
"\n",
|
||
"n = 500\n",
|
||
"n_boostraps = 100\n",
|
||
"degree = 18 # A quite high value, just to show.\n",
|
||
"noise = 0.1\n",
|
||
"\n",
|
||
"# Make data set.\n",
|
||
"x = np.linspace(-1, 3, n).reshape(-1, 1)\n",
|
||
"y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2) + np.random.normal(0, 0.1, x.shape)\n",
|
||
"\n",
|
||
"# Hold out some test data that is never used in training.\n",
|
||
"x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n",
|
||
"\n",
|
||
"# Combine x transformation and model into one operation.\n",
|
||
"# Not neccesary, but convenient.\n",
|
||
"model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False))\n",
|
||
"\n",
|
||
"# The following (m x n_bootstraps) matrix holds the column vectors y_pred\n",
|
||
"# for each bootstrap iteration.\n",
|
||
"y_pred = np.empty((y_test.shape[0], n_boostraps))\n",
|
||
"for i in range(n_boostraps):\n",
|
||
" x_, y_ = resample(x_train, y_train)\n",
|
||
"\n",
|
||
" # Evaluate the new model on the same test data each time.\n",
|
||
" y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel()\n",
|
||
"\n",
|
||
"# Note: Expectations and variances taken w.r.t. different training\n",
|
||
"# data sets, hence the axis=1. Subsequent means are taken across the test data\n",
|
||
"# set in order to obtain a total value, but before this we have error/bias/variance\n",
|
||
"# calculated per data point in the test set.\n",
|
||
"# Note 2: The use of keepdims=True is important in the calculation of bias as this \n",
|
||
"# maintains the column vector form. Dropping this yields very unexpected results.\n",
|
||
"error = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )\n",
|
||
"bias = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )\n",
|
||
"variance = np.mean( np.var(y_pred, axis=1, keepdims=True) )\n",
|
||
"print('Error:', error)\n",
|
||
"print('Bias^2:', bias)\n",
|
||
"print('Var:', variance)\n",
|
||
"print('{} >= {} + {} = {}'.format(error, bias, variance, bias+variance))\n",
|
||
"\n",
|
||
"plt.plot(x[::5, :], y[::5, :], label='f(x)')\n",
|
||
"plt.scatter(x_test, y_test, label='Data points')\n",
|
||
"plt.scatter(x_test, np.mean(y_pred, axis=1), label='Pred')\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"id": "bd636def",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Polynomial degree: 0\n",
|
||
"Error: 0.32149601703519115\n",
|
||
"Bias^2: 0.3123314713548606\n",
|
||
"Var: 0.009164545680330616\n",
|
||
"0.32149601703519115 >= 0.3123314713548606 + 0.009164545680330616 = 0.3214960170351912\n",
|
||
"Polynomial degree: 1\n",
|
||
"Error: 0.08426840630693411\n",
|
||
"Bias^2: 0.0796891867672603\n",
|
||
"Var: 0.004579219539673834\n",
|
||
"0.08426840630693411 >= 0.0796891867672603 + 0.004579219539673834 = 0.08426840630693413\n",
|
||
"Polynomial degree: 2\n",
|
||
"Error: 0.10398646080125035\n",
|
||
"Bias^2: 0.1007711427354898\n",
|
||
"Var: 0.0032153180657605116\n",
|
||
"0.10398646080125035 >= 0.1007711427354898 + 0.0032153180657605116 = 0.10398646080125032\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Polynomial degree: 3\n",
|
||
"Error: 0.06547790180152355\n",
|
||
"Bias^2: 0.06208238634231949\n",
|
||
"Var: 0.0033955154592040936\n",
|
||
"0.06547790180152355 >= 0.06208238634231949 + 0.0033955154592040936 = 0.06547790180152359\n",
|
||
"Polynomial degree: 4\n",
|
||
"Error: 0.06844519414009445\n",
|
||
"Bias^2: 0.06453579006728324\n",
|
||
"Var: 0.003909404072811226\n",
|
||
"0.06844519414009445 >= 0.06453579006728324 + 0.003909404072811226 = 0.06844519414009446\n",
|
||
"Polynomial degree: 5\n",
|
||
"Error: 0.05227921801205686\n",
|
||
"Bias^2: 0.0481872773043029\n",
|
||
"Var: 0.004091940707753939\n",
|
||
"0.05227921801205686 >= 0.0481872773043029 + 0.004091940707753939 = 0.052279218012056844\n",
|
||
"Polynomial degree: 6\n",
|
||
"Error: 0.037813671417389005\n",
|
||
"Bias^2: 0.033657685071527665\n",
|
||
"Var: 0.00415598634586135\n",
|
||
"0.037813671417389005 >= 0.033657685071527665 + 0.00415598634586135 = 0.03781367141738902\n",
|
||
"Polynomial degree: 7\n",
|
||
"Error: 0.02760977349102253\n",
|
||
"Bias^2: 0.022999498260366312\n",
|
||
"Var: 0.004610275230656212\n",
|
||
"0.02760977349102253 >= 0.022999498260366312 + 0.004610275230656212 = 0.027609773491022525\n",
|
||
"Polynomial degree: 8\n",
|
||
"Error: 0.017355848195593347\n",
|
||
"Bias^2: 0.010331721306655127\n",
|
||
"Var: 0.007024126888938232\n",
|
||
"0.017355848195593347 >= 0.010331721306655127 + 0.007024126888938232 = 0.01735584819559336\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Polynomial degree: 9\n",
|
||
"Error: 0.02660572763718093\n",
|
||
"Bias^2: 0.010018312644137363\n",
|
||
"Var: 0.016587414993043573\n",
|
||
"0.02660572763718093 >= 0.010018312644137363 + 0.016587414993043573 = 0.026605727637180936\n",
|
||
"Polynomial degree: 10\n",
|
||
"Error: 0.021592704588025025\n",
|
||
"Bias^2: 0.010516485576645508\n",
|
||
"Var: 0.011076219011379514\n",
|
||
"0.021592704588025025 >= 0.010516485576645508 + 0.011076219011379514 = 0.021592704588025022\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Polynomial degree: 11\n",
|
||
"Error: 0.07160048164233104\n",
|
||
"Bias^2: 0.014436800088904942\n",
|
||
"Var: 0.05716368155342608\n",
|
||
"0.07160048164233104 >= 0.014436800088904942 + 0.05716368155342608 = 0.07160048164233102\n",
|
||
"Polynomial degree: 12\n",
|
||
"Error: 0.11547777218872497\n",
|
||
"Bias^2: 0.01628578269596628\n",
|
||
"Var: 0.09919198949275869\n",
|
||
"0.11547777218872497 >= 0.01628578269596628 + 0.09919198949275869 = 0.11547777218872497\n",
|
||
"Polynomial degree: 13\n",
|
||
"Error: 0.22842468702219465\n",
|
||
"Bias^2: 0.01975416527185249\n",
|
||
"Var: 0.20867052175034223\n",
|
||
"0.22842468702219465 >= 0.01975416527185249 + 0.20867052175034223 = 0.2284246870221947\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_66_4.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.linear_model import LinearRegression, Ridge, Lasso\n",
|
||
"from sklearn.preprocessing import PolynomialFeatures\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.pipeline import make_pipeline\n",
|
||
"from sklearn.utils import resample\n",
|
||
"\n",
|
||
"np.random.seed(2018)\n",
|
||
"\n",
|
||
"n = 40\n",
|
||
"n_boostraps = 100\n",
|
||
"maxdegree = 14\n",
|
||
"\n",
|
||
"\n",
|
||
"# Make data set.\n",
|
||
"x = np.linspace(-3, 3, n).reshape(-1, 1)\n",
|
||
"y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)\n",
|
||
"error = np.zeros(maxdegree)\n",
|
||
"bias = np.zeros(maxdegree)\n",
|
||
"variance = np.zeros(maxdegree)\n",
|
||
"polydegree = np.zeros(maxdegree)\n",
|
||
"x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n",
|
||
"\n",
|
||
"for degree in range(maxdegree):\n",
|
||
" model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False))\n",
|
||
" y_pred = np.empty((y_test.shape[0], n_boostraps))\n",
|
||
" for i in range(n_boostraps):\n",
|
||
" x_, y_ = resample(x_train, y_train)\n",
|
||
" y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel()\n",
|
||
"\n",
|
||
" polydegree[degree] = degree\n",
|
||
" error[degree] = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )\n",
|
||
" bias[degree] = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )\n",
|
||
" variance[degree] = np.mean( np.var(y_pred, axis=1, keepdims=True) )\n",
|
||
" print('Polynomial degree:', degree)\n",
|
||
" print('Error:', error[degree])\n",
|
||
" print('Bias^2:', bias[degree])\n",
|
||
" print('Var:', variance[degree])\n",
|
||
" print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))\n",
|
||
"\n",
|
||
"plt.plot(polydegree, error, label='Error')\n",
|
||
"plt.plot(polydegree, bias, label='bias')\n",
|
||
"plt.plot(polydegree, variance, label='Variance')\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8cf88b3a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The bias-variance tradeoff summarizes the fundamental tension in\n",
|
||
"machine learning, particularly supervised learning, between the\n",
|
||
"complexity of a model and the amount of training data needed to train\n",
|
||
"it. Since data is often limited, in practice it is often useful to\n",
|
||
"use a less-complex model with higher bias, that is a model whose asymptotic\n",
|
||
"performance is worse than another model because it is easier to\n",
|
||
"train and less sensitive to sampling noise arising from having a\n",
|
||
"finite-sized training dataset (smaller variance). \n",
|
||
"\n",
|
||
"The above equations tell us that in\n",
|
||
"order to minimize the expected test error, we need to select a\n",
|
||
"statistical learning method that simultaneously achieves low variance\n",
|
||
"and low bias. Note that variance is inherently a nonnegative quantity,\n",
|
||
"and squared bias is also nonnegative. Hence, we see that the expected\n",
|
||
"test MSE can never lie below $Var(\\epsilon)$, the irreducible error.\n",
|
||
"\n",
|
||
"What do we mean by the variance and bias of a statistical learning\n",
|
||
"method? The variance refers to the amount by which our model would change if we\n",
|
||
"estimated it using a different training data set. Since the training\n",
|
||
"data are used to fit the statistical learning method, different\n",
|
||
"training data sets will result in a different estimate. But ideally the\n",
|
||
"estimate for our model should not vary too much between training\n",
|
||
"sets. However, if a method has high variance then small changes in\n",
|
||
"the training data can result in large changes in the model. In general, more\n",
|
||
"flexible statistical methods have higher variance.\n",
|
||
"\n",
|
||
"You may also find this recent [article](https://www.pnas.org/content/116/32/15849) of interest."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"id": "86bfc49a",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"\n",
|
||
"============================\n",
|
||
"Underfitting vs. Overfitting\n",
|
||
"============================\n",
|
||
"\n",
|
||
"This example demonstrates the problems of underfitting and overfitting and\n",
|
||
"how we can use linear regression with polynomial features to approximate\n",
|
||
"nonlinear functions. The plot shows the function that we want to approximate,\n",
|
||
"which is a part of the cosine function. In addition, the samples from the\n",
|
||
"real function and the approximations of different models are displayed. The\n",
|
||
"models have polynomial features of different degrees. We can see that a\n",
|
||
"linear function (polynomial with degree 1) is not sufficient to fit the\n",
|
||
"training samples. This is called **underfitting**. A polynomial of degree 4\n",
|
||
"approximates the true function almost perfectly. However, for higher degrees\n",
|
||
"the model will **overfit** the training data, i.e. it learns the noise of the\n",
|
||
"training data.\n",
|
||
"We evaluate quantitatively **overfitting** / **underfitting** by using\n",
|
||
"cross-validation. We calculate the mean squared error (MSE) on the validation\n",
|
||
"set, the higher, the less likely the model generalizes correctly from the\n",
|
||
"training data.\n",
|
||
"\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 1400x500 with 3 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_68_1.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"\"\"\"\n",
|
||
"============================\n",
|
||
"Underfitting vs. Overfitting\n",
|
||
"============================\n",
|
||
"\n",
|
||
"This example demonstrates the problems of underfitting and overfitting and\n",
|
||
"how we can use linear regression with polynomial features to approximate\n",
|
||
"nonlinear functions. The plot shows the function that we want to approximate,\n",
|
||
"which is a part of the cosine function. In addition, the samples from the\n",
|
||
"real function and the approximations of different models are displayed. The\n",
|
||
"models have polynomial features of different degrees. We can see that a\n",
|
||
"linear function (polynomial with degree 1) is not sufficient to fit the\n",
|
||
"training samples. This is called **underfitting**. A polynomial of degree 4\n",
|
||
"approximates the true function almost perfectly. However, for higher degrees\n",
|
||
"the model will **overfit** the training data, i.e. it learns the noise of the\n",
|
||
"training data.\n",
|
||
"We evaluate quantitatively **overfitting** / **underfitting** by using\n",
|
||
"cross-validation. We calculate the mean squared error (MSE) on the validation\n",
|
||
"set, the higher, the less likely the model generalizes correctly from the\n",
|
||
"training data.\n",
|
||
"\"\"\"\n",
|
||
"\n",
|
||
"print(__doc__)\n",
|
||
"\n",
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.pipeline import Pipeline\n",
|
||
"from sklearn.preprocessing import PolynomialFeatures\n",
|
||
"from sklearn.linear_model import LinearRegression\n",
|
||
"from sklearn.model_selection import cross_val_score\n",
|
||
"\n",
|
||
"\n",
|
||
"def true_fun(X):\n",
|
||
" return np.cos(1.5 * np.pi * X)\n",
|
||
"\n",
|
||
"np.random.seed(0)\n",
|
||
"\n",
|
||
"n_samples = 30\n",
|
||
"degrees = [1, 4, 15]\n",
|
||
"\n",
|
||
"X = np.sort(np.random.rand(n_samples))\n",
|
||
"y = true_fun(X) + np.random.randn(n_samples) * 0.1\n",
|
||
"\n",
|
||
"plt.figure(figsize=(14, 5))\n",
|
||
"for i in range(len(degrees)):\n",
|
||
" ax = plt.subplot(1, len(degrees), i + 1)\n",
|
||
" plt.setp(ax, xticks=(), yticks=())\n",
|
||
"\n",
|
||
" polynomial_features = PolynomialFeatures(degree=degrees[i],\n",
|
||
" include_bias=False)\n",
|
||
" linear_regression = LinearRegression()\n",
|
||
" pipeline = Pipeline([(\"polynomial_features\", polynomial_features),\n",
|
||
" (\"linear_regression\", linear_regression)])\n",
|
||
" pipeline.fit(X[:, np.newaxis], y)\n",
|
||
"\n",
|
||
" # Evaluate the models using crossvalidation\n",
|
||
" scores = cross_val_score(pipeline, X[:, np.newaxis], y,\n",
|
||
" scoring=\"neg_mean_squared_error\", cv=10)\n",
|
||
"\n",
|
||
" X_test = np.linspace(0, 1, 100)\n",
|
||
" plt.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label=\"Model\")\n",
|
||
" plt.plot(X_test, true_fun(X_test), label=\"True function\")\n",
|
||
" plt.scatter(X, y, edgecolor='b', s=20, label=\"Samples\")\n",
|
||
" plt.xlabel(\"x\")\n",
|
||
" plt.ylabel(\"y\")\n",
|
||
" plt.xlim((0, 1))\n",
|
||
" plt.ylim((-2, 2))\n",
|
||
" plt.legend(loc=\"best\")\n",
|
||
" plt.title(\"Degree {}\\nMSE = {:.2e}(+/- {:.2e})\".format(\n",
|
||
" degrees[i], -scores.mean(), scores.std()))\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"id": "0c2a183a",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 1\n",
|
||
"Mean squared error on training data: 439230.69504801\n",
|
||
"Mean squared error on test data: 481979.17861098\n",
|
||
"Degree of polynomial: 2\n",
|
||
"Mean squared error on training data: 115822.95008046\n",
|
||
"Mean squared error on test data: 123711.53703498\n",
|
||
"Degree of polynomial: 3\n",
|
||
"Mean squared error on training data: 9011.85263220\n",
|
||
"Mean squared error on test data: 10913.84780262\n",
|
||
"Degree of polynomial: 4\n",
|
||
"Mean squared error on training data: 303.47610036\n",
|
||
"Mean squared error on test data: 426.30787294\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 5\n",
|
||
"Mean squared error on training data: 3.80354994\n",
|
||
"Mean squared error on test data: 5.98822371\n",
|
||
"Degree of polynomial: 6\n",
|
||
"Mean squared error on training data: 3.66204648\n",
|
||
"Mean squared error on test data: 8.14812206\n",
|
||
"Degree of polynomial: 7\n",
|
||
"Mean squared error on training data: 0.47075725\n",
|
||
"Mean squared error on test data: 2.00607783\n",
|
||
"Degree of polynomial: 8\n",
|
||
"Mean squared error on training data: 0.04912436\n",
|
||
"Mean squared error on test data: 0.21596432\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 9\n",
|
||
"Mean squared error on training data: 0.02522069\n",
|
||
"Mean squared error on test data: 0.08576932\n",
|
||
"Degree of polynomial: 10\n",
|
||
"Mean squared error on training data: 0.02511518\n",
|
||
"Mean squared error on test data: 1.20015436\n",
|
||
"Degree of polynomial: 11\n",
|
||
"Mean squared error on training data: 0.01640891\n",
|
||
"Mean squared error on test data: 1.35533773\n",
|
||
"Degree of polynomial: 12\n",
|
||
"Mean squared error on training data: 0.00813803\n",
|
||
"Mean squared error on test data: 0.17446471\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 13\n",
|
||
"Mean squared error on training data: 0.00759119\n",
|
||
"Mean squared error on test data: 1.08131003\n",
|
||
"Degree of polynomial: 14\n",
|
||
"Mean squared error on training data: 0.00472199\n",
|
||
"Mean squared error on test data: 0.81333808\n",
|
||
"Degree of polynomial: 15\n",
|
||
"Mean squared error on training data: 0.00410478\n",
|
||
"Mean squared error on test data: 92.09163947\n",
|
||
"Degree of polynomial: 16\n",
|
||
"Mean squared error on training data: 0.00315593\n",
|
||
"Mean squared error on test data: 234.38827994\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 17\n",
|
||
"Mean squared error on training data: 0.00242999\n",
|
||
"Mean squared error on test data: 1271.34367970\n",
|
||
"Degree of polynomial: 18\n",
|
||
"Mean squared error on training data: 0.00228740\n",
|
||
"Mean squared error on test data: 108.21093775\n",
|
||
"Degree of polynomial: 19\n",
|
||
"Mean squared error on training data: 0.00156374\n",
|
||
"Mean squared error on test data: 1385.79778008\n",
|
||
"Degree of polynomial: 20\n",
|
||
"Mean squared error on training data: 0.00137814\n",
|
||
"Mean squared error on test data: 1944.86062977\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 21\n",
|
||
"Mean squared error on training data: 0.00118584\n",
|
||
"Mean squared error on test data: 14716.58827236\n",
|
||
"Degree of polynomial: 22\n",
|
||
"Mean squared error on training data: 0.00092678\n",
|
||
"Mean squared error on test data: 877.21517262\n",
|
||
"Degree of polynomial: 23\n",
|
||
"Mean squared error on training data: 0.00085892\n",
|
||
"Mean squared error on test data: 5567.04664255\n",
|
||
"Degree of polynomial: 24\n",
|
||
"Mean squared error on training data: 0.00084707\n",
|
||
"Mean squared error on test data: 1325.26124692\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 25\n",
|
||
"Mean squared error on training data: 0.00079125\n",
|
||
"Mean squared error on test data: 129012.83870189\n",
|
||
"Degree of polynomial: 26\n",
|
||
"Mean squared error on training data: 0.00076908\n",
|
||
"Mean squared error on test data: 18388.59354079\n",
|
||
"Degree of polynomial: 27\n",
|
||
"Mean squared error on training data: 0.00069123\n",
|
||
"Mean squared error on test data: 2351.97979891\n",
|
||
"Degree of polynomial: 28\n",
|
||
"Mean squared error on training data: 0.00062592\n",
|
||
"Mean squared error on test data: 3983.63037846\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 29\n",
|
||
"Mean squared error on training data: 0.00060704\n",
|
||
"Mean squared error on test data: 3262.26814548\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94076/626635268.py:73: RuntimeWarning: divide by zero encountered in log10\n",
|
||
" plt.plot(polynomial, np.log10(trainingerror), label='Training Error')\n",
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94076/626635268.py:74: RuntimeWarning: divide by zero encountered in log10\n",
|
||
" plt.plot(polynomial, np.log10(testerror), label='Test Error')\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_69_9.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Common imports\n",
|
||
"import os\n",
|
||
"import numpy as np\n",
|
||
"import pandas as pd\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.linear_model import LinearRegression, Ridge, Lasso\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.utils import resample\n",
|
||
"from sklearn.metrics import mean_squared_error\n",
|
||
"# Where to save the figures and data files\n",
|
||
"PROJECT_ROOT_DIR = \"Results\"\n",
|
||
"FIGURE_ID = \"Results/FigureFiles\"\n",
|
||
"DATA_ID = \"DataFiles/\"\n",
|
||
"\n",
|
||
"if not os.path.exists(PROJECT_ROOT_DIR):\n",
|
||
" os.mkdir(PROJECT_ROOT_DIR)\n",
|
||
"\n",
|
||
"if not os.path.exists(FIGURE_ID):\n",
|
||
" os.makedirs(FIGURE_ID)\n",
|
||
"\n",
|
||
"if not os.path.exists(DATA_ID):\n",
|
||
" os.makedirs(DATA_ID)\n",
|
||
"\n",
|
||
"def image_path(fig_id):\n",
|
||
" return os.path.join(FIGURE_ID, fig_id)\n",
|
||
"\n",
|
||
"def data_path(dat_id):\n",
|
||
" return os.path.join(DATA_ID, dat_id)\n",
|
||
"\n",
|
||
"def save_fig(fig_id):\n",
|
||
" plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
|
||
"\n",
|
||
"infile = open(data_path(\"EoS.csv\"),'r')\n",
|
||
"\n",
|
||
"# Read the EoS data as csv file and organize the data into two arrays with density and energies\n",
|
||
"EoS = pd.read_csv(infile, names=('Density', 'Energy'))\n",
|
||
"EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce')\n",
|
||
"EoS = EoS.dropna()\n",
|
||
"Energies = EoS['Energy']\n",
|
||
"Density = EoS['Density']\n",
|
||
"# The design matrix now as function of various polytrops\n",
|
||
"\n",
|
||
"Maxpolydegree = 30\n",
|
||
"X = np.zeros((len(Density),Maxpolydegree))\n",
|
||
"X[:,0] = 1.0\n",
|
||
"testerror = np.zeros(Maxpolydegree)\n",
|
||
"trainingerror = np.zeros(Maxpolydegree)\n",
|
||
"polynomial = np.zeros(Maxpolydegree)\n",
|
||
"\n",
|
||
"trials = 100\n",
|
||
"for polydegree in range(1, Maxpolydegree):\n",
|
||
" polynomial[polydegree] = polydegree\n",
|
||
" for degree in range(polydegree):\n",
|
||
" X[:,degree] = Density**(degree/3.0)\n",
|
||
"\n",
|
||
"# loop over trials in order to estimate the expectation value of the MSE\n",
|
||
" testerror[polydegree] = 0.0\n",
|
||
" trainingerror[polydegree] = 0.0\n",
|
||
" for samples in range(trials):\n",
|
||
" x_train, x_test, y_train, y_test = train_test_split(X, Energies, test_size=0.2)\n",
|
||
" model = LinearRegression(fit_intercept=False).fit(x_train, y_train)\n",
|
||
" ypred = model.predict(x_train)\n",
|
||
" ytilde = model.predict(x_test)\n",
|
||
" testerror[polydegree] += mean_squared_error(y_test, ytilde)\n",
|
||
" trainingerror[polydegree] += mean_squared_error(y_train, ypred) \n",
|
||
"\n",
|
||
" testerror[polydegree] /= trials\n",
|
||
" trainingerror[polydegree] /= trials\n",
|
||
" print(\"Degree of polynomial: %3d\"% polynomial[polydegree])\n",
|
||
" print(\"Mean squared error on training data: %.8f\" % trainingerror[polydegree])\n",
|
||
" print(\"Mean squared error on test data: %.8f\" % testerror[polydegree])\n",
|
||
"\n",
|
||
"plt.plot(polynomial, np.log10(trainingerror), label='Training Error')\n",
|
||
"plt.plot(polynomial, np.log10(testerror), label='Test Error')\n",
|
||
"plt.xlabel('Polynomial degree')\n",
|
||
"plt.ylabel('log10[MSE]')\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2c6c9e89",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Cross-validation\n",
|
||
"\n",
|
||
"When the repetitive splitting of the data set is done randomly,\n",
|
||
"samples may accidently end up in a fast majority of the splits in\n",
|
||
"either training or test set. Such samples may have an unbalanced\n",
|
||
"influence on either model building or prediction evaluation. To avoid\n",
|
||
"this $k$-fold cross-validation structures the data splitting. The\n",
|
||
"samples are divided into $k$ more or less equally sized exhaustive and\n",
|
||
"mutually exclusive subsets. In turn (at each split) one of these\n",
|
||
"subsets plays the role of the test set while the union of the\n",
|
||
"remaining subsets constitutes the training set. Such a splitting\n",
|
||
"warrants a balanced representation of each sample in both training and\n",
|
||
"test set over the splits. Still the division into the $k$ subsets\n",
|
||
"involves a degree of randomness. This may be fully excluded when\n",
|
||
"choosing $k=n$. This particular case is referred to as leave-one-out\n",
|
||
"cross-validation (LOOCV). \n",
|
||
"\n",
|
||
"* Define a range of interest for the penalty parameter.\n",
|
||
"\n",
|
||
"* Divide the data set into training and test set comprising samples $\\{1, \\ldots, n\\} \\setminus i$ and $\\{ i \\}$, respectively.\n",
|
||
"\n",
|
||
"* Fit the linear regression model by means of ridge estimation for each $\\lambda$ in the grid using the training set, and the corresponding estimate of the error variance $\\boldsymbol{\\sigma}_{-i}^2(\\lambda)$, as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "71738b2a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\begin{align*}\n",
|
||
"\\boldsymbol{\\beta}_{-i}(\\lambda) & = ( \\boldsymbol{X}_{-i, \\ast}^{T}\n",
|
||
"\\boldsymbol{X}_{-i, \\ast} + \\lambda \\boldsymbol{I}_{pp})^{-1}\n",
|
||
"\\boldsymbol{X}_{-i, \\ast}^{T} \\boldsymbol{y}_{-i}\n",
|
||
"\\end{align*}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "14db46b6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"* Evaluate the prediction performance of these models on the test set by $\\log\\{L[y_i, \\boldsymbol{X}_{i, \\ast}; \\boldsymbol{\\beta}_{-i}(\\lambda), \\boldsymbol{\\sigma}_{-i}^2(\\lambda)]\\}$. Or, by the prediction error $|y_i - \\boldsymbol{X}_{i, \\ast} \\boldsymbol{\\beta}_{-i}(\\lambda)|$, the relative error, the error squared or the R2 score function.\n",
|
||
"\n",
|
||
"* Repeat the first three steps such that each sample plays the role of the test set once.\n",
|
||
"\n",
|
||
"* Average the prediction performances of the test sets at each grid point of the penalty bias/parameter. It is an estimate of the prediction performance of the model corresponding to this value of the penalty parameter on novel data. It is defined as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "95e5c8e4",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\begin{align*}\n",
|
||
"\\frac{1}{n} \\sum_{i = 1}^n \\log\\{L[y_i, \\mathbf{X}_{i, \\ast}; \\boldsymbol{\\beta}_{-i}(\\lambda), \\boldsymbol{\\sigma}_{-i}^2(\\lambda)]\\}.\n",
|
||
"\\end{align*}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7e60f51d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"For the various values of $k$\n",
|
||
"\n",
|
||
"1. shuffle the dataset randomly.\n",
|
||
"\n",
|
||
"2. Split the dataset into $k$ groups.\n",
|
||
"\n",
|
||
"3. For each unique group:\n",
|
||
"\n",
|
||
"a. Decide which group to use as set for test data\n",
|
||
"\n",
|
||
"b. Take the remaining groups as a training data set\n",
|
||
"\n",
|
||
"c. Fit a model on the training set and evaluate it on the test set\n",
|
||
"\n",
|
||
"d. Retain the evaluation score and discard the model\n",
|
||
"\n",
|
||
"5. Summarize the model using the sample of model evaluation scores\n",
|
||
"\n",
|
||
"The code here uses Ridge regression with cross-validation (CV) resampling and $k$-fold CV in order to fit a specific polynomial."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"id": "2cef0eb7",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_75_0.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.model_selection import KFold\n",
|
||
"from sklearn.linear_model import Ridge\n",
|
||
"from sklearn.model_selection import cross_val_score\n",
|
||
"from sklearn.preprocessing import PolynomialFeatures\n",
|
||
"\n",
|
||
"# A seed just to ensure that the random numbers are the same for every run.\n",
|
||
"# Useful for eventual debugging.\n",
|
||
"np.random.seed(3155)\n",
|
||
"\n",
|
||
"# Generate the data.\n",
|
||
"nsamples = 100\n",
|
||
"x = np.random.randn(nsamples)\n",
|
||
"y = 3*x**2 + np.random.randn(nsamples)\n",
|
||
"\n",
|
||
"## Cross-validation on Ridge regression using KFold only\n",
|
||
"\n",
|
||
"# Decide degree on polynomial to fit\n",
|
||
"poly = PolynomialFeatures(degree = 6)\n",
|
||
"\n",
|
||
"# Decide which values of lambda to use\n",
|
||
"nlambdas = 500\n",
|
||
"lambdas = np.logspace(-3, 5, nlambdas)\n",
|
||
"\n",
|
||
"# Initialize a KFold instance\n",
|
||
"k = 5\n",
|
||
"kfold = KFold(n_splits = k)\n",
|
||
"\n",
|
||
"# Perform the cross-validation to estimate MSE\n",
|
||
"scores_KFold = np.zeros((nlambdas, k))\n",
|
||
"\n",
|
||
"i = 0\n",
|
||
"for lmb in lambdas:\n",
|
||
" ridge = Ridge(alpha = lmb)\n",
|
||
" j = 0\n",
|
||
" for train_inds, test_inds in kfold.split(x):\n",
|
||
" xtrain = x[train_inds]\n",
|
||
" ytrain = y[train_inds]\n",
|
||
"\n",
|
||
" xtest = x[test_inds]\n",
|
||
" ytest = y[test_inds]\n",
|
||
"\n",
|
||
" Xtrain = poly.fit_transform(xtrain[:, np.newaxis])\n",
|
||
" ridge.fit(Xtrain, ytrain[:, np.newaxis])\n",
|
||
"\n",
|
||
" Xtest = poly.fit_transform(xtest[:, np.newaxis])\n",
|
||
" ypred = ridge.predict(Xtest)\n",
|
||
"\n",
|
||
" scores_KFold[i,j] = np.sum((ypred - ytest[:, np.newaxis])**2)/np.size(ypred)\n",
|
||
"\n",
|
||
" j += 1\n",
|
||
" i += 1\n",
|
||
"\n",
|
||
"\n",
|
||
"estimated_mse_KFold = np.mean(scores_KFold, axis = 1)\n",
|
||
"\n",
|
||
"## Cross-validation using cross_val_score from sklearn along with KFold\n",
|
||
"\n",
|
||
"# kfold is an instance initialized above as:\n",
|
||
"# kfold = KFold(n_splits = k)\n",
|
||
"\n",
|
||
"estimated_mse_sklearn = np.zeros(nlambdas)\n",
|
||
"i = 0\n",
|
||
"for lmb in lambdas:\n",
|
||
" ridge = Ridge(alpha = lmb)\n",
|
||
"\n",
|
||
" X = poly.fit_transform(x[:, np.newaxis])\n",
|
||
" estimated_mse_folds = cross_val_score(ridge, X, y[:, np.newaxis], scoring='neg_mean_squared_error', cv=kfold)\n",
|
||
"\n",
|
||
" # cross_val_score return an array containing the estimated negative mse for every fold.\n",
|
||
" # we have to the the mean of every array in order to get an estimate of the mse of the model\n",
|
||
" estimated_mse_sklearn[i] = np.mean(-estimated_mse_folds)\n",
|
||
"\n",
|
||
" i += 1\n",
|
||
"\n",
|
||
"## Plot and compare the slightly different ways to perform cross-validation\n",
|
||
"\n",
|
||
"plt.figure()\n",
|
||
"\n",
|
||
"plt.plot(np.log10(lambdas), estimated_mse_sklearn, label = 'cross_val_score')\n",
|
||
"plt.plot(np.log10(lambdas), estimated_mse_KFold, 'r--', label = 'KFold')\n",
|
||
"\n",
|
||
"plt.xlabel('log10(lambda)')\n",
|
||
"plt.ylabel('mse')\n",
|
||
"\n",
|
||
"plt.legend()\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f501c9cf",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"More examples of the application of cross-validation follow here."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"id": "30e1e320",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94076/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10\n",
|
||
" plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_77_1.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Common imports\n",
|
||
"import os\n",
|
||
"import numpy as np\n",
|
||
"import pandas as pd\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.linear_model import LinearRegression, Ridge, Lasso\n",
|
||
"from sklearn.metrics import mean_squared_error\n",
|
||
"from sklearn.model_selection import KFold\n",
|
||
"from sklearn.model_selection import cross_val_score\n",
|
||
"\n",
|
||
"\n",
|
||
"# Where to save the figures and data files\n",
|
||
"PROJECT_ROOT_DIR = \"Results\"\n",
|
||
"FIGURE_ID = \"Results/FigureFiles\"\n",
|
||
"DATA_ID = \"DataFiles/\"\n",
|
||
"\n",
|
||
"if not os.path.exists(PROJECT_ROOT_DIR):\n",
|
||
" os.mkdir(PROJECT_ROOT_DIR)\n",
|
||
"\n",
|
||
"if not os.path.exists(FIGURE_ID):\n",
|
||
" os.makedirs(FIGURE_ID)\n",
|
||
"\n",
|
||
"if not os.path.exists(DATA_ID):\n",
|
||
" os.makedirs(DATA_ID)\n",
|
||
"\n",
|
||
"def image_path(fig_id):\n",
|
||
" return os.path.join(FIGURE_ID, fig_id)\n",
|
||
"\n",
|
||
"def data_path(dat_id):\n",
|
||
" return os.path.join(DATA_ID, dat_id)\n",
|
||
"\n",
|
||
"def save_fig(fig_id):\n",
|
||
" plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
|
||
"\n",
|
||
"infile = open(data_path(\"EoS.csv\"),'r')\n",
|
||
"\n",
|
||
"# Read the EoS data as csv file and organize the data into two arrays with density and energies\n",
|
||
"EoS = pd.read_csv(infile, names=('Density', 'Energy'))\n",
|
||
"EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce')\n",
|
||
"EoS = EoS.dropna()\n",
|
||
"Energies = EoS['Energy']\n",
|
||
"Density = EoS['Density']\n",
|
||
"# The design matrix now as function of various polytrops\n",
|
||
"\n",
|
||
"Maxpolydegree = 30\n",
|
||
"X = np.zeros((len(Density),Maxpolydegree))\n",
|
||
"X[:,0] = 1.0\n",
|
||
"estimated_mse_sklearn = np.zeros(Maxpolydegree)\n",
|
||
"polynomial = np.zeros(Maxpolydegree)\n",
|
||
"k =5\n",
|
||
"kfold = KFold(n_splits = k)\n",
|
||
"\n",
|
||
"for polydegree in range(1, Maxpolydegree):\n",
|
||
" polynomial[polydegree] = polydegree\n",
|
||
" for degree in range(polydegree):\n",
|
||
" X[:,degree] = Density**(degree/3.0)\n",
|
||
" OLS = LinearRegression(fit_intercept=False)\n",
|
||
"# loop over trials in order to estimate the expectation value of the MSE\n",
|
||
" estimated_mse_folds = cross_val_score(OLS, X, Energies, scoring='neg_mean_squared_error', cv=kfold)\n",
|
||
"#[:, np.newaxis]\n",
|
||
" estimated_mse_sklearn[polydegree] = np.mean(-estimated_mse_folds)\n",
|
||
"\n",
|
||
"plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')\n",
|
||
"plt.xlabel('Polynomial degree')\n",
|
||
"plt.ylabel('log10[MSE]')\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "383e5c2a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Note that we have kept the intercept in the first column of design matrix $\\boldsymbol{X}$. When we call the corresponding **Scikit-Learn** function we need thus to set the intercept to **False**. Libraries like **Scikit-Learn** normally scale the design matrix and do not fit intercept. See the discussions below."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1f9cd409",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## More on Rescaling data\n",
|
||
"\n",
|
||
"We end this chapter by adding some words on scaling and how to deal with the intercept for regression cases.\n",
|
||
"\n",
|
||
"When you are comparing your own code with for example **Scikit-Learn**'s\n",
|
||
"library, there are some technicalities to keep in mind. The examples\n",
|
||
"here demonstrate some of these aspects with potential pitfalls.\n",
|
||
"\n",
|
||
"The discussion here focuses on the role of the intercept, how we can\n",
|
||
"set up the design matrix, what scaling we should use and other topics\n",
|
||
"which tend confuse us.\n",
|
||
"\n",
|
||
"The intercept can be interpreted as the expected value of our\n",
|
||
"target/output variables when all other predictors are set to zero.\n",
|
||
"Thus, if we cannot assume that the expected outputs/targets are zero\n",
|
||
"when all predictors are zero (the columns in the design matrix), it\n",
|
||
"may be a bad idea to implement a model which penalizes the intercept.\n",
|
||
"Furthermore, in for example Ridge and Lasso regression, the default solutions\n",
|
||
"from the library **Scikit-Learn** (when not shrinking $\\beta_0$) for the unknown parameters\n",
|
||
"$\\boldsymbol{\\beta}$, are derived under the assumption that both $\\boldsymbol{y}$ and\n",
|
||
"$\\boldsymbol{X}$ are zero centered, that is we subtract the mean values.\n",
|
||
"\n",
|
||
"If our predictors represent different scales, then it is important to\n",
|
||
"standardize the design matrix $\\boldsymbol{X}$ by subtracting the mean of each\n",
|
||
"column from the corresponding column and dividing the column with its\n",
|
||
"standard deviation. Most machine learning libraries do this as a default. This means that if you compare your code with the results from a given library,\n",
|
||
"the results may differ. \n",
|
||
"\n",
|
||
"The\n",
|
||
"[Standardscaler](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.StandardScaler.html)\n",
|
||
"function in **Scikit-Learn** does this for us. For the data sets we\n",
|
||
"have been studying in our various examples, the data are in many cases\n",
|
||
"already scaled and there is no need to scale them. You as a user of different machine learning algorithms, should always perform a\n",
|
||
"survey of your data, with a critical assessment of them in case you need to scale the data.\n",
|
||
"\n",
|
||
"If you need to scale the data, not doing so will give an *unfair*\n",
|
||
"penalization of the parameters since their magnitude depends on the\n",
|
||
"scale of their corresponding predictor.\n",
|
||
"\n",
|
||
"Suppose as an example that you \n",
|
||
"you have an input variable given by the heights of different persons.\n",
|
||
"Human height might be measured in inches or meters or\n",
|
||
"kilometers. If measured in kilometers, a standard linear regression\n",
|
||
"model with this predictor would probably give a much bigger\n",
|
||
"coefficient term, than if measured in millimeters.\n",
|
||
"This can clearly lead to problems in evaluating the cost/loss functions.\n",
|
||
"\n",
|
||
"Keep in mind that when you transform your data set before training a model, the same transformation needs to be done\n",
|
||
"on your eventual new data set before making a prediction. If we translate this into a Python code, it would could be implemented as follows"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"id": "eab81633",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"'\\n#Model training, we compute the mean value of y and X\\ny_train_mean = np.mean(y_train)\\nX_train_mean = np.mean(X_train,axis=0)\\nX_train = X_train - X_train_mean\\ny_train = y_train - y_train_mean\\n\\n# The we fit our model with the training data\\ntrained_model = some_model.fit(X_train,y_train)\\n\\n\\n#Model prediction, we need also to transform our data set used for the prediction.\\nX_test = X_test - X_train_mean #Use mean from training data\\ny_pred = trained_model(X_test)\\ny_pred = y_pred + y_train_mean\\n'"
|
||
]
|
||
},
|
||
"execution_count": 10,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"\"\"\"\n",
|
||
"#Model training, we compute the mean value of y and X\n",
|
||
"y_train_mean = np.mean(y_train)\n",
|
||
"X_train_mean = np.mean(X_train,axis=0)\n",
|
||
"X_train = X_train - X_train_mean\n",
|
||
"y_train = y_train - y_train_mean\n",
|
||
"\n",
|
||
"# The we fit our model with the training data\n",
|
||
"trained_model = some_model.fit(X_train,y_train)\n",
|
||
"\n",
|
||
"\n",
|
||
"#Model prediction, we need also to transform our data set used for the prediction.\n",
|
||
"X_test = X_test - X_train_mean #Use mean from training data\n",
|
||
"y_pred = trained_model(X_test)\n",
|
||
"y_pred = y_pred + y_train_mean\n",
|
||
"\"\"\""
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0ca51a54",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Let us try to understand what this may imply mathematically when we\n",
|
||
"subtract the mean values, also known as *zero centering*. For\n",
|
||
"simplicity, we will focus on ordinary regression, as done in the above example.\n",
|
||
"\n",
|
||
"The cost/loss function for regression is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fa3a4110",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\beta_0, \\beta_1, ... , \\beta_{p-1}) = \\frac{1}{n}\\sum_{i=0}^{n} \\left(y_i - \\beta_0 - \\sum_{j=1}^{p-1} X_{ij}\\beta_j\\right)^2,.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9f499302",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Recall also that we use the squared value. This expression can lead to an\n",
|
||
"increased penalty for higher differences between predicted and\n",
|
||
"output/target values.\n",
|
||
"\n",
|
||
"What we have done is to single out the $\\beta_0$ term in the\n",
|
||
"definition of the mean squared error (MSE). The design matrix $X$\n",
|
||
"does in this case not contain any intercept column. When we take the\n",
|
||
"derivative with respect to $\\beta_0$, we want the derivative to obey"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b1f7ba52",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial C}{\\partial \\beta_j} = 0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7ff75b7f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"for all $j$. For $\\beta_0$ we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "eac37d3c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial C}{\\partial \\beta_0} = -\\frac{2}{n}\\sum_{i=0}^{n-1} \\left(y_i - \\beta_0 - \\sum_{j=1}^{p-1} X_{ij} \\beta_j\\right).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6e653464",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Multiplying away the constant $2/n$, we obtain"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8afa60a1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sum_{i=0}^{n-1} \\beta_0 = \\sum_{i=0}^{n-1}y_i - \\sum_{i=0}^{n-1} \\sum_{j=1}^{p-1} X_{ij} \\beta_j.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "055b7975",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Let us specialize first to the case where we have only two parameters $\\beta_0$ and $\\beta_1$.\n",
|
||
"Our result for $\\beta_0$ simplifies then to"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a2bf6e5d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"n\\beta_0 = \\sum_{i=0}^{n-1}y_i - \\sum_{i=0}^{n-1} X_{i1} \\beta_1.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e15afbd5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We obtain then"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d2f9a064",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\beta_0 = \\frac{1}{n}\\sum_{i=0}^{n-1}y_i - \\beta_1\\frac{1}{n}\\sum_{i=0}^{n-1} X_{i1}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8e8035d8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"If we define"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0bbcef44",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mu_{\\boldsymbol{x}_1}=\\frac{1}{n}\\sum_{i=0}^{n-1} X_{i1},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "919462c2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and the mean value of the outputs as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3a0899ec",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mu_y=\\frac{1}{n}\\sum_{i=0}^{n-1}y_i,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9b255ec5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7716aca1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\beta_0 = \\mu_y - \\beta_1\\mu_{\\boldsymbol{x}_1}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "24863f48",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"In the general case with more parameters than $\\beta_0$ and $\\beta_1$, we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6c10f940",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\beta_0 = \\frac{1}{n}\\sum_{i=0}^{n-1}y_i - \\frac{1}{n}\\sum_{i=0}^{n-1}\\sum_{j=1}^{p-1} X_{ij}\\beta_j.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7afefe95",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We can rewrite the latter equation as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a2e7bc1a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\beta_0 = \\frac{1}{n}\\sum_{i=0}^{n-1}y_i - \\sum_{j=1}^{p-1} \\mu_{\\boldsymbol{x}_j}\\beta_j,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5ded7d78",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where we have defined"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bcac7366",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mu_{\\boldsymbol{x}_j}=\\frac{1}{n}\\sum_{i=0}^{n-1} X_{ij},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bafe8156",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"the mean value for all elements of the column vector $\\boldsymbol{x}_j$.\n",
|
||
"\n",
|
||
"Replacing $y_i$ with $y_i - y_i - \\overline{\\boldsymbol{y}}$ and centering also our design matrix results in a cost function (in vector-matrix disguise)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7c91d280",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\boldsymbol{\\beta}) = (\\boldsymbol{\\tilde{y}} - \\tilde{X}\\boldsymbol{\\beta})^T(\\boldsymbol{\\tilde{y}} - \\tilde{X}\\boldsymbol{\\beta}).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1b81d6de",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"If we minimize with respect to $\\boldsymbol{\\beta}$ we have then"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7d6d497e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\hat{\\boldsymbol{\\beta}} = (\\tilde{X}^T\\tilde{X})^{-1}\\tilde{X}^T\\boldsymbol{\\tilde{y}},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "772593b2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where $\\boldsymbol{\\tilde{y}} = \\boldsymbol{y} - \\overline{\\boldsymbol{y}}$\n",
|
||
"and $\\tilde{X}_{ij} = X_{ij} - \\frac{1}{n}\\sum_{k=0}^{n-1}X_{kj}$.\n",
|
||
"\n",
|
||
"For Ridge regression we need to add $\\lambda \\boldsymbol{\\beta}^T\\boldsymbol{\\beta}$ to the cost function and get then"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3edbdb56",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\hat{\\boldsymbol{\\beta}} = (\\tilde{X}^T\\tilde{X} + \\lambda I)^{-1}\\tilde{X}^T\\boldsymbol{\\tilde{y}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7de9723e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"What does this mean? And why do we insist on all this? Let us look at some examples.\n",
|
||
"\n",
|
||
"This code shows a simple first-order fit to a data set using the above transformed data, where we consider the role of the intercept first, by either excluding it or including it (*code example thanks to Øyvind Sigmundson Schøyen*). Here our scaling of the data is done by subtracting the mean values only.\n",
|
||
"Note also that we do not split the data into training and test."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"id": "2e4a0363",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"True beta: [2, 0.5, 3.7]\n",
|
||
"Fitted beta: [2.08376632 0.19569961 3.97898392]\n",
|
||
"Sklearn fitted beta: [2.08376632 0.19569961 3.97898392]\n",
|
||
"MSE with intercept column\n",
|
||
"0.00411363461744314\n",
|
||
"MSE with intercept column from SKL\n",
|
||
"0.004113634617443147\n",
|
||
"Manual intercept: 2.083766322923899\n",
|
||
"Fitted beta (wiothout intercept): [0.19569961 3.97898392]\n",
|
||
"Sklearn intercept: 2.0837663229239043\n",
|
||
"Sklearn fitted beta (without intercept): [0.19569961 3.97898392]\n",
|
||
"MSE with Manual intercept\n",
|
||
"0.00411363461744314\n",
|
||
"MSE with Sklearn intercept\n",
|
||
"0.004113634617443131\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_112_1.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"from sklearn.linear_model import LinearRegression\n",
|
||
"\n",
|
||
"\n",
|
||
"np.random.seed(2021)\n",
|
||
"\n",
|
||
"def MSE(y_data,y_model):\n",
|
||
" n = np.size(y_model)\n",
|
||
" return np.sum((y_data-y_model)**2)/n\n",
|
||
"\n",
|
||
"\n",
|
||
"def fit_beta(X, y):\n",
|
||
" return np.linalg.pinv(X.T @ X) @ X.T @ y\n",
|
||
"\n",
|
||
"\n",
|
||
"true_beta = [2, 0.5, 3.7]\n",
|
||
"\n",
|
||
"x = np.linspace(0, 1, 11)\n",
|
||
"y = np.sum(\n",
|
||
" np.asarray([x ** p * b for p, b in enumerate(true_beta)]), axis=0\n",
|
||
") + 0.1 * np.random.normal(size=len(x))\n",
|
||
"\n",
|
||
"degree = 3\n",
|
||
"X = np.zeros((len(x), degree))\n",
|
||
"\n",
|
||
"# Include the intercept in the design matrix\n",
|
||
"for p in range(degree):\n",
|
||
" X[:, p] = x ** p\n",
|
||
"\n",
|
||
"beta = fit_beta(X, y)\n",
|
||
"\n",
|
||
"# Intercept is included in the design matrix\n",
|
||
"skl = LinearRegression(fit_intercept=False).fit(X, y)\n",
|
||
"\n",
|
||
"print(f\"True beta: {true_beta}\")\n",
|
||
"print(f\"Fitted beta: {beta}\")\n",
|
||
"print(f\"Sklearn fitted beta: {skl.coef_}\")\n",
|
||
"ypredictOwn = X @ beta\n",
|
||
"ypredictSKL = skl.predict(X)\n",
|
||
"print(f\"MSE with intercept column\")\n",
|
||
"print(MSE(y,ypredictOwn))\n",
|
||
"print(f\"MSE with intercept column from SKL\")\n",
|
||
"print(MSE(y,ypredictSKL))\n",
|
||
"\n",
|
||
"\n",
|
||
"plt.figure()\n",
|
||
"plt.scatter(x, y, label=\"Data\")\n",
|
||
"plt.plot(x, X @ beta, label=\"Fit\")\n",
|
||
"plt.plot(x, skl.predict(X), label=\"Sklearn (fit_intercept=False)\")\n",
|
||
"\n",
|
||
"\n",
|
||
"# Do not include the intercept in the design matrix\n",
|
||
"X = np.zeros((len(x), degree - 1))\n",
|
||
"\n",
|
||
"for p in range(degree - 1):\n",
|
||
" X[:, p] = x ** (p + 1)\n",
|
||
"\n",
|
||
"# Intercept is not included in the design matrix\n",
|
||
"skl = LinearRegression(fit_intercept=True).fit(X, y)\n",
|
||
"\n",
|
||
"# Use centered values for X and y when computing coefficients\n",
|
||
"y_offset = np.average(y, axis=0)\n",
|
||
"X_offset = np.average(X, axis=0)\n",
|
||
"\n",
|
||
"beta = fit_beta(X - X_offset, y - y_offset)\n",
|
||
"intercept = np.mean(y_offset - X_offset @ beta)\n",
|
||
"\n",
|
||
"print(f\"Manual intercept: {intercept}\")\n",
|
||
"print(f\"Fitted beta (wiothout intercept): {beta}\")\n",
|
||
"print(f\"Sklearn intercept: {skl.intercept_}\")\n",
|
||
"print(f\"Sklearn fitted beta (without intercept): {skl.coef_}\")\n",
|
||
"ypredictOwn = X @ beta\n",
|
||
"ypredictSKL = skl.predict(X)\n",
|
||
"print(f\"MSE with Manual intercept\")\n",
|
||
"print(MSE(y,ypredictOwn+intercept))\n",
|
||
"print(f\"MSE with Sklearn intercept\")\n",
|
||
"print(MSE(y,ypredictSKL))\n",
|
||
"\n",
|
||
"plt.plot(x, X @ beta + intercept, \"--\", label=\"Fit (manual intercept)\")\n",
|
||
"plt.plot(x, skl.predict(X), \"--\", label=\"Sklearn (fit_intercept=True)\")\n",
|
||
"plt.grid()\n",
|
||
"plt.legend()\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c6d3a071",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The intercept is the value of our output/target variable\n",
|
||
"when all our features are zero and our function crosses the $y$-axis (for a one-dimensional case). \n",
|
||
"\n",
|
||
"Printing the MSE, we see first that both methods give the same MSE, as\n",
|
||
"they should. However, when we move to for example Ridge regression,\n",
|
||
"the way we treat the intercept may give a larger or smaller MSE,\n",
|
||
"meaning that the MSE can be penalized by the value of the\n",
|
||
"intercept. Not including the intercept in the fit, means that the\n",
|
||
"regularization term does not include $\\beta_0$. For different values\n",
|
||
"of $\\lambda$, this may lead to different MSE values. \n",
|
||
"\n",
|
||
"To remind the reader, the regularization term, with the intercept in Ridge regression, is given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "db803b77",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\lambda \\vert\\vert \\boldsymbol{\\beta} \\vert\\vert_2^2 = \\lambda \\sum_{j=0}^{p-1}\\beta_j^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d7a9c9d8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"but when we take out the intercept, this equation becomes"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e08af763",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\lambda \\vert\\vert \\boldsymbol{\\beta} \\vert\\vert_2^2 = \\lambda \\sum_{j=1}^{p-1}\\beta_j^2.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "10fe24e4",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"For Lasso regression we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6feb3bdd",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\lambda \\vert\\vert \\boldsymbol{\\beta} \\vert\\vert_1 = \\lambda \\sum_{j=1}^{p-1}\\vert\\beta_j\\vert.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "657a0777",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"It means that, when scaling the design matrix and the outputs/targets,\n",
|
||
"by subtracting the mean values, we have an optimization problem which\n",
|
||
"is not penalized by the intercept. The MSE value can then be smaller\n",
|
||
"since it focuses only on the remaining quantities. If we however bring\n",
|
||
"back the intercept, we will get a MSE which then contains the\n",
|
||
"intercept.\n",
|
||
"\n",
|
||
"Armed with this wisdom, we attempt first to simply set the intercept equal to **False** in our implementation of Ridge regression for our well-known vanilla data set."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"id": "9f21317d",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Beta values for own Ridge implementation\n",
|
||
"[ 1.03032441e+00 6.28336218e-02 -6.24175744e-01 5.21169159e-02\n",
|
||
" 2.80847477e-01 2.12552073e-01 8.13220608e-02 -1.69634577e-02\n",
|
||
" -6.50846111e-02 -7.38962192e-02 -5.94226022e-02 -3.50227564e-02\n",
|
||
" -9.80609616e-03 1.08299273e-02 2.41882037e-02 2.93492130e-02\n",
|
||
" 2.64742912e-02 1.63249532e-02 -5.01831050e-05 -2.15098090e-02]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[ 1.03032441e+00 6.28336218e-02 -6.24175744e-01 5.21169159e-02\n",
|
||
" 2.80847477e-01 2.12552073e-01 8.13220608e-02 -1.69634577e-02\n",
|
||
" -6.50846112e-02 -7.38962192e-02 -5.94226022e-02 -3.50227564e-02\n",
|
||
" -9.80609615e-03 1.08299273e-02 2.41882037e-02 2.93492130e-02\n",
|
||
" 2.64742912e-02 1.63249532e-02 -5.01831190e-05 -2.15098090e-02]\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"4.3632959111950474e-07\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"4.363295916366933e-07\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[ 1.03630548 -0.01963611 -0.37900111 -0.07062318 0.12182967 0.16343471\n",
|
||
" 0.13003291 0.07490892 0.02365049 -0.01449782 -0.03814292 -0.04909093\n",
|
||
" -0.05009826 -0.04389027 -0.03279636 -0.01866537 -0.00289724 0.01348565\n",
|
||
" 0.02976145 0.04543942]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[ 1.03630548 -0.01963611 -0.37900111 -0.07062318 0.12182967 0.16343471\n",
|
||
" 0.13003291 0.07490892 0.02365049 -0.01449782 -0.03814292 -0.04909093\n",
|
||
" -0.05009826 -0.04389027 -0.03279636 -0.01866537 -0.00289724 0.01348565\n",
|
||
" 0.02976145 0.04543942]\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"5.194042826649355e-06\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"5.194042826815211e-06\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[ 1.04220758 -0.10931453 -0.17641709 -0.06020587 0.02208512 0.05789007\n",
|
||
" 0.06491736 0.05785343 0.04537385 0.03196357 0.01969145 0.00934499\n",
|
||
" 0.00107405 -0.00526348 -0.00992331 -0.01318643 -0.01531845 -0.01655318\n",
|
||
" -0.01708852 -0.01708781]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[ 1.04220758 -0.10931453 -0.17641709 -0.06020587 0.02208512 0.05789007\n",
|
||
" 0.06491736 0.05785343 0.04537385 0.03196357 0.01969145 0.00934499\n",
|
||
" 0.00107405 -0.00526348 -0.00992331 -0.01318643 -0.01531845 -0.01655318\n",
|
||
" -0.01708852 -0.01708781]\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"2.0940821989652176e-05\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"2.0940821989627646e-05\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[ 1.01219292 -0.06043581 -0.10391807 -0.05651951 -0.01898855 0.00312361\n",
|
||
" 0.01463049 0.01975848 0.02123176 0.02068067 0.01905883 0.01691985\n",
|
||
" 0.01458337 0.01223198 0.00996754 0.00784393 0.00588657 0.00410387\n",
|
||
" 0.00249435 0.00105081]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[ 1.01219292 -0.06043581 -0.10391807 -0.05651951 -0.01898855 0.00312361\n",
|
||
" 0.01463049 0.01975848 0.02123176 0.02068067 0.01905883 0.01691985\n",
|
||
" 0.01458337 0.01223198 0.00996754 0.00784393 0.00588657 0.00410387\n",
|
||
" 0.00249435 0.00105081]\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"0.00031535148309577417\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"0.0003153514830958095\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[ 8.38916861e-01 1.31276579e-01 8.97497404e-03 -1.72271878e-02\n",
|
||
" -2.11744554e-02 -1.91492986e-02 -1.57201944e-02 -1.23002365e-02\n",
|
||
" -9.30466214e-03 -6.81048318e-03 -4.78184120e-03 -3.15130074e-03\n",
|
||
" -1.84923989e-03 -8.13661243e-04 7.46984697e-06 6.56636616e-04\n",
|
||
" 1.16805821e-03 1.56912044e-03 1.88168312e-03 2.12318726e-03]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[ 8.38916861e-01 1.31276579e-01 8.97497404e-03 -1.72271878e-02\n",
|
||
" -2.11744554e-02 -1.91492986e-02 -1.57201944e-02 -1.23002365e-02\n",
|
||
" -9.30466214e-03 -6.81048318e-03 -4.78184120e-03 -3.15130074e-03\n",
|
||
" -1.84923989e-03 -8.13661243e-04 7.46984697e-06 6.56636616e-04\n",
|
||
" 1.16805821e-03 1.56912044e-03 1.88168312e-03 2.12318726e-03]\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"0.01507238889517717\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"0.01507238889517706\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[0.37396662 0.14174745 0.0764924 0.04892055 0.03447512 0.02586427\n",
|
||
" 0.02024962 0.01633913 0.01347916 0.0113104 0.0096208 0.00827728\n",
|
||
" 0.00719176 0.00630331 0.00556826 0.0049544 0.00443743 0.0039987\n",
|
||
" 0.0036237 0.003301 ]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[0.37396662 0.14174745 0.0764924 0.04892055 0.03447512 0.02586427\n",
|
||
" 0.02024962 0.01633913 0.01347916 0.0113104 0.0096208 0.00827728\n",
|
||
" 0.00719176 0.00630331 0.00556826 0.0049544 0.00443743 0.0039987\n",
|
||
" 0.0036237 0.003301 ]\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"0.2640931530791004\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"0.26409315307910025\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_120_1.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import pandas as pd\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn import linear_model\n",
|
||
"\n",
|
||
"def MSE(y_data,y_model):\n",
|
||
" n = np.size(y_model)\n",
|
||
" return np.sum((y_data-y_model)**2)/n\n",
|
||
"\n",
|
||
"\n",
|
||
"# A seed just to ensure that the random numbers are the same for every run.\n",
|
||
"# Useful for eventual debugging.\n",
|
||
"np.random.seed(3155)\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"x = np.random.rand(n)\n",
|
||
"y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)\n",
|
||
"\n",
|
||
"Maxpolydegree = 20\n",
|
||
"X = np.zeros((n,Maxpolydegree))\n",
|
||
"#We include explicitely the intercept column\n",
|
||
"for degree in range(Maxpolydegree):\n",
|
||
" X[:,degree] = x**degree\n",
|
||
"# We split the data in test and training data\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
|
||
"\n",
|
||
"p = Maxpolydegree\n",
|
||
"I = np.eye(p,p)\n",
|
||
"# Decide which values of lambda to use\n",
|
||
"nlambdas = 6\n",
|
||
"MSEOwnRidgePredict = np.zeros(nlambdas)\n",
|
||
"MSERidgePredict = np.zeros(nlambdas)\n",
|
||
"lambdas = np.logspace(-4, 2, nlambdas)\n",
|
||
"for i in range(nlambdas):\n",
|
||
" lmb = lambdas[i]\n",
|
||
" OwnRidgeBeta = np.linalg.pinv(X_train.T @ X_train+lmb*I) @ X_train.T @ y_train\n",
|
||
" # Note: we include the intercept column and no scaling\n",
|
||
" RegRidge = linear_model.Ridge(lmb,fit_intercept=False)\n",
|
||
" RegRidge.fit(X_train,y_train)\n",
|
||
" # and then make the prediction\n",
|
||
" ytildeOwnRidge = X_train @ OwnRidgeBeta\n",
|
||
" ypredictOwnRidge = X_test @ OwnRidgeBeta\n",
|
||
" ytildeRidge = RegRidge.predict(X_train)\n",
|
||
" ypredictRidge = RegRidge.predict(X_test)\n",
|
||
" MSEOwnRidgePredict[i] = MSE(y_test,ypredictOwnRidge)\n",
|
||
" MSERidgePredict[i] = MSE(y_test,ypredictRidge)\n",
|
||
" print(\"Beta values for own Ridge implementation\")\n",
|
||
" print(OwnRidgeBeta)\n",
|
||
" print(\"Beta values for Scikit-Learn Ridge implementation\")\n",
|
||
" print(RegRidge.coef_)\n",
|
||
" print(\"MSE values for own Ridge implementation\")\n",
|
||
" print(MSEOwnRidgePredict[i])\n",
|
||
" print(\"MSE values for Scikit-Learn Ridge implementation\")\n",
|
||
" print(MSERidgePredict[i])\n",
|
||
"\n",
|
||
"# Now plot the results\n",
|
||
"plt.figure()\n",
|
||
"plt.plot(np.log10(lambdas), MSEOwnRidgePredict, 'r', label = 'MSE own Ridge Test')\n",
|
||
"plt.plot(np.log10(lambdas), MSERidgePredict, 'g', label = 'MSE Ridge Test')\n",
|
||
"\n",
|
||
"plt.xlabel('log10(lambda)')\n",
|
||
"plt.ylabel('MSE')\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "20de82fd",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The results here agree when we force **Scikit-Learn**'s Ridge function to include the first column in our design matrix.\n",
|
||
"We see that the results agree very well. Here we have thus explicitely included the intercept column in the design matrix.\n",
|
||
"What happens if we do not include the intercept in our fit?\n",
|
||
"Let us see how we can change this code by zero centering."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 13,
|
||
"id": "4138ed50",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Beta values for own Ridge implementation\n",
|
||
"[ 3.43579948e-02 -5.43330971e-01 -3.10141413e-03 2.47116868e-01\n",
|
||
" 2.18613217e-01 1.02054837e-01 -4.25617658e-04 -5.90475506e-02\n",
|
||
" -7.68534263e-02 -6.68929213e-02 -4.24906604e-02 -1.40927184e-02\n",
|
||
" 1.11482289e-02 2.88529063e-02 3.67047975e-02 3.38135733e-02\n",
|
||
" 2.02198703e-02 -3.46383926e-03 -3.63025821e-02]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[ 3.43579948e-02 -5.43330971e-01 -3.10141413e-03 2.47116868e-01\n",
|
||
" 2.18613217e-01 1.02054837e-01 -4.25617655e-04 -5.90475506e-02\n",
|
||
" -7.68534263e-02 -6.68929213e-02 -4.24906604e-02 -1.40927184e-02\n",
|
||
" 1.11482289e-02 2.88529063e-02 3.67047975e-02 3.38135733e-02\n",
|
||
" 2.02198702e-02 -3.46383925e-03 -3.63025821e-02]\n",
|
||
"Intercept from own implementation:\n",
|
||
"1.0330308045187757\n",
|
||
"Intercept from Scikit-Learn Ridge implementation\n",
|
||
"1.0330308045183194\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"3.139255958997547e-06\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"3.1392559585020426e-06\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[-0.05807125 -0.29822833 -0.08551306 0.08156108 0.13679863 0.12333649\n",
|
||
" 0.08251519 0.03815288 0.00111756 -0.02498832 -0.04010697 -0.04566964\n",
|
||
" -0.04355837 -0.03562355 -0.02348765 -0.00848904 0.00831018 0.0260906\n",
|
||
" 0.04423486]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[-0.05807125 -0.29822833 -0.08551306 0.08156108 0.13679863 0.12333649\n",
|
||
" 0.08251519 0.03815288 0.00111756 -0.02498832 -0.04010697 -0.04566964\n",
|
||
" -0.04355837 -0.03562355 -0.02348765 -0.00848904 0.00831018 0.0260906\n",
|
||
" 0.04423486]\n",
|
||
"Intercept from own implementation:\n",
|
||
"1.0411487294305088\n",
|
||
"Intercept from Scikit-Learn Ridge implementation\n",
|
||
"1.0411487294305226\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"1.9601304850035702e-05\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"1.9601304850073734e-05\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[-0.1416398 -0.14021063 -0.05383795 0.01367553 0.04784395 0.05796251\n",
|
||
" 0.05447415 0.044613 0.03267527 0.02098261 0.01066519 0.00217499\n",
|
||
" -0.00440346 -0.00917248 -0.01231917 -0.01405935 -0.0146081 -0.01416528\n",
|
||
" -0.01290947]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[-0.1416398 -0.14021063 -0.05383795 0.01367553 0.04784395 0.05796251\n",
|
||
" 0.05447415 0.044613 0.03267527 0.02098261 0.01066519 0.00217499\n",
|
||
" -0.00440346 -0.00917248 -0.01231917 -0.01405935 -0.0146081 -0.01416528\n",
|
||
" -0.01290947]\n",
|
||
"Intercept from own implementation:\n",
|
||
"1.049556996627824\n",
|
||
"Intercept from Scikit-Learn Ridge implementation\n",
|
||
"1.0495569966278269\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"5.4959161509357395e-05\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"5.4959161509366685e-05\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[-0.13535942 -0.08593216 -0.03568439 -0.0036367 0.01397146 0.02229529\n",
|
||
" 0.02503753 0.0245528 0.02228115 0.01908936 0.01549377 0.01179792\n",
|
||
" 0.00817631 0.00472512 0.00149311 -0.00149956 -0.00424967 -0.00676387\n",
|
||
" -0.00905423]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[-0.13535942 -0.08593216 -0.03568439 -0.0036367 0.01397146 0.02229529\n",
|
||
" 0.02503753 0.0245528 0.02228115 0.01908936 0.01549377 0.01179792\n",
|
||
" 0.00817631 0.00472512 0.00149311 -0.00149956 -0.00424967 -0.00676387\n",
|
||
" -0.00905423]\n",
|
||
"Intercept from own implementation:\n",
|
||
"1.039967668952797\n",
|
||
"Intercept from Scikit-Learn Ridge implementation\n",
|
||
"1.0399676689527975\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"7.571105947979344e-05\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"7.571105947979412e-05\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[-0.05100875 -0.04063602 -0.02723445 -0.01713366 -0.0100706 -0.00517114\n",
|
||
" -0.00174276 0.00068734 0.00243186 0.00369758 0.00462287 0.0053018\n",
|
||
" 0.00579953 0.006162 0.00642221 0.00660427 0.00672607 0.0068011\n",
|
||
" 0.00683964]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[-0.05100875 -0.04063602 -0.02723445 -0.01713366 -0.0100706 -0.00517114\n",
|
||
" -0.00174276 0.00068734 0.00243186 0.00369758 0.00462287 0.0053018\n",
|
||
" 0.00579953 0.006162 0.00642221 0.00660427 0.00672607 0.0068011\n",
|
||
" 0.00683964]\n",
|
||
"Intercept from own implementation:\n",
|
||
"0.999955585168597\n",
|
||
"Intercept from Scikit-Learn Ridge implementation\n",
|
||
"0.999955585168597\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"0.0007698473260556343\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"0.0007698473260556325\n",
|
||
"Beta values for own Ridge implementation\n",
|
||
"[-0.00834567 -0.00803064 -0.00673407 -0.00554552 -0.00458878 -0.0038335\n",
|
||
" -0.00323332 -0.00274989 -0.0023548 -0.00202756 -0.00175331 -0.00152117\n",
|
||
" -0.001323 -0.0011526 -0.00100519 -0.00087697 -0.00076495 -0.00066668\n",
|
||
" -0.00058016]\n",
|
||
"Beta values for Scikit-Learn Ridge implementation\n",
|
||
"[-0.00834567 -0.00803064 -0.00673407 -0.00554552 -0.00458878 -0.0038335\n",
|
||
" -0.00323332 -0.00274989 -0.0023548 -0.00202756 -0.00175331 -0.00152117\n",
|
||
" -0.001323 -0.0011526 -0.00100519 -0.00087697 -0.00076495 -0.00066668\n",
|
||
" -0.00058016]\n",
|
||
"Intercept from own implementation:\n",
|
||
"0.9637117593816477\n",
|
||
"Intercept from Scikit-Learn Ridge implementation\n",
|
||
"0.9637117593816477\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"0.0023813163025848865\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"0.002381316302584885\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_122_1.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import pandas as pd\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn import linear_model\n",
|
||
"from sklearn.preprocessing import StandardScaler\n",
|
||
"\n",
|
||
"def MSE(y_data,y_model):\n",
|
||
" n = np.size(y_model)\n",
|
||
" return np.sum((y_data-y_model)**2)/n\n",
|
||
"# A seed just to ensure that the random numbers are the same for every run.\n",
|
||
"# Useful for eventual debugging.\n",
|
||
"np.random.seed(315)\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"x = np.random.rand(n)\n",
|
||
"y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)\n",
|
||
"\n",
|
||
"Maxpolydegree = 20\n",
|
||
"X = np.zeros((n,Maxpolydegree-1))\n",
|
||
"\n",
|
||
"for degree in range(1,Maxpolydegree): #No intercept column\n",
|
||
" X[:,degree-1] = x**(degree)\n",
|
||
"\n",
|
||
"# We split the data in test and training data\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
|
||
"\n",
|
||
"#For our own implementation, we will need to deal with the intercept by centering the design matrix and the target variable\n",
|
||
"X_train_mean = np.mean(X_train,axis=0)\n",
|
||
"#Center by removing mean from each feature\n",
|
||
"X_train_scaled = X_train - X_train_mean \n",
|
||
"X_test_scaled = X_test - X_train_mean\n",
|
||
"#The model intercept (called y_scaler) is given by the mean of the target variable (IF X is centered)\n",
|
||
"#Remove the intercept from the training data.\n",
|
||
"y_scaler = np.mean(y_train) \n",
|
||
"y_train_scaled = y_train - y_scaler \n",
|
||
"\n",
|
||
"p = Maxpolydegree-1\n",
|
||
"I = np.eye(p,p)\n",
|
||
"# Decide which values of lambda to use\n",
|
||
"nlambdas = 6\n",
|
||
"MSEOwnRidgePredict = np.zeros(nlambdas)\n",
|
||
"MSERidgePredict = np.zeros(nlambdas)\n",
|
||
"\n",
|
||
"lambdas = np.logspace(-4, 2, nlambdas)\n",
|
||
"for i in range(nlambdas):\n",
|
||
" lmb = lambdas[i]\n",
|
||
" OwnRidgeBeta = np.linalg.pinv(X_train_scaled.T @ X_train_scaled+lmb*I) @ X_train_scaled.T @ (y_train_scaled)\n",
|
||
" intercept_ = y_scaler - X_train_mean@OwnRidgeBeta #The intercept can be shifted so the model can predict on uncentered data\n",
|
||
" #Add intercept to prediction\n",
|
||
" ypredictOwnRidge = X_test_scaled @ OwnRidgeBeta + y_scaler \n",
|
||
" RegRidge = linear_model.Ridge(lmb)\n",
|
||
" RegRidge.fit(X_train,y_train)\n",
|
||
" ypredictRidge = RegRidge.predict(X_test)\n",
|
||
" MSEOwnRidgePredict[i] = MSE(y_test,ypredictOwnRidge)\n",
|
||
" MSERidgePredict[i] = MSE(y_test,ypredictRidge)\n",
|
||
" print(\"Beta values for own Ridge implementation\")\n",
|
||
" print(OwnRidgeBeta) #Intercept is given by mean of target variable\n",
|
||
" print(\"Beta values for Scikit-Learn Ridge implementation\")\n",
|
||
" print(RegRidge.coef_)\n",
|
||
" print('Intercept from own implementation:')\n",
|
||
" print(intercept_)\n",
|
||
" print('Intercept from Scikit-Learn Ridge implementation')\n",
|
||
" print(RegRidge.intercept_)\n",
|
||
" print(\"MSE values for own Ridge implementation\")\n",
|
||
" print(MSEOwnRidgePredict[i])\n",
|
||
" print(\"MSE values for Scikit-Learn Ridge implementation\")\n",
|
||
" print(MSERidgePredict[i])\n",
|
||
"\n",
|
||
"\n",
|
||
"# Now plot the results\n",
|
||
"plt.figure()\n",
|
||
"plt.plot(np.log10(lambdas), MSEOwnRidgePredict, 'b--', label = 'MSE own Ridge Test')\n",
|
||
"plt.plot(np.log10(lambdas), MSERidgePredict, 'g--', label = 'MSE SL Ridge Test')\n",
|
||
"plt.xlabel('log10(lambda)')\n",
|
||
"plt.ylabel('MSE')\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7e9dfda5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We see here, when compared to the code which includes explicitely the\n",
|
||
"intercept column, that our MSE value is actually smaller. This is\n",
|
||
"because the regularization term does not include the intercept value\n",
|
||
"$\\beta_0$ in the fitting. This applies to Lasso regularization as\n",
|
||
"well. It means that our optimization is now done only with the\n",
|
||
"centered matrix and/or vector that enter the fitting procedure. Note\n",
|
||
"also that the problem with the intercept occurs mainly in these type\n",
|
||
"of polynomial fitting problem.\n",
|
||
"\n",
|
||
"The next example is indeed an example where all these discussions about the role of intercept are not present."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a7eb252c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## More complicated Example: The Ising model\n",
|
||
"\n",
|
||
"The one-dimensional Ising model with nearest neighbor interaction, no\n",
|
||
"external field and a constant coupling constant $J$ is given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "990ff280",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto1\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" H = -J \\sum_{k}^L s_k s_{k + 1},\n",
|
||
"\\label{_auto1} \\tag{1}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5ea46b31",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where $s_i \\in \\{-1, 1\\}$ and $s_{N + 1} = s_1$. The number of spins\n",
|
||
"in the system is determined by $L$. For the one-dimensional system\n",
|
||
"there is no phase transition.\n",
|
||
"\n",
|
||
"We will look at a system of $L = 40$ spins with a coupling constant of\n",
|
||
"$J = 1$. To get enough training data we will generate 10000 states\n",
|
||
"with their respective energies."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"id": "fa60aaab",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
|
||
"import seaborn as sns\n",
|
||
"import scipy.linalg as scl\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"import tqdm\n",
|
||
"sns.set(color_codes=True)\n",
|
||
"cmap_args=dict(vmin=-1., vmax=1., cmap='seismic')\n",
|
||
"\n",
|
||
"L = 40\n",
|
||
"n = int(1e4)\n",
|
||
"\n",
|
||
"spins = np.random.choice([-1, 1], size=(n, L))\n",
|
||
"J = 1.0\n",
|
||
"\n",
|
||
"energies = np.zeros(n)\n",
|
||
"\n",
|
||
"for i in range(n):\n",
|
||
" energies[i] = - J * np.dot(spins[i], np.roll(spins[i], 1))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b9e8214e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Here we use ordinary least squares\n",
|
||
"regression to predict the energy for the nearest neighbor\n",
|
||
"one-dimensional Ising model on a ring, i.e., the endpoints wrap\n",
|
||
"around. We will use linear regression to fit a value for\n",
|
||
"the coupling constant to achieve this.\n",
|
||
"\n",
|
||
"A more general form for the one-dimensional Ising model is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a578cd63",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto2\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" H = - \\sum_j^L \\sum_k^L s_j s_k J_{jk}.\n",
|
||
"\\label{_auto2} \\tag{2}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d90dcfee",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Here we allow for interactions beyond the nearest neighbors and a state dependent\n",
|
||
"coupling constant. This latter expression can be formulated as\n",
|
||
"a matrix-product"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c4eec69a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto3\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" \\boldsymbol{H} = \\boldsymbol{X} J,\n",
|
||
"\\label{_auto3} \\tag{3}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ae46a11b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where $X_{jk} = s_j s_k$ and $J$ is a matrix which consists of the\n",
|
||
"elements $-J_{jk}$. This form of writing the energy fits perfectly\n",
|
||
"with the form utilized in linear regression, that is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "87ebb9b8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto4\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" \\boldsymbol{y} = \\boldsymbol{X}\\boldsymbol{\\beta} + \\boldsymbol{\\epsilon},\n",
|
||
"\\label{_auto4} \\tag{4}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "856efd3f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We split the data in training and test data as discussed in the previous example"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 15,
|
||
"id": "5ae2828f",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"X = np.zeros((n, L ** 2))\n",
|
||
"for i in range(n):\n",
|
||
" X[i] = np.outer(spins[i], spins[i]).ravel()\n",
|
||
"y = energies\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0d6201d9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"In the ordinary least squares method we choose the cost function"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4af380a7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto5\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" C(\\boldsymbol{X}, \\boldsymbol{\\beta})= \\frac{1}{n}\\left\\{(\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y})^T(\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y})\\right\\}.\n",
|
||
"\\label{_auto5} \\tag{5}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8e8eefa3",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We then find the extremal point of $C$ by taking the derivative with respect to $\\boldsymbol{\\beta}$ as discussed above.\n",
|
||
"This yields the expression for $\\boldsymbol{\\beta}$ to be"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a1c0765c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{\\beta} = \\frac{\\boldsymbol{X}^T \\boldsymbol{y}}{\\boldsymbol{X}^T \\boldsymbol{X}},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c754e28b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which immediately imposes some requirements on $\\boldsymbol{X}$ as there must exist\n",
|
||
"an inverse of $\\boldsymbol{X}^T \\boldsymbol{X}$. If the expression we are modeling contains an\n",
|
||
"intercept, i.e., a constant term, we must make sure that the\n",
|
||
"first column of $\\boldsymbol{X}$ consists of $1$. We do this here"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 16,
|
||
"id": "ff056cf9",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"X_train_own = np.concatenate(\n",
|
||
" (np.ones(len(X_train))[:, np.newaxis], X_train),\n",
|
||
" axis=1\n",
|
||
")\n",
|
||
"X_test_own = np.concatenate(\n",
|
||
" (np.ones(len(X_test))[:, np.newaxis], X_test),\n",
|
||
" axis=1\n",
|
||
")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "524f259e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Doing the inversion directly turns out to be a bad idea since the matrix\n",
|
||
"$\\boldsymbol{X}^T\\boldsymbol{X}$ is singular. An alternative approach is to use the **singular\n",
|
||
"value decomposition**. Using the definition of the Moore-Penrose\n",
|
||
"pseudoinverse we can write the equation for $\\boldsymbol{\\beta}$ as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "52be4553",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{\\beta} = \\boldsymbol{X}^{+}\\boldsymbol{y},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c37ff09a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where the pseudoinverse of $\\boldsymbol{X}$ is given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ea49a105",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{X}^{+} = \\frac{\\boldsymbol{X}^T}{\\boldsymbol{X}^T\\boldsymbol{X}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bf31067a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Using singular value decomposition we can decompose the matrix $\\boldsymbol{X} = \\boldsymbol{U}\\boldsymbol{\\Sigma} \\boldsymbol{V}^T$,\n",
|
||
"where $\\boldsymbol{U}$ and $\\boldsymbol{V}$ are orthogonal(unitary) matrices and $\\boldsymbol{\\Sigma}$ contains the singular values (more details below).\n",
|
||
"where $X^{+} = V\\Sigma^{+} U^T$. This reduces the equation for\n",
|
||
"$\\omega$ to"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5ef2c839",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto6\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" \\boldsymbol{\\beta} = \\boldsymbol{V}\\boldsymbol{\\Sigma}^{+} \\boldsymbol{U}^T \\boldsymbol{y}.\n",
|
||
"\\label{_auto6} \\tag{6}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "96bbf134",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Note that solving this equation by actually doing the pseudoinverse\n",
|
||
"(which is what we will do) is not a good idea as this operation scales\n",
|
||
"as $\\mathcal{O}(n^3)$, where $n$ is the number of elements in a\n",
|
||
"general matrix. Instead, doing $QR$-factorization and solving the\n",
|
||
"linear system as an equation would reduce this down to\n",
|
||
"$\\mathcal{O}(n^2)$ operations."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 17,
|
||
"id": "5e729b1e",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"def ols_svd(x: np.ndarray, y: np.ndarray) -> np.ndarray:\n",
|
||
" u, s, v = scl.svd(x)\n",
|
||
" return v.T @ scl.pinv(scl.diagsvd(s, u.shape[0], v.shape[0])) @ u.T @ y"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 18,
|
||
"id": "80b923d1",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"beta = ols_svd(X_train_own,y_train)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b4cf2f1a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"When extracting the $J$-matrix we need to make sure that we remove the intercept, as is done here"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 19,
|
||
"id": "93be2c0d",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"J = beta[1:].reshape(L, L)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ae869089",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"A way of looking at the coefficients in $J$ is to plot the matrices as images."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 20,
|
||
"id": "8d6d8152",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94076/4162706317.py:7: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.\n",
|
||
" cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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|
||
"text/plain": [
|
||
"<Figure size 2000x1400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_154_1.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"fig = plt.figure(figsize=(20, 14))\n",
|
||
"im = plt.imshow(J, **cmap_args)\n",
|
||
"plt.title(\"OLS\", fontsize=18)\n",
|
||
"plt.xticks(fontsize=18)\n",
|
||
"plt.yticks(fontsize=18)\n",
|
||
"cb = fig.colorbar(im)\n",
|
||
"cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8092ac84",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"It is interesting to note that OLS\n",
|
||
"considers both $J_{j, j + 1} = -0.5$ and $J_{j, j - 1} = -0.5$ as\n",
|
||
"valid matrix elements for $J$.\n",
|
||
"In our discussion below on hyperparameters and Ridge and Lasso regression we will see that\n",
|
||
"this problem can be removed, partly and only with Lasso regression. \n",
|
||
"\n",
|
||
"In this case our matrix inversion was actually possible. The obvious question now is what is the mathematics behind the SVD?\n",
|
||
"\n",
|
||
"Let us now \n",
|
||
"focus on Ridge and Lasso regression as well. We repeat some of the\n",
|
||
"basic parts of the Ising model and the setup of the training and test\n",
|
||
"data. The one-dimensional Ising model with nearest neighbor\n",
|
||
"interaction, no external field and a constant coupling constant $J$ is\n",
|
||
"given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d9251cde",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto7\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" H = -J \\sum_{k}^L s_k s_{k + 1},\n",
|
||
"\\label{_auto7} \\tag{7}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "abe454c9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where $s_i \\in \\{-1, 1\\}$ and $s_{N + 1} = s_1$. The number of spins in the system is determined by $L$. For the one-dimensional system there is no phase transition.\n",
|
||
"\n",
|
||
"We will look at a system of $L = 40$ spins with a coupling constant of $J = 1$. To get enough training data we will generate 10000 states with their respective energies."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 21,
|
||
"id": "89f8fbd0",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
|
||
"import seaborn as sns\n",
|
||
"import scipy.linalg as scl\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"import sklearn.linear_model as skl\n",
|
||
"import tqdm\n",
|
||
"sns.set(color_codes=True)\n",
|
||
"cmap_args=dict(vmin=-1., vmax=1., cmap='seismic')\n",
|
||
"\n",
|
||
"L = 40\n",
|
||
"n = int(1e4)\n",
|
||
"\n",
|
||
"spins = np.random.choice([-1, 1], size=(n, L))\n",
|
||
"J = 1.0\n",
|
||
"\n",
|
||
"energies = np.zeros(n)\n",
|
||
"\n",
|
||
"for i in range(n):\n",
|
||
" energies[i] = - J * np.dot(spins[i], np.roll(spins[i], 1))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e06639d4",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"A more general form for the one-dimensional Ising model is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "43ef0f40",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto8\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" H = - \\sum_j^L \\sum_k^L s_j s_k J_{jk}.\n",
|
||
"\\label{_auto8} \\tag{8}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "523dc03b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Here we allow for interactions beyond the nearest neighbors and a more\n",
|
||
"adaptive coupling matrix. This latter expression can be formulated as\n",
|
||
"a matrix-product on the form"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0f389eef",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto9\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" H = X J,\n",
|
||
"\\label{_auto9} \\tag{9}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b6e00f24",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where $X_{jk} = s_j s_k$ and $J$ is the matrix consisting of the\n",
|
||
"elements $-J_{jk}$. This form of writing the energy fits perfectly\n",
|
||
"with the form utilized in linear regression, viz."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5ea1084d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto10\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" \\boldsymbol{y} = \\boldsymbol{X}\\boldsymbol{\\beta} + \\boldsymbol{\\epsilon}.\n",
|
||
"\\label{_auto10} \\tag{10}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5551bb05",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We organize the data as we did above"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 22,
|
||
"id": "f5dd7795",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"X = np.zeros((n, L ** 2))\n",
|
||
"for i in range(n):\n",
|
||
" X[i] = np.outer(spins[i], spins[i]).ravel()\n",
|
||
"y = energies\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.96)\n",
|
||
"\n",
|
||
"X_train_own = np.concatenate(\n",
|
||
" (np.ones(len(X_train))[:, np.newaxis], X_train),\n",
|
||
" axis=1\n",
|
||
")\n",
|
||
"\n",
|
||
"X_test_own = np.concatenate(\n",
|
||
" (np.ones(len(X_test))[:, np.newaxis], X_test),\n",
|
||
" axis=1\n",
|
||
")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f36c807b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We will do all fitting with **Scikit-Learn**,"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 23,
|
||
"id": "eb701dd4",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"clf = skl.LinearRegression().fit(X_train, y_train)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bd356ada",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"When extracting the $J$-matrix we make sure to remove the intercept"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 24,
|
||
"id": "ae737db8",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"J_sk = clf.coef_.reshape(L, L)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d152a32a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"And then we plot the results"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 25,
|
||
"id": "8d713977",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94076/3777801602.py:7: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.\n",
|
||
" cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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|
||
"text/plain": [
|
||
"<Figure size 2000x1400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_172_1.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"fig = plt.figure(figsize=(20, 14))\n",
|
||
"im = plt.imshow(J_sk, **cmap_args)\n",
|
||
"plt.title(\"LinearRegression from Scikit-learn\", fontsize=18)\n",
|
||
"plt.xticks(fontsize=18)\n",
|
||
"plt.yticks(fontsize=18)\n",
|
||
"cb = fig.colorbar(im)\n",
|
||
"cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ede30c18",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The results agree perfectly with our previous discussion where we used our own code.\n",
|
||
"\n",
|
||
"Having explored the ordinary least squares we move on to ridge\n",
|
||
"regression. In ridge regression we include a **regularizer**. This\n",
|
||
"involves a new cost function which leads to a new estimate for the\n",
|
||
"weights $\\boldsymbol{\\beta}$. This results in a penalized regression problem. The\n",
|
||
"cost function is given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "eac772e9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto11\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" C(\\boldsymbol{X}, \\boldsymbol{\\beta}; \\lambda) = (\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y})^T(\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y}) + \\lambda \\boldsymbol{\\beta}^T\\boldsymbol{\\beta}.\n",
|
||
"\\label{_auto11} \\tag{11}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 26,
|
||
"id": "b66675f0",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94076/438060758.py:10: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.\n",
|
||
" cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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|
||
"text/plain": [
|
||
"<Figure size 2000x1400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_175_1.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"_lambda = 0.1\n",
|
||
"clf_ridge = skl.Ridge(alpha=_lambda).fit(X_train, y_train)\n",
|
||
"J_ridge_sk = clf_ridge.coef_.reshape(L, L)\n",
|
||
"fig = plt.figure(figsize=(20, 14))\n",
|
||
"im = plt.imshow(J_ridge_sk, **cmap_args)\n",
|
||
"plt.title(\"Ridge from Scikit-learn\", fontsize=18)\n",
|
||
"plt.xticks(fontsize=18)\n",
|
||
"plt.yticks(fontsize=18)\n",
|
||
"cb = fig.colorbar(im)\n",
|
||
"cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "71aa37b5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"In the **Least Absolute Shrinkage and Selection Operator** (LASSO)-method we get a third cost function."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8b70ef66",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto12\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
" C(\\boldsymbol{X}, \\boldsymbol{\\beta}; \\lambda) = (\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y})^T(\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y}) + \\lambda \\sqrt{\\boldsymbol{\\beta}^T\\boldsymbol{\\beta}}.\n",
|
||
"\\label{_auto12} \\tag{12}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "079981ff",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Finding the extremal point of this cost function is not so straight-forward as in least squares and ridge. We will therefore rely solely on the function ``Lasso`` from **Scikit-Learn**."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 27,
|
||
"id": "c8d4a180",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_94076/3544313922.py:9: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.\n",
|
||
" cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 2000x1400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_179_1.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"clf_lasso = skl.Lasso(alpha=_lambda).fit(X_train, y_train)\n",
|
||
"J_lasso_sk = clf_lasso.coef_.reshape(L, L)\n",
|
||
"fig = plt.figure(figsize=(20, 14))\n",
|
||
"im = plt.imshow(J_lasso_sk, **cmap_args)\n",
|
||
"plt.title(\"Lasso from Scikit-learn\", fontsize=18)\n",
|
||
"plt.xticks(fontsize=18)\n",
|
||
"plt.yticks(fontsize=18)\n",
|
||
"cb = fig.colorbar(im)\n",
|
||
"cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "57839941",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"It is quite striking how LASSO breaks the symmetry of the coupling\n",
|
||
"constant as opposed to ridge and OLS. We get a sparse solution with\n",
|
||
"$J_{j, j + 1} = -1$.\n",
|
||
"\n",
|
||
"We see how the different models perform for a different set of values for $\\lambda$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 28,
|
||
"id": "0e3bbb4e",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"\r",
|
||
" 0%| | 0/10 [00:00<?, ?it/s]"
|
||
]
|
||
},
|
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"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_coordinate_descent.py:628: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 3.924e+00, tolerance: 1.797e+00\n",
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|
||
"text/plain": [
|
||
"<Figure size 3200x5400 with 30 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_181_13.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"lambdas = np.logspace(-4, 5, 10)\n",
|
||
"\n",
|
||
"train_errors = {\n",
|
||
" \"ols_sk\": np.zeros(lambdas.size),\n",
|
||
" \"ridge_sk\": np.zeros(lambdas.size),\n",
|
||
" \"lasso_sk\": np.zeros(lambdas.size)\n",
|
||
"}\n",
|
||
"\n",
|
||
"test_errors = {\n",
|
||
" \"ols_sk\": np.zeros(lambdas.size),\n",
|
||
" \"ridge_sk\": np.zeros(lambdas.size),\n",
|
||
" \"lasso_sk\": np.zeros(lambdas.size)\n",
|
||
"}\n",
|
||
"\n",
|
||
"plot_counter = 1\n",
|
||
"\n",
|
||
"fig = plt.figure(figsize=(32, 54))\n",
|
||
"\n",
|
||
"for i, _lambda in enumerate(tqdm.tqdm(lambdas)):\n",
|
||
" for key, method in zip(\n",
|
||
" [\"ols_sk\", \"ridge_sk\", \"lasso_sk\"],\n",
|
||
" [skl.LinearRegression(), skl.Ridge(alpha=_lambda), skl.Lasso(alpha=_lambda)]\n",
|
||
" ):\n",
|
||
" method = method.fit(X_train, y_train)\n",
|
||
"\n",
|
||
" train_errors[key][i] = method.score(X_train, y_train)\n",
|
||
" test_errors[key][i] = method.score(X_test, y_test)\n",
|
||
"\n",
|
||
" omega = method.coef_.reshape(L, L)\n",
|
||
"\n",
|
||
" plt.subplot(10, 5, plot_counter)\n",
|
||
" plt.imshow(omega, **cmap_args)\n",
|
||
" plt.title(r\"%s, $\\lambda = %.4f$\" % (key, _lambda))\n",
|
||
" plot_counter += 1\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "14711abd",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We see that LASSO reaches a good solution for low\n",
|
||
"values of $\\lambda$, but will \"wither\" when we increase $\\lambda$ too\n",
|
||
"much. Ridge is more stable over a larger range of values for\n",
|
||
"$\\lambda$, but eventually also fades away.\n",
|
||
"\n",
|
||
"To determine which value of $\\lambda$ is best we plot the accuracy of\n",
|
||
"the models when predicting the training and the testing set. We expect\n",
|
||
"the accuracy of the training set to be quite good, but if the accuracy\n",
|
||
"of the testing set is much lower this tells us that we might be\n",
|
||
"subject to an overfit model. The ideal scenario is an accuracy on the\n",
|
||
"testing set that is close to the accuracy of the training set."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 29,
|
||
"id": "9ff29a72",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
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"image/png": 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|
||
"text/plain": [
|
||
"<Figure size 2000x1400 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_183_0.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"fig = plt.figure(figsize=(20, 14))\n",
|
||
"\n",
|
||
"colors = {\n",
|
||
" \"ols_sk\": \"r\",\n",
|
||
" \"ridge_sk\": \"y\",\n",
|
||
" \"lasso_sk\": \"c\"\n",
|
||
"}\n",
|
||
"\n",
|
||
"for key in train_errors:\n",
|
||
" plt.semilogx(\n",
|
||
" lambdas,\n",
|
||
" train_errors[key],\n",
|
||
" colors[key],\n",
|
||
" label=\"Train {0}\".format(key),\n",
|
||
" linewidth=4.0\n",
|
||
" )\n",
|
||
"\n",
|
||
"for key in test_errors:\n",
|
||
" plt.semilogx(\n",
|
||
" lambdas,\n",
|
||
" test_errors[key],\n",
|
||
" colors[key] + \"--\",\n",
|
||
" label=\"Test {0}\".format(key),\n",
|
||
" linewidth=4.0\n",
|
||
" )\n",
|
||
"plt.legend(loc=\"best\", fontsize=18)\n",
|
||
"plt.xlabel(r\"$\\lambda$\", fontsize=18)\n",
|
||
"plt.ylabel(r\"$R^2$\", fontsize=18)\n",
|
||
"plt.tick_params(labelsize=18)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9c10be56",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"From the above figure we can see that LASSO with $\\lambda = 10^{-2}$\n",
|
||
"achieves a very good accuracy on the test set. This by far surpasses the\n",
|
||
"other models for all values of $\\lambda$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "efce3b63",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Exercises and Projects\n",
|
||
"\n",
|
||
"The main aim of this project is to study in more detail various\n",
|
||
"regression methods, including the Ordinary Least Squares (OLS) method,\n",
|
||
"The total score is **100** points. Each subtask has its own final score.\n",
|
||
"\n",
|
||
"We will first study how to fit polynomials to a specific\n",
|
||
"two-dimensional function called [Franke's\n",
|
||
"function](http://www.dtic.mil/dtic/tr/fulltext/u2/a081688.pdf). This\n",
|
||
"is a function which has been widely used when testing various\n",
|
||
"interpolation and fitting algorithms. Furthermore, after having\n",
|
||
"established the model and the method, we will employ resamling\n",
|
||
"techniques such as cross-validation and/or bootstrap in order to perform a\n",
|
||
"proper assessment of our models. We will also study in detail the\n",
|
||
"so-called Bias-Variance trade off.\n",
|
||
"\n",
|
||
"The Franke function, which is a weighted sum of four exponentials reads as follows"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ef5a4df0",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\begin{align*}\n",
|
||
"f(x,y) &= \\frac{3}{4}\\exp{\\left(-\\frac{(9x-2)^2}{4} - \\frac{(9y-2)^2}{4}\\right)}+\\frac{3}{4}\\exp{\\left(-\\frac{(9x+1)^2}{49}- \\frac{(9y+1)}{10}\\right)} \\\\\n",
|
||
"&+\\frac{1}{2}\\exp{\\left(-\\frac{(9x-7)^2}{4} - \\frac{(9y-3)^2}{4}\\right)} -\\frac{1}{5}\\exp{\\left(-(9x-4)^2 - (9y-7)^2\\right) }.\n",
|
||
"\\end{align*}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b085eff4",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The function will be defined for $x,y\\in [0,1]$. Our first step will\n",
|
||
"be to perform an OLS regression analysis of this function, trying out\n",
|
||
"a polynomial fit with an $x$ and $y$ dependence of the form $[x, y,\n",
|
||
"x^2, y^2, xy, \\dots]$. We will also include bootstrap first as\n",
|
||
"a resampling technique. After that we will include the cross-validation technique. As in homeworks 1 and 2, we can use a uniform\n",
|
||
"distribution to set up the arrays of values for $x$ and $y$, or as in\n",
|
||
"the example below just a set of fixed \n",
|
||
"values for $x$ and $y$ with a given step\n",
|
||
"size. We will fit a\n",
|
||
"function (for example a polynomial) of $x$ and $y$. Thereafter we\n",
|
||
"will repeat much of the same procedure using the Ridge and Lasso\n",
|
||
"regression methods, introducing thus a dependence on the bias\n",
|
||
"(penalty) $\\lambda$.\n",
|
||
"\n",
|
||
"Finally we are going to use (real) digital terrain data and try to\n",
|
||
"reproduce these data using the same methods. We will also try to go\n",
|
||
"beyond the second-order polynomials metioned above and explore \n",
|
||
"which polynomial fits the data best.\n",
|
||
"\n",
|
||
"The Python code for the Franke function is included here (it performs also a three-dimensional plot of it)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 30,
|
||
"id": "5056dccb",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"ename": "TypeError",
|
||
"evalue": "gca() got an unexpected keyword argument 'projection'",
|
||
"output_type": "error",
|
||
"traceback": [
|
||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||
"\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
|
||
"Cell \u001b[0;32mIn[30], line 9\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mrandom\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m random, seed\n\u001b[1;32m 8\u001b[0m fig \u001b[38;5;241m=\u001b[39m plt\u001b[38;5;241m.\u001b[39mfigure()\n\u001b[0;32m----> 9\u001b[0m ax \u001b[38;5;241m=\u001b[39m \u001b[43mfig\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgca\u001b[49m\u001b[43m(\u001b[49m\u001b[43mprojection\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43m3d\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m 11\u001b[0m \u001b[38;5;66;03m# Make data.\u001b[39;00m\n\u001b[1;32m 12\u001b[0m x \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marange(\u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m0.05\u001b[39m)\n",
|
||
"\u001b[0;31mTypeError\u001b[0m: gca() got an unexpected keyword argument 'projection'"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 0 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"from mpl_toolkits.mplot3d import Axes3D\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from matplotlib import cm\n",
|
||
"from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
|
||
"import numpy as np\n",
|
||
"from random import random, seed\n",
|
||
"\n",
|
||
"fig = plt.figure()\n",
|
||
"ax = fig.gca(projection='3d')\n",
|
||
"\n",
|
||
"# Make data.\n",
|
||
"x = np.arange(0, 1, 0.05)\n",
|
||
"y = np.arange(0, 1, 0.05)\n",
|
||
"x, y = np.meshgrid(x,y)\n",
|
||
"\n",
|
||
"\n",
|
||
"def FrankeFunction(x,y):\n",
|
||
" term1 = 0.75*np.exp(-(0.25*(9*x-2)**2) - 0.25*((9*y-2)**2))\n",
|
||
" term2 = 0.75*np.exp(-((9*x+1)**2)/49.0 - 0.1*(9*y+1))\n",
|
||
" term3 = 0.5*np.exp(-(9*x-7)**2/4.0 - 0.25*((9*y-3)**2))\n",
|
||
" term4 = -0.2*np.exp(-(9*x-4)**2 - (9*y-7)**2)\n",
|
||
" return term1 + term2 + term3 + term4\n",
|
||
"\n",
|
||
"\n",
|
||
"z = FrankeFunction(x, y)\n",
|
||
"\n",
|
||
"# Plot the surface.\n",
|
||
"surf = ax.plot_surface(x, y, z, cmap=cm.coolwarm,\n",
|
||
" linewidth=0, antialiased=False)\n",
|
||
"\n",
|
||
"# Customize the z axis.\n",
|
||
"ax.set_zlim(-0.10, 1.40)\n",
|
||
"ax.zaxis.set_major_locator(LinearLocator(10))\n",
|
||
"ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))\n",
|
||
"\n",
|
||
"# Add a color bar which maps values to colors.\n",
|
||
"fig.colorbar(surf, shrink=0.5, aspect=5)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f5e72aef",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"### Exercise: Ordinary Least Square (OLS) on the Franke function\n",
|
||
"\n",
|
||
"We will generate our own dataset for a function\n",
|
||
"$\\mathrm{FrankeFunction}(x,y)$ with $x,y \\in [0,1]$. The function\n",
|
||
"$f(x,y)$ is the Franke function. You should explore also the addition\n",
|
||
"of an added stochastic noise to this function using the normal\n",
|
||
"distribution $N(0,1)$.\n",
|
||
"\n",
|
||
"*Write your own code* (using either a matrix inversion or a singular\n",
|
||
"value decomposition from e.g., **numpy** ) or use your code from\n",
|
||
"homeworks 1 and 2 and perform a standard least square regression\n",
|
||
"analysis using polynomials in $x$ and $y$ up to fifth order. Find the\n",
|
||
"[confidence intervals](https://en.wikipedia.org/wiki/Confidence_interval) of the parameters (estimators) $\\beta$ by computing their\n",
|
||
"variances, evaluate the Mean Squared error (MSE)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0ba33237",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"MSE(\\hat{y},\\hat{\\tilde{y}}) = \\frac{1}{n}\n",
|
||
"\\sum_{i=0}^{n-1}(y_i-\\tilde{y}_i)^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1f9af2ef",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and the $R^2$ score function. If $\\tilde{\\hat{y}}_i$ is the predicted\n",
|
||
"value of the $i-th$ sample and $y_i$ is the corresponding true value,\n",
|
||
"then the score $R^2$ is defined as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "77d5b0f2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"R^2(\\hat{y}, \\tilde{\\hat{y}}) = 1 - \\frac{\\sum_{i=0}^{n - 1} (y_i - \\tilde{y}_i)^2}{\\sum_{i=0}^{n - 1} (y_i - \\bar{y})^2},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6c1f9df9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where we have defined the mean value of $\\hat{y}$ as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1d06102c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\bar{y} = \\frac{1}{n} \\sum_{i=0}^{n - 1} y_i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8fb40b08",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Your code has to include a scaling of the data (for example by\n",
|
||
"subtracting the mean value), and\n",
|
||
"a split of the data in training and test data. For this exercise you can\n",
|
||
"either write your own code or use for example the function for\n",
|
||
"splitting training data provided by the library **Scikit-Learn** (make\n",
|
||
"sure you have installed it). This function is called\n",
|
||
"$train\\_test\\_split$. **You should present a critical discussion of why and how you have scaled or not scaled the data**.\n",
|
||
"\n",
|
||
"It is normal in essentially all Machine Learning studies to split the\n",
|
||
"data in a training set and a test set (eventually also an additional\n",
|
||
"validation set). There\n",
|
||
"is no explicit recipe for how much data should be included as training\n",
|
||
"data and say test data. An accepted rule of thumb is to use\n",
|
||
"approximately $2/3$ to $4/5$ of the data as training data.\n",
|
||
"\n",
|
||
"You can easily reuse the solutions to your exercises from week 35 and week 36."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1701de47",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"### Exercise: Bias-variance trade-off and resampling techniques\n",
|
||
"\n",
|
||
"Our aim here is to study the bias-variance trade-off by implementing the **bootstrap** resampling technique.\n",
|
||
"\n",
|
||
"With a code which does OLS and includes resampling techniques, \n",
|
||
"we will now discuss the bias-variance trade-off in the context of\n",
|
||
"continuous predictions such as regression. However, many of the\n",
|
||
"intuitions and ideas discussed here also carry over to classification\n",
|
||
"tasks and basically all Machine Learning algorithms. \n",
|
||
"\n",
|
||
"Before you perform an analysis of the bias-variance trade-off on your test data, make\n",
|
||
"first a figure similar to Fig. 2.11 of Hastie, Tibshirani, and\n",
|
||
"Friedman. Figure 2.11 of this reference displays only the test and training MSEs. The test MSE can be used to \n",
|
||
"indicate possible regions of low/high bias and variance. You will most likely not get an\n",
|
||
"equally smooth curve!\n",
|
||
"\n",
|
||
"With this result we move on to the bias-variance trade-off analysis.\n",
|
||
"\n",
|
||
"Consider a\n",
|
||
"dataset $\\mathcal{L}$ consisting of the data\n",
|
||
"$\\mathbf{X}_\\mathcal{L}=\\{(y_j, \\boldsymbol{x}_j), j=0\\ldots n-1\\}$.\n",
|
||
"\n",
|
||
"Let us assume that the true data is generated from a noisy model"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "15110cdf",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{y}=f(\\boldsymbol{x}) + \\boldsymbol{\\epsilon}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "33046595",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Here $\\epsilon$ is normally distributed with mean zero and standard\n",
|
||
"deviation $\\sigma^2$.\n",
|
||
"\n",
|
||
"In our derivation of the ordinary least squares method we defined then\n",
|
||
"an approximation to the function $f$ in terms of the parameters\n",
|
||
"$\\boldsymbol{\\beta}$ and the design matrix $\\boldsymbol{X}$ which embody our model,\n",
|
||
"that is $\\boldsymbol{\\tilde{y}}=\\boldsymbol{X}\\boldsymbol{\\beta}$.\n",
|
||
"\n",
|
||
"The parameters $\\boldsymbol{\\beta}$ are in turn found by optimizing the means\n",
|
||
"squared error via the so-called cost function"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "84527747",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\boldsymbol{X},\\boldsymbol{\\beta}) =\\frac{1}{n}\\sum_{i=0}^{n-1}(y_i-\\tilde{y}_i)^2=\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right].\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "da2f876d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Here the expected value $\\mathbb{E}$ is the sample value. \n",
|
||
"\n",
|
||
"Show that you can rewrite this as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1845a7dc",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\frac{1}{n}\\sum_i(f_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\frac{1}{n}\\sum_i(\\tilde{y}_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\sigma^2.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d2f1d7d7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Explain what the terms mean, which one is the bias and which one is\n",
|
||
"the variance and discuss their interpretations.\n",
|
||
"\n",
|
||
"Perform then a bias-variance analysis of the Franke function by\n",
|
||
"studying the MSE value as function of the complexity of your model.\n",
|
||
"\n",
|
||
"Discuss the bias and variance trade-off as function\n",
|
||
"of your model complexity (the degree of the polynomial) and the number\n",
|
||
"of data points, and possibly also your training and test data using the **bootstrap** resampling method.\n",
|
||
"\n",
|
||
"Note also that when you calculate the bias, in all applications you don't know the function values $f_i$. You would hence replace them with the actual data points $y_i$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e898c902",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"### Exercise: Cross-validation as resampling techniques, adding more complexity\n",
|
||
"\n",
|
||
"The aim here is to write your own code for another widely popular\n",
|
||
"resampling technique, the so-called cross-validation method. Again,\n",
|
||
"before you start with cross-validation approach, you should scale your\n",
|
||
"data.\n",
|
||
"\n",
|
||
"Implement the $k$-fold cross-validation algorithm (write your own\n",
|
||
"code) and evaluate again the MSE function resulting\n",
|
||
"from the test folds. You can compare your own code with that from\n",
|
||
"**Scikit-Learn** if needed. \n",
|
||
"\n",
|
||
"Compare the MSE you get from your cross-validation code with the one\n",
|
||
"you got from your **bootstrap** code. Comment your results. Try $5-10$\n",
|
||
"folds. You can also compare your own cross-validation code with the\n",
|
||
"one provided by **Scikit-Learn**."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d23dc734",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"### Exercise: Ridge Regression on the Franke function with resampling\n",
|
||
"\n",
|
||
"Write your own code for the Ridge method, either using matrix\n",
|
||
"inversion or the singular value decomposition as done in the previous\n",
|
||
"exercise. Perform the same bootstrap analysis as in the\n",
|
||
"Exercise 2 (for the same polynomials) and the cross-validation in exercise 3 but now for different values of $\\lambda$. Compare and\n",
|
||
"analyze your results with those obtained in exercises 1-3. Study the\n",
|
||
"dependence on $\\lambda$.\n",
|
||
"\n",
|
||
"Study also the bias-variance trade-off as function of various values of\n",
|
||
"the parameter $\\lambda$. For the bias-variance trade-off, use the **bootstrap** resampling method. Comment your results."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "39a35330",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"### Exercise: Lasso Regression on the Franke function with resampling\n",
|
||
"\n",
|
||
"This exercise is essentially a repeat of the previous two ones, but now\n",
|
||
"with Lasso regression. Write either your own code (difficult and optional) or, in this case,\n",
|
||
"you can also use the functionalities of **Scikit-Learn** (recommended). \n",
|
||
"Give a\n",
|
||
"critical discussion of the three methods and a judgement of which\n",
|
||
"model fits the data best. Perform here as well an analysis of the bias-variance trade-off using the **bootstrap** resampling technique and an analysis of the mean squared error using cross-validation."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "44d9e821",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"### Exercise: Analysis of real data\n",
|
||
"\n",
|
||
"With our codes functioning and having been tested properly on a\n",
|
||
"simpler function we are now ready to look at real data. We will\n",
|
||
"essentially repeat in this exercise what was done in exercises 1-5. However, we\n",
|
||
"need first to download the data and prepare properly the inputs to our\n",
|
||
"codes. We are going to download digital terrain data from the website\n",
|
||
"<https://earthexplorer.usgs.gov/>,\n",
|
||
"\n",
|
||
"Or, if you prefer, we have placed selected datafiles at <https://github.com/CompPhysics/MachineLearning/tree/master/doc/Projects/2021/Project1/DataFiles>\n",
|
||
"\n",
|
||
"In order to obtain data for a specific region, you need to register as\n",
|
||
"a user (free) at this website and then decide upon which area you want\n",
|
||
"to fetch the digital terrain data from. In order to be able to read\n",
|
||
"the data properly, you need to specify that the format should be **SRTM\n",
|
||
"Arc-Second Global** and download the data as a **GeoTIF** file. The\n",
|
||
"files are then stored in *tif* format which can be imported into a\n",
|
||
"Python program using"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 31,
|
||
"id": "0a4e6d7e",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"scipy.misc.imread"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "16a73292",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Here is a simple part of a Python code which reads and plots the data\n",
|
||
"from such files"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 32,
|
||
"id": "168356a4",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"\"\"\"\n",
|
||
"import numpy as np\n",
|
||
"from imageio import imread\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from mpl_toolkits.mplot3d import Axes3D\n",
|
||
"from matplotlib import cm\n",
|
||
"\n",
|
||
"# Load the terrain\n",
|
||
"terrain1 = imread('SRTM_data_Norway_1.tif')\n",
|
||
"# Show the terrain\n",
|
||
"plt.figure()\n",
|
||
"plt.title('Terrain over Norway 1')\n",
|
||
"plt.imshow(terrain1, cmap='gray')\n",
|
||
"plt.xlabel('X')\n",
|
||
"plt.ylabel('Y')\n",
|
||
"plt.show()\n",
|
||
"\"\"\""
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e9ec3e68",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"If you should have problems in downloading the digital terrain data,\n",
|
||
"we provide two examples under the data folder of project 1. One is\n",
|
||
"from a region close to Stavanger in Norway and the other Møsvatn\n",
|
||
"Austfjell, again in Norway.\n",
|
||
"Feel free to produce your own terrain data.\n",
|
||
"\n",
|
||
"Alternatively, if you would like to use another data set, feel free to do so. This could be data close to your reseach area or simply a data set you found interesting. See for example [kaggle.com](https://www.kaggle.com/datasets) for examples.\n",
|
||
"\n",
|
||
"Our final part deals with the parameterization of your digital terrain\n",
|
||
"data (or your own data). We will apply all three methods for linear regression, the same type (or higher order) of polynomial\n",
|
||
"approximation and cross-validation as resampling technique to evaluate which\n",
|
||
"model fits the data best.\n",
|
||
"\n",
|
||
"At the end, you should present a critical evaluation of your results\n",
|
||
"and discuss the applicability of these regression methods to the type\n",
|
||
"of data presented here (either the terrain data we propose or other data sets)."
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.9.15"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
} |