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: 0.0893679 sec\n",
|
||
"Jackknife Statistics :\n",
|
||
"original bias std. error\n",
|
||
" 99.9524 99.9424 0.148854\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",
|
||
" 100.188 15.1133 100.19 0.149655\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": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
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||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_51_0.png"
|
||
}
|
||
},
|
||
"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",
|
||
"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",
|
||
"id": "ca3fde4a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{y}=f(\\boldsymbol{x}) + \\boldsymbol{\\epsilon}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8e11f84b",
|
||
"metadata": {
|
||
"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",
|
||
"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: 0.013121574062587286\n",
|
||
"Bias^2: 0.012073649469946107\n",
|
||
"Var: 0.0010479245926411787\n",
|
||
"0.013121574062587286 >= 0.012073649469946107 + 0.0010479245926411787 = 0.013121574062587286\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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\n",
|
||
"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: 0.08426840630693412\n",
|
||
"Bias^2: 0.0796891867672603\n",
|
||
"Var: 0.004579219539673834\n",
|
||
"0.08426840630693412 >= 0.0796891867672603 + 0.004579219539673834 = 0.08426840630693413\n",
|
||
"Polynomial degree: 2\n",
|
||
"Error: 0.10398646080125037\n",
|
||
"Bias^2: 0.10077114273548984\n",
|
||
"Var: 0.0032153180657605116\n",
|
||
"0.10398646080125037 >= 0.10077114273548984 + 0.0032153180657605116 = 0.10398646080125036\n",
|
||
"Polynomial degree: 3\n",
|
||
"Error: 0.06547790180152352\n",
|
||
"Bias^2: 0.062082386342319454\n",
|
||
"Var: 0.0033955154592040923\n",
|
||
"0.06547790180152352 >= 0.062082386342319454 + 0.0033955154592040923 = 0.06547790180152355\n",
|
||
"Polynomial degree: 4\n",
|
||
"Error: 0.06844519414009445\n",
|
||
"Bias^2: 0.06453579006728322\n",
|
||
"Var: 0.003909404072811221\n",
|
||
"0.06844519414009445 >= 0.06453579006728322 + 0.003909404072811221 = 0.06844519414009444\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Polynomial degree: 5\n",
|
||
"Error: 0.05227921801205679\n",
|
||
"Bias^2: 0.04818727730430286\n",
|
||
"Var: 0.004091940707753925\n",
|
||
"0.05227921801205679 >= 0.04818727730430286 + 0.004091940707753925 = 0.05227921801205679\n",
|
||
"Polynomial degree: 6\n",
|
||
"Error: 0.03781367141738902\n",
|
||
"Bias^2: 0.03365768507152769\n",
|
||
"Var: 0.0041559863458613296\n",
|
||
"0.03781367141738902 >= 0.03365768507152769 + 0.0041559863458613296 = 0.03781367141738902\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Polynomial degree: 7\n",
|
||
"Error: 0.027609773491022394\n",
|
||
"Bias^2: 0.022999498260366198\n",
|
||
"Var: 0.004610275230656182\n",
|
||
"0.027609773491022394 >= 0.022999498260366198 + 0.004610275230656182 = 0.02760977349102238\n",
|
||
"Polynomial degree: 8\n",
|
||
"Error: 0.017355848195593312\n",
|
||
"Bias^2: 0.010331721306655165\n",
|
||
"Var: 0.007024126888938144\n",
|
||
"0.017355848195593312 >= 0.010331721306655165 + 0.007024126888938144 = 0.01735584819559331\n",
|
||
"Polynomial degree: 9\n",
|
||
"Error: 0.026605727637184558\n",
|
||
"Bias^2: 0.010018312644139219\n",
|
||
"Var: 0.016587414993045335\n",
|
||
"0.026605727637184558 >= 0.010018312644139219 + 0.016587414993045335 = 0.026605727637184554\n",
|
||
"Polynomial degree: 10\n",
|
||
"Error: 0.021592704588021178\n",
|
||
"Bias^2: 0.010516485576646504\n",
|
||
"Var: 0.01107621901137467\n",
|
||
"0.021592704588021178 >= 0.010516485576646504 + 0.01107621901137467 = 0.021592704588021174\n",
|
||
"Polynomial degree: 11\n",
|
||
"Error: 0.07160048164232538\n",
|
||
"Bias^2: 0.014436800088896381\n",
|
||
"Var: 0.05716368155342902\n",
|
||
"0.07160048164232538 >= 0.014436800088896381 + 0.05716368155342902 = 0.0716004816423254\n",
|
||
"Polynomial degree: 12\n",
|
||
"Error: 0.11547777218876518\n",
|
||
"Bias^2: 0.016285782696017142\n",
|
||
"Var: 0.09919198949274803\n",
|
||
"0.11547777218876518 >= 0.016285782696017142 + 0.09919198949274803 = 0.11547777218876518\n",
|
||
"Polynomial degree: 13\n",
|
||
"Error: 0.2284246870217162\n",
|
||
"Bias^2: 0.01975416527168255\n",
|
||
"Var: 0.20867052175003364\n",
|
||
"0.2284246870217162 >= 0.01975416527168255 + 0.20867052175003364 = 0.2284246870217162\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_66_3.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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\n",
|
||
"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",
|
||
"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"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 8\n",
|
||
"Mean squared error on training data: 0.04912436\n",
|
||
"Mean squared error on test data: 0.21596432\n",
|
||
"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",
|
||
"Degree of polynomial: 13\n",
|
||
"Mean squared error on training data: 0.00759119\n",
|
||
"Mean squared error on test data: 1.08131003\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 14\n",
|
||
"Mean squared error on training data: 0.00472199\n",
|
||
"Mean squared error on test data: 0.81333804\n",
|
||
"Degree of polynomial: 15\n",
|
||
"Mean squared error on training data: 0.00410478\n",
|
||
"Mean squared error on test data: 92.09172409\n",
|
||
"Degree of polynomial: 16\n",
|
||
"Mean squared error on training data: 0.00315593\n",
|
||
"Mean squared error on test data: 234.38533185\n",
|
||
"Degree of polynomial: 17\n",
|
||
"Mean squared error on training data: 0.00242999\n",
|
||
"Mean squared error on test data: 1271.35771826\n",
|
||
"Degree of polynomial: 18\n",
|
||
"Mean squared error on training data: 0.00228742\n",
|
||
"Mean squared error on test data: 108.27092910\n",
|
||
"Degree of polynomial: 19\n",
|
||
"Mean squared error on training data: 0.00156376\n",
|
||
"Mean squared error on test data: 1371.99051150\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 20\n",
|
||
"Mean squared error on training data: 0.00137818\n",
|
||
"Mean squared error on test data: 1887.86252988\n",
|
||
"Degree of polynomial: 21\n",
|
||
"Mean squared error on training data: 0.00118508\n",
|
||
"Mean squared error on test data: 14859.69908626\n",
|
||
"Degree of polynomial: 22\n",
|
||
"Mean squared error on training data: 0.00092647\n",
|
||
"Mean squared error on test data: 876.51191552\n",
|
||
"Degree of polynomial: 23\n",
|
||
"Mean squared error on training data: 0.00085889\n",
|
||
"Mean squared error on test data: 5594.60815105\n",
|
||
"Degree of polynomial: 24\n",
|
||
"Mean squared error on training data: 0.00084705\n",
|
||
"Mean squared error on test data: 1277.61702282\n",
|
||
"Degree of polynomial: 25\n",
|
||
"Mean squared error on training data: 0.00079129\n",
|
||
"Mean squared error on test data: 128664.31650694\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 26\n",
|
||
"Mean squared error on training data: 0.00076905\n",
|
||
"Mean squared error on test data: 19003.94822514\n",
|
||
"Degree of polynomial: 27\n",
|
||
"Mean squared error on training data: 0.00068946\n",
|
||
"Mean squared error on test data: 2379.66219404\n",
|
||
"Degree of polynomial: 28\n",
|
||
"Mean squared error on training data: 0.00062595\n",
|
||
"Mean squared error on test data: 4082.19983530\n",
|
||
"Degree of polynomial: 29\n",
|
||
"Mean squared error on training data: 0.00060705\n",
|
||
"Mean squared error on test data: 3250.17647619\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_41811/626635268.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_41811/626635268.py:74: RuntimeWarning: divide by zero encountered in log10\n",
|
||
" plt.plot(polynomial, np.log10(testerror), label='Test Error')\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_69_6.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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\n",
|
||
"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_41811/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10\n",
|
||
" plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"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",
|
||
"0.004113634617443139\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": {
|
||
"image/png": 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\n",
|
||
"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",
|
||
" -6.50846112e-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 -5.01831251e-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 -5.01831207e-05 -2.15098090e-02]\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"4.3632959215700067e-07\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"4.363295916323784e-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",
|
||
"5.194042827197027e-06\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"5.1940428268204826e-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",
|
||
"2.0940821989643363e-05\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"2.094082198961999e-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",
|
||
"0.0003153514830957865\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"0.00031535148309580783\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",
|
||
"0.015072388895177157\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"0.0150723888951771\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",
|
||
"0.26409315307910036\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"0.26409315307910025\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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\n",
|
||
"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 -3.46383925e-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 -4.25617654e-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",
|
||
"1.0330308045188872\n",
|
||
"Intercept from Scikit-Learn Ridge implementation\n",
|
||
"1.0330308045183219\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"3.1392559591206444e-06\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"3.1392559585048734e-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",
|
||
"1.041148729430595\n",
|
||
"Intercept from Scikit-Learn Ridge implementation\n",
|
||
"1.041148729430523\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"1.96013048502692e-05\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"1.960130485007504e-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",
|
||
"1.0495569966278295\n",
|
||
"Intercept from Scikit-Learn Ridge implementation\n",
|
||
"1.0495569966278269\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"5.4959161509377256e-05\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"5.495916150936645e-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",
|
||
"1.0399676689527966\n",
|
||
"Intercept from Scikit-Learn Ridge implementation\n",
|
||
"1.0399676689527975\n",
|
||
"MSE values for own Ridge implementation\n",
|
||
"7.571105947979352e-05\n",
|
||
"MSE values for Scikit-Learn Ridge implementation\n",
|
||
"7.571105947979394e-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",
|
||
"0.0007698473260556344\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",
|
||
"0.002381316302584886\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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\n",
|
||
"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_41811/4162706317.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
|
||
" cb = fig.colorbar(im)\n",
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_41811/4162706317.py:7: UserWarning: FixedFormatter should only be used together with 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_41811/3777801602.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
|
||
" cb = fig.colorbar(im)\n",
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_41811/3777801602.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
|
||
" cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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\n",
|
||
"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_41811/438060758.py:9: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
|
||
" cb = fig.colorbar(im)\n",
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_41811/438060758.py:10: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
|
||
" cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"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_41811/3544313922.py:8: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
|
||
" cb = fig.colorbar(im)\n",
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_41811/3544313922.py:9: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
|
||
" cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"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": [
|
||
{
|
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\r",
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|
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"text": [
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_coordinate_descent.py:647: 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",
|
||
" model = cd_fast.enet_coordinate_descent(\n",
|
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"\r",
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AAAAAAAiIfGJZKpXS3XffrVNPPVVHHXWUPvjBD+rFF1+MejUAAGCaIQYAAGBmIgYAAGBmIgYAAGDmIg4AgJkjlk6n01FWeM899+jBBx/U3/zN36ihoUFf+tKX9NJLL+nRRx9VWVlZwfWlUtLAwMjrWEwqK8u8N7zlPT12PXXVA6HL06X2tg0N2etJJu0ys2bZZWIpe2XJdEno8kQ8Za9o9IeKxaSSksz7ext4IF1qVlMWtz94Kp4wy8TT4Z97d2/4Z5akgw4yiyg+uMcsky6zd1RsT3/o8lRZ+dj/Exs5dodfRyHl2N0lg+HbK+Xe5kLFY3a3khyyP3iJvbs1ugcb3b6SFE+FH5/pEvvYjA2G9yGSNBiz+5HSlH3sydNXWjs8bs8b3tUdvg9mz3ZVA+wTdQww5mTOYWen3ZfMqw2vJ5W26/D0sZ44YVZZNGGX1Ycm5AhIcnWgo2KAQdkxQGnMXtdQzO5nS+LhbdPbZ++nUntzVapBs0yqxK4ovqcvdHmytGLMe8PNO8wTq6UcvwPxxBJWzCLZMYBnfE/L3hjPueKJATxiQxHEAEYdkvMYd8Rhri8KRgN6PpP1/emgg4gBUJipiAEAAEUS1YUqzAiRxwAK5gNy5QIk8gH5FJwPyHEdQCIfEKbQfECua9XkA/IrNB+Qq30l8gH5hOUDZs/OrCJhNw2wz1RcC3ily+5L5tZMTj7AU6asNJrrG0Op8G0uSTsCkjH/qWRMsDOYtjuB0rgdswzJ7tCtfEBffzTjRlksonzAQPiYmkyMjKexWKZbTqWCh3WixD4ePMenhyf2GUqExz7WPpKmYT7AiKnTcXtFnrjcdYwP2bGE5zuJlZ/wxNyvvpp/2UEH+WKASCeWDQwM6MQTT9QnP/lJ/X//3/8nSeru7tapp56qW265RW9961sLrrO/X/rd70ZeV1ZKRx4p/f73Um9v5r3vfMeu5+7LNoRv+6IWs46ODns9mzfbZY47zi5T1rXDLLM9PT90eUNFt72i0R+qrExqbpZaW/d9g9+QXGxW01K+xSzTXbPQLFOd7Axd/q1Ha8063vUus4gq1z9rlhlYcaxZpuzpx0OX9x59cuB1LCZVVEh9fSMDSVSBuueCSu368O2VpO4VJ5tlLNXldke5pc3uKBsb7XVlX7zJ1b6SVNm1NbSOVGOTuZ74xvA+RJI2Jex+ZHGXfezp6KPtMlaHVFNjVvGV+8L3wXnnSXPm2JsCSMWJAZRO55gpGg98Y/vEVfZFkztuDe+TepN2f9TVZRZxxQkrl9n9o8fWjvBtbkra4/KYq985YoBNsmOAxeXhfawkdZbb/WxtVXjb/PSX9n5assQsosXaZJbprrM/d/Xqx0KXb11yWuB1aalUXy+1t0uDe7/LNtX02tuSrDTLlDuuAZetfspe17ITQpdXV0UzEa611SziigGyxWKZNh4cDHYbZR3hx+dAnX1sWnVIzmN8o70PXF8UjAYcaLRj7gceCF/+V3+VuagMeExVDICI0b7FRfsWF+0bnViMiWVwK0oMoGA+IFcuQCIfkE/B+YAc1wEk8gFhCskH5LtWTT4gv0LyAfnaVyIfkE9YPuC88zJ/kw+A16RcC8gR53/+Jvva4w3XTDwfsHu3WUS7dtllWhY58gGOgaGzK/xz1/bb1y8D+YDSUmnBAmnbtpGL1ZI2Je2xe3GVHbN0JsJjFsnOB/ziN/Z+am42i6glYecDehvt2KdydfiYuv2wkfE0kZDmzZN27gw2e8Nc+3jwHJ8elRvXmGU6m1eGLrf2kSSlEvb2trebRTR3rl1mWL5cgGTH1Kk6+9iMd4XHp5LUKTtGrW1bZ5ZJLVtub09reNzdW2eftw8/nH/ZOedk/rbyAZH+Dn39+vV69dVXdeKJJ+57r7q6WsuXL9f//u//RrkqAAAwjRADAAAwMxEDAAAwMxEDAAAwcxEHAMDMEulNTdva2iRJCxYsCLw/f/58bdu2bVx1xmKZXyYNG74jQ/adGTyzUa37TXt+jOd5vJLntsuuH/45ZicnrHvNeZ5fM/pWpMMfMuvDzvLcetDROK7H6Rj3Oay1J3/62rdi7OOpxlWPscNH1zH8Ovv9qH4I6rpFpOMAjeSxR44P5TmfXI/2ytGWY/6fZ2UWxz3ryzz7wHHsuZj3o7Qbr64ufHlUtx3FzFCMGMDjNa9xFDLOh6hiANfpHVGnb25PzLHBozv8HDGA67cxjsZx9SdG23junuS7w7pdyDUWVlWFLh7dLMPddqD7dhwPnm1xHVaV9p3PJuvRh1HFAK7/a6zMtZ6ojnHHPnCJ4DPNmxe+nMdgohBTFQMAAICpVawYIDsfkCsXIJEPyKvQfECO6wAS+YBQBeQD8l2rJh8woWrGtGvO/0M+IKewfECOJ+IBoabqWoDrKQcR5AM8d5f0POo6qk7f7PML7WRzXqyWyjxjgqNxosgHGJffJTn3QYnjUYMRxADZzTL8+ce0g2NFkd1A2jH+mPspoo3xnE/jXdWY/xfFrWEdB7Arhe551IxHBPmAsJjaexP4SCeW9fX1SdKY5ybPmjVLuzz3g8yhrCxzu+vRDj985N+5lo91SOhST5hZXx9NGRfHNyYjHyTJ0ePm65UbGvb9M7zlhi0wSzi2RlL4fXbf9jZXJbYjjjCLuL56HHVU6OJ8XXZU/Ug21y2Kje2VvPvJYrfeAvuQ8a0px6rGtG9F+Inp+u58iH0meK5pSfax5+K5qmL4f/8vgu0A9ipGDCAp99WtrPeuvNJTSXifVBHRpDFfDBDBhS3XuibQyWbFAL5+zf7gvrvoh7fNSSe5KnGwP5VrLDw2/BEZ+VoleEtn+8CKZlyWtGJFBOuyR0zPmBpVDJDLmLjAOFlcZ6Tj5HYd43PsfeBiNKDnM73jHdFsCiBNXQyAIqB9i4v2LS7aF5h0xYoBcuUDsnMBEvmA/MaZD8i6DiCRDwg1jnxAMXIBEvmAYTnbl3xATlY+YCJf3zDzTNq1gFGvL7nEU8nk5AOsH256tsXL7vPHGZCMCmR8/ZrdH0WRDzjhBFclDvanck0BNsbUXIfD2KcU28eD5/h0GR1A52DvJ8cPCRyb4jtXCpdzvpUxXrpiAEeQ5csH2I9YdW2PEUR5jl8rpvY8/jfSiWXleyO4gYGBff+WpD179qhinLPyBwakDVmPMi8vz5wHzz8v9fdn3vvxj+16rn73i6HLB5vsILGry17PVscjjJfbj0pV6W772a070+EnxrxZPfaKRn+o0tLMF8nt2/c9U/nFIbvDPaTMnn3eM9vxZXMoPNh49Nf2aXrWWWYRVWx+ziwzuMTxZXPd70KX97UEB5lYLHMM9/ePPPM3iomzktTba5eZszl8eyWp5zD7y6alatagWWZbhz0YWXfUkoLPps7VvpJU0RP+8ObUPDvgir8U3odIUmuJ48vmbvvY09KldhmrQ3Lc2ue7/xq+D97yFt8vAgCpODGApLHT5EdNnb/9y3bYdeVHw/ukvqTdH/WMY0jN5fBFdv/o0d4Vvs31Scevwkb/DDFHDNDq+NLVPCu8j5WkXWWOiTmV4W3z26ft/XTwwWYRNavVLNNT45h8tuHZ0OXtBwcnniUSmUllr7wyMnbVV/XZ2zJknz+eX2aV/nGtva5F4ROfqirtn62kHF+Ftm83i7higNFKS/cduiPvdYUfn4M19rFp1SE5j/GX7H3g+qJgNOBgnR1z/+hH4cvf8AbfnRcAaepiAESM9i0u2re4aN/oxGIR/kQeB7pixQDZ+YBcuQCJfEA+BecDclwHkMgHhCkkH5DvWjX5gPwKyQfka1+JfEA+YfmAt7zF3gQg26RcC8gR53/tPvva4yUXTjwf4OljPTmDQ5oc+QDH3ZF27Q7/3HMG7OuXgYRqIpGZVNbeHni/dcgeu5sr7ZhlV4lj8pmRD3jq/+z9NGpufE6HlNj5gL55jslnG8LH1J3NI+NpSUlmUllXVzANM6/aPh48x6dHRevzZpld88Mnn1n7SJJSJfb2vvKKWUTV1XaZbLlyAZIdU6dq7GMzvtueHLvLMbVszs5NZpnUIsfks+3hcXdfjX3e/td/5V925pnmf5cU8cSy4dtd7tixQwsXLtz3/o4dO7Rs2bJx1ZlO5+68+/tH3m+1+wNpzx5zPZZcB+dor75ql/GsK9C55yti1VPquKg2MJD7/cHBfcv22JsixRwdi+can3Gv3U57rPK1b5+dyHXVY+zwfHWk0yPLXOtxcN2m2HGARnIt1vGhPOeTp21ylcluX/fKLEYfIkkDnh7Vcey5WH2Eo/E6OsKXc+trFKIYMYDHyy87ChnnQ1QxgOv0jqjTN7cn6djgfP1IVgyQJ0oIitvrGvLcF9hoG88vJvKFNaNKmSVcY6Fx5SDfPkoms5Y5jgfPtrgOK8fVkMnKx0YVA2TLzn8WEgO41uPYYNcx7rki5RHBZ9q5M3w5uXkUYqpiAAAAMLWKFQPkygdk5wIk8gF5jTcfkHUdQCIfEGoc+YDR16rJB0yomjFlxuQCvCuzzLB8ALkAFGqqrgXsfQJnuAjyAY5h2dNNRNbpm+eop9/L9aECF6ulAU8MUGYXcnUpRtt4Ju6NvSNYDgk7HxBFDJCreYeGRr3vWFFUcYJn/DGPq4g2xnM+FbKqvLkA78osjkHRdYxn/zJmIiLIB4TF1N5YMNL7xC9btkxVVVV68skn973X3d2tdevW6bjjjotyVQAAYBohBgAAYGYiBgAAYGYiBgAAYOYiDgCAmSXSO5aVlZXp/PPP12233aba2lq95jWv0Ze+9CU1NjbqjW9847jq7O2V/v3fR143NUlHHin96lcjt5m+8Ua7nk/c1BK6/Ior7Do8M2NPrlpjltn+ykqzzJ49880yCzf+InR56oxVZh39ieB9BWOxzHNY++Y175vd2NKzw6ynu3yhWSbns+5H2dQafvvBd73LrmPjRrvMymb7lpZlPfbPodZUnRy+nv5RdZSUSBVzVDGwa2S2q6dhHB+q1nOANjaaRdYaT2k6eUW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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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|
||
"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": [
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_41811/3980313467.py:9: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
|
||
" ax = fig.gca(projection='3d')\n",
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_41811/3980313467.py:37: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
|
||
" fig.colorbar(surf, shrink=0.5, aspect=5)\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_188_1.png"
|
||
}
|
||
},
|
||
"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": [
|
||
{
|
||
"ename": "NameError",
|
||
"evalue": "name 'scipy' is not defined",
|
||
"output_type": "error",
|
||
"traceback": [
|
||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||
"\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
|
||
"Input \u001b[0;32mIn [31]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mscipy\u001b[49m\u001b[38;5;241m.\u001b[39mmisc\u001b[38;5;241m.\u001b[39mimread\n",
|
||
"\u001b[0;31mNameError\u001b[0m: name 'scipy' is not defined"
|
||
]
|
||
}
|
||
],
|
||
"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": "3.9.10"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
} |