Morten Hjorth-Jensen
5004 lines
1.3 MiB
Plaintext
5004 lines
1.3 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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"$$\n",
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"\\begin{align*} \n",
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"\\mbox{Cov}(\\varepsilon_{i_1},\n",
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"\\varepsilon_{i_2}) & = \\left\\{ \\begin{array}{lcc} \\sigma^2 & \\mbox{if}\n",
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"& i_1 = i_2, \\\\ 0 & \\mbox{if} & i_1 \\not= i_2. \\end{array} \\right.\n",
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"\\end{align*}\n",
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"$$"
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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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"$$\n",
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"\\boldsymbol{y} = f(\\boldsymbol{x})+\\boldsymbol{\\varepsilon}\n",
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"$$"
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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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"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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"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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"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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"$$\n",
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||
"\\mbox{Var}[\\boldsymbol{\\beta}^{\\mathrm{OLS}}]-\\mbox{Var}(\\boldsymbol{\\beta}^{\\mathrm{Ridge}})=\\sigma^2 [ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}[ 2\\lambda\\mathbf{I} + \\lambda^2 (\\mathbf{X}^{T} \\mathbf{X})^{-1} ] \\{ [ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}\\}^{T}.\n",
|
||
"$$"
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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: 0.183636 sec\n",
|
||
"Jackknife Statistics :\n",
|
||
"original bias std. error\n",
|
||
" 100.145 100.135 0.150131\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"from numpy import *\n",
|
||
"from numpy.random import randint, randn\n",
|
||
"from time import time\n",
|
||
"\n",
|
||
"def jackknife(data, stat):\n",
|
||
" n = len(data);t = zeros(n); inds = arange(n); t0 = time()\n",
|
||
" ## 'jackknifing' by leaving out an observation for each i \n",
|
||
" for i in range(n):\n",
|
||
" t[i] = stat(delete(data,i) )\n",
|
||
"\n",
|
||
" # analysis \n",
|
||
" print(\"Runtime: %g sec\" % (time()-t0)); print(\"Jackknife Statistics :\")\n",
|
||
" print(\"original bias std. error\")\n",
|
||
" print(\"%8g %14g %15g\" % (stat(data),(n-1)*mean(t)/n, (n*var(t))**.5))\n",
|
||
"\n",
|
||
" return t\n",
|
||
"\n",
|
||
"\n",
|
||
"# Returns mean of data samples \n",
|
||
"def stat(data):\n",
|
||
" return mean(data)\n",
|
||
"\n",
|
||
"\n",
|
||
"mu, sigma = 100, 15\n",
|
||
"datapoints = 10000\n",
|
||
"x = mu + sigma*random.randn(datapoints)\n",
|
||
"# jackknife returns the data sample \n",
|
||
"t = jackknife(x, stat)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "25ff562a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"### Bootstrap\n",
|
||
"\n",
|
||
"Bootstrapping is a nonparametric approach to statistical inference\n",
|
||
"that substitutes computation for more traditional distributional\n",
|
||
"assumptions and asymptotic results. Bootstrapping offers a number of\n",
|
||
"advantages: \n",
|
||
"1. The bootstrap is quite general, although there are some cases in which it fails. \n",
|
||
"\n",
|
||
"2. Because it does not require distributional assumptions (such as normally distributed errors), the bootstrap can provide more accurate inferences when the data are not well behaved or when the sample size is small. \n",
|
||
"\n",
|
||
"3. It is possible to apply the bootstrap to statistics with sampling distributions that are difficult to derive, even asymptotically. \n",
|
||
"\n",
|
||
"4. It is relatively simple to apply the bootstrap to complex data-collection plans (such as stratified and clustered samples).\n",
|
||
"\n",
|
||
"Since $\\widehat{\\beta} = \\widehat{\\beta}(\\boldsymbol{X})$ is a function of random variables,\n",
|
||
"$\\widehat{\\beta}$ itself must be a random variable. Thus it has\n",
|
||
"a pdf, call this function $p(\\boldsymbol{t})$. The aim of the bootstrap is to\n",
|
||
"estimate $p(\\boldsymbol{t})$ by the relative frequency of\n",
|
||
"$\\widehat{\\beta}$. You can think of this as using a histogram\n",
|
||
"in the place of $p(\\boldsymbol{t})$. If the relative frequency closely\n",
|
||
"resembles $p(\\vec{t})$, then using numerics, it is straight forward to\n",
|
||
"estimate all the interesting parameters of $p(\\boldsymbol{t})$ using point\n",
|
||
"estimators. \n",
|
||
"\n",
|
||
"In the case that $\\widehat{\\beta}$ has\n",
|
||
"more than one component, and the components are independent, we use the\n",
|
||
"same estimator on each component separately. If the probability\n",
|
||
"density function of $X_i$, $p(x)$, had been known, then it would have\n",
|
||
"been straight forward to do this by: \n",
|
||
"1. Drawing lots of numbers from $p(x)$, suppose we call one such set of numbers $(X_1^*, X_2^*, \\cdots, X_n^*)$. \n",
|
||
"\n",
|
||
"2. Then using these numbers, we could compute a replica of $\\widehat{\\beta}$ called $\\widehat{\\beta}^*$. \n",
|
||
"\n",
|
||
"By repeated use of (1) and (2), many\n",
|
||
"estimates of $\\widehat{\\beta}$ could have been obtained. The\n",
|
||
"idea is to use the relative frequency of $\\widehat{\\beta}^*$\n",
|
||
"(think of a histogram) as an estimate of $p(\\boldsymbol{t})$.\n",
|
||
"\n",
|
||
"But\n",
|
||
"unless there is enough information available about the process that\n",
|
||
"generated $X_1,X_2,\\cdots,X_n$, $p(x)$ is in general\n",
|
||
"unknown. Therefore, [Efron in 1979](https://projecteuclid.org/euclid.aos/1176344552) asked the\n",
|
||
"question: What if we replace $p(x)$ by the relative frequency\n",
|
||
"of the observation $X_i$; if we draw observations in accordance with\n",
|
||
"the relative frequency of the observations, will we obtain the same\n",
|
||
"result in some asymptotic sense? The answer is yes.\n",
|
||
"\n",
|
||
"Instead of generating the histogram for the relative\n",
|
||
"frequency of the observation $X_i$, just draw the values\n",
|
||
"$(X_1^*,X_2^*,\\cdots,X_n^*)$ with replacement from the vector\n",
|
||
"$\\boldsymbol{X}$. \n",
|
||
"\n",
|
||
"The independent bootstrap works like this: \n",
|
||
"\n",
|
||
"1. Draw with replacement $n$ numbers for the observed variables $\\boldsymbol{x} = (x_1,x_2,\\cdots,x_n)$. \n",
|
||
"\n",
|
||
"2. Define a vector $\\boldsymbol{x}^*$ containing the values which were drawn from $\\boldsymbol{x}$. \n",
|
||
"\n",
|
||
"3. Using the vector $\\boldsymbol{x}^*$ compute $\\widehat{\\beta}^*$ by evaluating $\\widehat \\beta$ under the observations $\\boldsymbol{x}^*$. \n",
|
||
"\n",
|
||
"4. Repeat this process $k$ times. \n",
|
||
"\n",
|
||
"When you are done, you can draw a histogram of the relative frequency\n",
|
||
"of $\\widehat \\beta^*$. This is your estimate of the probability\n",
|
||
"distribution $p(t)$. Using this probability distribution you can\n",
|
||
"estimate any statistics thereof. In principle you never draw the\n",
|
||
"histogram of the relative frequency of $\\widehat{\\beta}^*$. Instead\n",
|
||
"you use the estimators corresponding to the statistic of interest. For\n",
|
||
"example, if you are interested in estimating the variance of $\\widehat\n",
|
||
"\\beta$, apply the estimator $\\widehat \\sigma^2$ to the values\n",
|
||
"$\\widehat \\beta^*$.\n",
|
||
"\n",
|
||
"Before we proceed however, we need to remind ourselves about a central\n",
|
||
"theorem in statistics, namely the so-called **central limit theorem**.\n",
|
||
"This theorem plays a central role in understanding why the Bootstrap\n",
|
||
"(and other resampling methods) work so well on independent and\n",
|
||
"identically distributed variables.\n",
|
||
"\n",
|
||
"Suppose we have a PDF $p(x)$ from which we generate a series $N$\n",
|
||
"of averages $\\langle x_i \\rangle$. Each mean value $\\langle x_i \\rangle$\n",
|
||
"is viewed as the average of a specific measurement, e.g., throwing \n",
|
||
"dice 100 times and then taking the average value, or producing a certain\n",
|
||
"amount of random numbers. \n",
|
||
"For notational ease, we set $\\langle x_i \\rangle=x_i$ in the discussion\n",
|
||
"which follows. \n",
|
||
"\n",
|
||
"If we compute the mean $z$ of $m$ such mean values $x_i$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fa55ab5a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"z=\\frac{x_1+x_2+\\dots+x_m}{m},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "697c0c94",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"the question we pose is which is the PDF of the new variable $z$.\n",
|
||
"\n",
|
||
"The probability of obtaining an average value $z$ is the product of the \n",
|
||
"probabilities of obtaining arbitrary individual mean values $x_i$,\n",
|
||
"but with the constraint that the average is $z$. We can express this through\n",
|
||
"the following expression"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bd26bbd1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\tilde{p}(z)=\\int dx_1p(x_1)\\int dx_2p(x_2)\\dots\\int dx_mp(x_m)\n",
|
||
" \\delta(z-\\frac{x_1+x_2+\\dots+x_m}{m}),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "68664e4f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where the $\\delta$-function enbodies the constraint that the mean is $z$.\n",
|
||
"All measurements that lead to each individual $x_i$ are expected to\n",
|
||
"be independent, which in turn means that we can express $\\tilde{p}$ as the \n",
|
||
"product of individual $p(x_i)$. The independence assumption is important in the derivation of the central limit theorem.\n",
|
||
"\n",
|
||
"If we use the integral expression for the $\\delta$-function"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "742a107a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\delta(z-\\frac{x_1+x_2+\\dots+x_m}{m})=\\frac{1}{2\\pi}\\int_{-\\infty}^{\\infty}\n",
|
||
" dq\\exp{\\left(iq(z-\\frac{x_1+x_2+\\dots+x_m}{m})\\right)},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b6d624c1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and inserting $e^{i\\mu q-i\\mu q}$ where $\\mu$ is the mean value\n",
|
||
"we arrive at"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "46458586",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\tilde{p}(z)=\\frac{1}{2\\pi}\\int_{-\\infty}^{\\infty}\n",
|
||
" dq\\exp{\\left(iq(z-\\mu)\\right)}\\left[\\int_{-\\infty}^{\\infty}\n",
|
||
" dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}\\right]^m,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ca119461",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"with the integral over $x$ resulting in"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f75b40fc",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\int_{-\\infty}^{\\infty}dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}=\n",
|
||
" \\int_{-\\infty}^{\\infty}dxp(x)\n",
|
||
" \\left[1+\\frac{iq(\\mu-x)}{m}-\\frac{q^2(\\mu-x)^2}{2m^2}+\\dots\\right].\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a4b64e20",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The second term on the rhs disappears since this is just the mean and \n",
|
||
"employing the definition of $\\sigma^2$ we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fc76951f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\int_{-\\infty}^{\\infty}dxp(x)e^{\\left(iq(\\mu-x)/m\\right)}=\n",
|
||
" 1-\\frac{q^2\\sigma^2}{2m^2}+\\dots,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "76979572",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"resulting in"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3edff7d2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\left[\\int_{-\\infty}^{\\infty}dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}\\right]^m\\approx\n",
|
||
" \\left[1-\\frac{q^2\\sigma^2}{2m^2}+\\dots \\right]^m,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "73a9341f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and in the limit $m\\rightarrow \\infty$ we obtain"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "88f1cc30",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\tilde{p}(z)=\\frac{1}{\\sqrt{2\\pi}(\\sigma/\\sqrt{m})}\n",
|
||
" \\exp{\\left(-\\frac{(z-\\mu)^2}{2(\\sigma/\\sqrt{m})^2}\\right)},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1aec913e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which is the normal distribution with variance\n",
|
||
"$\\sigma^2_m=\\sigma^2/m$, where $\\sigma$ is the variance of the PDF $p(x)$\n",
|
||
"and $\\mu$ is also the mean of the PDF $p(x)$. \n",
|
||
"\n",
|
||
"Thus, the central limit theorem states that the PDF $\\tilde{p}(z)$ of\n",
|
||
"the average of $m$ random values corresponding to a PDF $p(x)$ \n",
|
||
"is a normal distribution whose mean is the \n",
|
||
"mean value of the PDF $p(x)$ and whose variance is the variance\n",
|
||
"of the PDF $p(x)$ divided by $m$, the number of values used to compute $z$.\n",
|
||
"\n",
|
||
"The central limit theorem leads to the well-known expression for the\n",
|
||
"standard deviation, given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "42b317e7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sigma_m=\n",
|
||
"\\frac{\\sigma}{\\sqrt{m}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e5baf71d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The latter is true only if the average value is known exactly. This is obtained in the limit\n",
|
||
"$m\\rightarrow \\infty$ only. Because the mean and the variance are measured quantities we obtain \n",
|
||
"the familiar expression in statistics"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8e2b39e5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sigma_m\\approx \n",
|
||
"\\frac{\\sigma}{\\sqrt{m-1}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "472e7c2c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"In many cases however the above estimate for the standard deviation,\n",
|
||
"in particular if correlations are strong, may be too simplistic. Keep\n",
|
||
"in mind that we have assumed that the variables $x$ are independent\n",
|
||
"and identically distributed. This is obviously not always the\n",
|
||
"case. For example, the random numbers (or better pseudorandom numbers)\n",
|
||
"we generate in various calculations do always exhibit some\n",
|
||
"correlations.\n",
|
||
"\n",
|
||
"The theorem is satisfied by a large class of PDFs. Note however that for a\n",
|
||
"finite $m$, it is not always possible to find a closed form /analytic expression for\n",
|
||
"$\\tilde{p}(x)$.\n",
|
||
"\n",
|
||
"The following code starts with a Gaussian distribution with mean value\n",
|
||
"$\\mu =100$ and variance $\\sigma=15$. We use this to generate the data\n",
|
||
"used in the bootstrap analysis. The bootstrap analysis returns a data\n",
|
||
"set after a given number of bootstrap operations (as many as we have\n",
|
||
"data points). This data set consists of estimated mean values for each\n",
|
||
"bootstrap operation. The histogram generated by the bootstrap method\n",
|
||
"shows that the distribution for these mean values is also a Gaussian,\n",
|
||
"centered around the mean value $\\mu=100$ but with standard deviation\n",
|
||
"$\\sigma/\\sqrt{n}$, where $n$ is the number of bootstrap samples (in\n",
|
||
"this case the same as the number of original data points). The value\n",
|
||
"of the standard deviation is what we expect from the central limit\n",
|
||
"theorem."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"id": "0ff7b796",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Bootstrap Statistics :\n",
|
||
"original bias std. error\n",
|
||
" 99.9814 14.7814 99.9836 0.147736\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"%matplotlib inline\n",
|
||
"\n",
|
||
"import numpy as np\n",
|
||
"from time import time\n",
|
||
"from scipy.stats import norm\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"# Returns mean of bootstrap samples \n",
|
||
"# Bootstrap algorithm\n",
|
||
"def bootstrap(data, datapoints):\n",
|
||
" t = np.zeros(datapoints)\n",
|
||
" n = len(data)\n",
|
||
" # non-parametric bootstrap \n",
|
||
" for i in range(datapoints):\n",
|
||
" t[i] = np.mean(data[np.random.randint(0,n,n)])\n",
|
||
" # analysis \n",
|
||
" print(\"Bootstrap Statistics :\")\n",
|
||
" print(\"original bias std. error\")\n",
|
||
" print(\"%8g %8g %14g %15g\" % (np.mean(data), np.std(data),np.mean(t),np.std(t)))\n",
|
||
" return t\n",
|
||
"\n",
|
||
"# We set the mean value to 100 and the standard deviation to 15\n",
|
||
"mu, sigma = 100, 15\n",
|
||
"datapoints = 10000\n",
|
||
"# We generate random numbers according to the normal distribution\n",
|
||
"x = mu + sigma*np.random.randn(datapoints)\n",
|
||
"# bootstrap returns the data sample \n",
|
||
"t = bootstrap(x, datapoints)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "22680159",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We see that our new variance and from that the standard deviation, agrees with the central limit theorem.\n",
|
||
"\n",
|
||
"We plot then the histogram together with a best fit for the data set."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"id": "fe018bb3",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"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",
|
||
"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",
|
||
"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"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"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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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.linear_model import LinearRegression, Ridge, Lasso\n",
|
||
"from sklearn.preprocessing import PolynomialFeatures\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.pipeline import make_pipeline\n",
|
||
"from sklearn.utils import resample\n",
|
||
"\n",
|
||
"np.random.seed(2018)\n",
|
||
"\n",
|
||
"n = 40\n",
|
||
"n_boostraps = 100\n",
|
||
"maxdegree = 14\n",
|
||
"\n",
|
||
"\n",
|
||
"# Make data set.\n",
|
||
"x = np.linspace(-3, 3, n).reshape(-1, 1)\n",
|
||
"y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)\n",
|
||
"error = np.zeros(maxdegree)\n",
|
||
"bias = np.zeros(maxdegree)\n",
|
||
"variance = np.zeros(maxdegree)\n",
|
||
"polydegree = np.zeros(maxdegree)\n",
|
||
"x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n",
|
||
"\n",
|
||
"for degree in range(maxdegree):\n",
|
||
" model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False))\n",
|
||
" y_pred = np.empty((y_test.shape[0], n_boostraps))\n",
|
||
" for i in range(n_boostraps):\n",
|
||
" x_, y_ = resample(x_train, y_train)\n",
|
||
" y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel()\n",
|
||
"\n",
|
||
" polydegree[degree] = degree\n",
|
||
" error[degree] = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )\n",
|
||
" bias[degree] = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )\n",
|
||
" variance[degree] = np.mean( np.var(y_pred, axis=1, keepdims=True) )\n",
|
||
" print('Polynomial degree:', degree)\n",
|
||
" print('Error:', error[degree])\n",
|
||
" print('Bias^2:', bias[degree])\n",
|
||
" print('Var:', variance[degree])\n",
|
||
" print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))\n",
|
||
"\n",
|
||
"plt.plot(polydegree, error, label='Error')\n",
|
||
"plt.plot(polydegree, bias, label='bias')\n",
|
||
"plt.plot(polydegree, variance, label='Variance')\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8cf88b3a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The bias-variance tradeoff summarizes the fundamental tension in\n",
|
||
"machine learning, particularly supervised learning, between the\n",
|
||
"complexity of a model and the amount of training data needed to train\n",
|
||
"it. Since data is often limited, in practice it is often useful to\n",
|
||
"use a less-complex model with higher bias, that is a model whose asymptotic\n",
|
||
"performance is worse than another model because it is easier to\n",
|
||
"train and less sensitive to sampling noise arising from having a\n",
|
||
"finite-sized training dataset (smaller variance). \n",
|
||
"\n",
|
||
"The above equations tell us that in\n",
|
||
"order to minimize the expected test error, we need to select a\n",
|
||
"statistical learning method that simultaneously achieves low variance\n",
|
||
"and low bias. Note that variance is inherently a nonnegative quantity,\n",
|
||
"and squared bias is also nonnegative. Hence, we see that the expected\n",
|
||
"test MSE can never lie below $Var(\\epsilon)$, the irreducible error.\n",
|
||
"\n",
|
||
"What do we mean by the variance and bias of a statistical learning\n",
|
||
"method? The variance refers to the amount by which our model would change if we\n",
|
||
"estimated it using a different training data set. Since the training\n",
|
||
"data are used to fit the statistical learning method, different\n",
|
||
"training data sets will result in a different estimate. But ideally the\n",
|
||
"estimate for our model should not vary too much between training\n",
|
||
"sets. However, if a method has high variance then small changes in\n",
|
||
"the training data can result in large changes in the model. In general, more\n",
|
||
"flexible statistical methods have higher variance.\n",
|
||
"\n",
|
||
"You may also find this recent [article](https://www.pnas.org/content/116/32/15849) of interest."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"id": "86bfc49a",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"\n",
|
||
"============================\n",
|
||
"Underfitting vs. Overfitting\n",
|
||
"============================\n",
|
||
"\n",
|
||
"This example demonstrates the problems of underfitting and overfitting and\n",
|
||
"how we can use linear regression with polynomial features to approximate\n",
|
||
"nonlinear functions. The plot shows the function that we want to approximate,\n",
|
||
"which is a part of the cosine function. In addition, the samples from the\n",
|
||
"real function and the approximations of different models are displayed. The\n",
|
||
"models have polynomial features of different degrees. We can see that a\n",
|
||
"linear function (polynomial with degree 1) is not sufficient to fit the\n",
|
||
"training samples. This is called **underfitting**. A polynomial of degree 4\n",
|
||
"approximates the true function almost perfectly. However, for higher degrees\n",
|
||
"the model will **overfit** the training data, i.e. it learns the noise of the\n",
|
||
"training data.\n",
|
||
"We evaluate quantitatively **overfitting** / **underfitting** by using\n",
|
||
"cross-validation. We calculate the mean squared error (MSE) on the validation\n",
|
||
"set, the higher, the less likely the model generalizes correctly from the\n",
|
||
"training data.\n",
|
||
"\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 1400x500 with 3 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 6\n",
|
||
"Mean squared error on training data: 3.66204648\n",
|
||
"Mean squared error on test data: 8.14812206\n",
|
||
"Degree of polynomial: 7\n",
|
||
"Mean squared error on training data: 0.47075725\n",
|
||
"Mean squared error on test data: 2.00607783\n",
|
||
"Degree of polynomial: 8\n",
|
||
"Mean squared error on training data: 0.04912436\n",
|
||
"Mean squared error on test data: 0.21596432\n",
|
||
"Degree of polynomial: 9\n",
|
||
"Mean squared error on training data: 0.02522069\n",
|
||
"Mean squared error on test data: 0.08576932\n",
|
||
"Degree of polynomial: 10\n",
|
||
"Mean squared error on training data: 0.02511518\n",
|
||
"Mean squared error on test data: 1.20015436\n",
|
||
"Degree of polynomial: 11\n",
|
||
"Mean squared error on training data: 0.01640891\n",
|
||
"Mean squared error on test data: 1.35533773\n",
|
||
"Degree of polynomial: 12\n",
|
||
"Mean squared error on training data: 0.00813803\n",
|
||
"Mean squared error on test data: 0.17446471\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 13\n",
|
||
"Mean squared error on training data: 0.00759119\n",
|
||
"Mean squared error on test data: 1.08131003\n",
|
||
"Degree of polynomial: 14\n",
|
||
"Mean squared error on training data: 0.00472199\n",
|
||
"Mean squared error on test data: 0.81333804\n",
|
||
"Degree of polynomial: 15\n",
|
||
"Mean squared error on training data: 0.00410478\n",
|
||
"Mean squared error on test data: 92.09164879\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 16\n",
|
||
"Mean squared error on training data: 0.00315593\n",
|
||
"Mean squared error on test data: 234.38479049\n",
|
||
"Degree of polynomial: 17\n",
|
||
"Mean squared error on training data: 0.00242998\n",
|
||
"Mean squared error on test data: 1271.35772794\n",
|
||
"Degree of polynomial: 18\n",
|
||
"Mean squared error on training data: 0.00229441\n",
|
||
"Mean squared error on test data: 20.17975580\n",
|
||
"Degree of polynomial: 19\n",
|
||
"Mean squared error on training data: 0.00205364\n",
|
||
"Mean squared error on test data: 82.28863096\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 20\n",
|
||
"Mean squared error on training data: 0.00153654\n",
|
||
"Mean squared error on test data: 23.03093570\n",
|
||
"Degree of polynomial: 21\n",
|
||
"Mean squared error on training data: 0.00158669\n",
|
||
"Mean squared error on test data: 361.88200597\n",
|
||
"Degree of polynomial: 22\n",
|
||
"Mean squared error on training data: 0.00148217\n",
|
||
"Mean squared error on test data: 100.56677583\n",
|
||
"Degree of polynomial: 23\n",
|
||
"Mean squared error on training data: 0.00124060\n",
|
||
"Mean squared error on test data: 1742.84477975\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 24\n",
|
||
"Mean squared error on training data: 0.00112079\n",
|
||
"Mean squared error on test data: 1607.25907550\n",
|
||
"Degree of polynomial: 25\n",
|
||
"Mean squared error on training data: 0.00103739\n",
|
||
"Mean squared error on test data: 4608.96962992\n",
|
||
"Degree of polynomial: 26\n",
|
||
"Mean squared error on training data: 0.00095521\n",
|
||
"Mean squared error on test data: 292.94291957\n",
|
||
"Degree of polynomial: 27\n",
|
||
"Mean squared error on training data: 0.00091518\n",
|
||
"Mean squared error on test data: 655269.76536679\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Degree of polynomial: 28\n",
|
||
"Mean squared error on training data: 0.00090601\n",
|
||
"Mean squared error on test data: 346.43611299\n",
|
||
"Degree of polynomial: 29\n",
|
||
"Mean squared error on training data: 0.00084423\n",
|
||
"Mean squared error on test data: 1001.72392087\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_72209/626635268.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_72209/626635268.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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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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_72209/3817475779.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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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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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rLBYLwcHBFZpdREREivdH2k42BZy/fFKsdZTJaZyZdgQoNzeXzZs3Ex0d7bQ9Ojqa9evXl2gfdrudkydPUrduXaftp06dIiwsjMaNG3P77bcXOEJ0uZycHLKyspxuYq79+/djsVhITU0tcszKlSuxWCycOHHimuUSEZGSW54wHcMCHU5406iF+RdAvZRpBejIkSPk5+cTFBTktD0oKIiMjIwS7ePf//43p0+f5t5773Vsa9WqFfHx8SxZsoR58+bh7e1Njx492LNnT5H7mThxIgEBAY5bSEhI2d5UJTd06FAsFgsjR44s8Njjjz+OxWJxusr74cOHeeyxxwgNDcXLy4vg4GBiYmJITk52jGnSpEmhc67++c9/FpmjT58+jnGenp40b96cuLg4cnJyHGNCQkJIT0+nXbt25fPmy6io93fxdjXXJevTpw9jx44tt6wiIpWNbY8NAKvfTeYGKYTp5wG69CKRAIZhFNhWmHnz5vHKK6+wePFiGjRo4NjerVs3unXr5rjfo0cPOnXqxPTp05k2bVqh+4qLi2PcuHGO+1lZWdW2BIWEhDB//nzeeOMNfHx8gPOXOpg3bx6hoaFOYwcNGkReXh4fffQRzZo14/fff+frr7/m2LFjTuMmTJjAiBEjnLZd6WrtI0aMYMKECeTm5pKSksLDDz8M4Pjq093dvVJ8jZmSkuK4Wvr69esZNGgQu3fvdpxi/eIV10VExJk9/xzLPH4FwBpxn8lpCjLtCFBgYCDu7u4FjvYcPny4wFGhyy1YsIBhw4bx6aefcttttxU71s3NjYiIiGKPAHl5eTkuDFrcBUKrg06dOhEaGsqiRYsc2xYtWkRISIjTPKoTJ06wdu1aJk2aRN++fQkLC6NLly7ExcXRv39/p33WqlWL4OBgp1vNmjWLzeHr60twcDChoaEMGjSIqKgoli9f7ni8sK/AEhISuOGGG/Dx8aFv377s37+/wH7fe+89QkJC8PX1ZeDAgUyZMoXatWs7jfnyyy8JDw/H29ubZs2a8eqrr3Lu3LlCc9avX9/xni5+1dqgQQPHtl27dtGrVy98fHwICQlh9OjRnD592vH8GTNm0KJFC7y9vQkKCuLuu+8Gzh+NW7VqFW+++abjaFJh70dEpKra9PV/OOJj4J8DkdHDzI5TgGkFyNPTk/DwcJKSkpy2JyUl0b179yKfN2/ePIYOHcrcuXML/CIujGEYpKamOq6OXREMw+B07mlTbmW5lu3DDz/M7NmzHfc//PBDHnnE+dwMfn5++Pn58cUXXzh9NVURtm7dyrp165yuBn+5AwcOcNddd9GvXz9SU1MZPnw4zz//vNOYdevWMXLkSMaMGUNqaipRUVG89tprTmOWLVvGAw88wOjRo9mxYwezZs0iPj6+wLiS+OGHH4iJieGuu+5i27ZtLFiwgLVr1/Lkk08CsGnTJkaPHs2ECRPYvXs3iYmJ9OrVC4A333yTyMhIRowY4VipWF2POoqIa7IlzwEgKvs6PLx9TU5TkKlfgY0bN44hQ4bQuXNnIiMjeffdd0lLS3PMUYmLi+PgwYPMmXP+Q5w3bx4PPvggb775Jt26dXMcPfLx8SEgIACAV199lW7dutGiRQuysrKYNm0aqampvP322xX2Ps7kncFvol+F7b84p+JOUdOz+KMtlxsyZAhxcXGOoyzr1q1j/vz5rFy50jGmRo0axMfHM2LECGbOnEmnTp3o3bs3f/7zn2nf3vk6Ls899xwvvPCC07alS5cWOz9mxowZvP/+++Tl5ZGbm4ubm1ux/4zeeecdmjVrxhtvvIHFYqFly5b88MMPTJo0yTFm+vTpWK1Wnn76aQBuuOEG1q9fz9KlSx1jXnvtNZ5//nkeeughAJo1a8b//d//8eyzz/Lyyy9f8bO71L/+9S/uu+8+xzyeFi1aMG3aNHr37s0777xDWloaNWvW5Pbbb6dWrVqEhYU5jrIFBATg6enpOBImIlLd2E6kQG2IDbvV7CiFMrUADR48mKNHjzJhwgTHhNeEhATCwsIASE9Pdzon0KxZszh37hxPPPEETzzxhGP7Qw89RHx8PHD+q5tHH32UjIwMAgIC6NixI6tXr6ZLly7X9L1VZoGBgfTv35+PPvoIwzDo378/gYGBBcYNGjSI/v37s2bNGpKTk0lMTGTy5Mm8//77TpOln3nmGaf7ANddd12xGe6//37Gjx9PVlYWkyZNwt/fn0GDBhU5fufOnXTr1s1pflhkZKTTmN27dzNw4ECnbV26dHEqQJs3byYlJcXpiE9+fj7Z2dmcOXMGX9+S/1/K5s2b+fnnn/nkk08c2wzDwG63s2/fPqKioggLC6NZs2bExsYSGxvLwIEDS/UaIiJV0ZEDu9l4cfl77JMmpymc6ZOgH3/8cR5//PFCH7tYai669AhFUd544w3eeOONckhWcr4evpyKO3VNX/PS1y6LRx55xPFVTXFHXry9vYmKiiIqKoqXXnqJ4cOH8/LLLzsVnsDAQK6//vpSvX5AQIDjOR9//DFt27blgw8+YNiwwr8nLslXfYVNoL/8eXa7nVdffZW77rqrwPNLe7JMu93OY489xujRows8FhoaiqenJ99//z0rV65k+fLlvPTSS7zyyiukpKQUmJckIlKdLP9qGoYFbsz0pnHLCLPjFMr0AlQdWCyWUn8NZbbY2Fhyc3MBiImJKfHz2rRpwxdffFGuWTw8PPjb3/5GXFwcf/nLXwo9QlLY63733XdO91u1asXGjRudtm3atMnpfqdOndi9e3epC1thOnXqxPbt24vdV40aNbjtttu47bbbePnll6lduzbffPMNd911F56eno4VZiIi1Uniz4lQC6y+7a882CSmXwtMzOHu7s7OnTvZuXMn7u7uBR4/evQot9xyCx9//DHbtm1j3759fPbZZ0yePJkBAwY4jT158iQZGRlOt9KeTPK+++7DYrEwY8aMQh8fOXIke/fuZdy4cezevZu5c+cWOEI4atQoEhISmDJlCnv27GHWrFnYbDano0IvvfQSc+bM4ZVXXmH79u3s3LmTBQsWFJjDVBLPPfccycnJPPHEE6SmprJnzx6WLFnCqFHnz3a6dOlSxxy0X3/9lTlz5mC322nZsiVw/hxDGzZsYP/+/Rw5cgS73V7qDCIilY09/xyJ7vsAsHb+i8lpiqYC5MKKW/Lv5+dH165deeONN+jVqxft2rXjxRdfZMSIEbz11ltOY1966SUaNmzodHv22WdLlcXT05Mnn3ySyZMnc+pUwa8TQ0NDWbhwIV9++SUdOnRg5syZ/OMf/3Aa06NHD2bOnMmUKVPo0KEDiYmJPPXUU05fbcXExLB06VKSkpKIiIigW7duTJkyxTHvrDTat2/PqlWr2LNnDz179qRjx468+OKLjhWHtWvXZtGiRdxyyy20bt2amTNnMm/ePNq2bQvA008/jbu7O23atKF+/fpFXgNPRKQq+f7bufzha1ArB3rEPmp2nCJZjLKso67msrKyCAgIIDMzs0BByM7OZt++fY4r2EvlNmLECHbt2sWaNWvMjlJl6WdeRErj/ybcykvGNww80ZBFbxy6pq9d3O/vy2kOkFQrr7/+OlFRUdSsWRObzcZHH31U5NdqIiJS/mzHNkIdsIYVf6Jis6kASbWyceNGJk+ezMmTJ2nWrBnTpk1j+PDhZscSEXEJxw7tZUPA+WkMsTFPXGG0uVSApFr59NNPzY4gIuKyli99E7sbtM30IqR1V7PjFEuToEVERKRcJP6UAIDV50aTk1yZClAZae64uAr9rItISTgtfw//s8lprkwFqJQuXrDzzJkzJicRuTYu/qwXd7FaEZHUVQv43deOXy7cbH3M7DhXpDlApeTu7k7t2rU5fPgwAL6+vgUuvyBSHRiGwZkzZzh8+DC1a9cu9ISZIiIX2dbFA3DrmWA8fcy5QHhpqACVwcWrd18sQSLVWe3atXXFehG5ItvRDeeXv4feYnaUElEBKgOLxULDhg1p0KABeXl5ZscRqTAeHh468iMiV3Q8fR/JAScBiI0u/ALnlY0K0FVwd3fXLwcREXF5SV9Nw+4GrTM9CWvbw+w4JaJJ0CIiInJVbLuWAmD1rvzL3y9SARIREZEyM+x2Et1+AcDa6V6T05ScCpCIiIiU2dY1n5FR007NXOhpHWl2nBJTARIREZEys635EIBbzgThVbP4K7BXJipAIiIiUma2I98BYG3c1+QkpaMCJCIiImVy4vdfWR+QBUBs1F9NTlM6KkAiIiJSJiuWTiPfDVpmedK0fS+z45SKCpCIiIiUiW3XlwBYPduanKT0VIBERESk1Ay7nUTLXgCsHe8xOU3pqQCJiIhIqf2wbhGHatrxzYVe/arW/B9QARIREZEysK3+AIC+Zxrg7Vfb3DBloAIkIiIipWb7IxkA63W9TU5SNipAIiIiUipZf/zGOv9MAKxRVePq75dTARIREZFSWbF0Gufc4YYsD5p16GN2nDJRARIREZFSse1YAkCsZxuTk5SdCpCIiIiUmGG3Y2MPANYOd5ucpuxUgERERKTEticv5qCfHe886N2vas7/ARUgERERKQXbqvcB6Hu6Pj7+dU1OU3YqQCIiIlJitsPrAbA2qlrX/rqcCpCIiIiUyMmjh1jrfwIA621V7+zPl1IBEhERkRL5eul08tzh+iwPru94q9lxrooKkIiIiJSIbfsXAFg9WpsbpByoAImIiMgVGXY7NuP88vfY9neZnObqqQCJiIjIFe347ksO+OXjdQ769H/C7DhXTQVIRERErijxwvL3Pqfq4RsQaHKaq6cCJCIiIldk+30dANaGVXv5+0UqQCIiIlKsU8cyWFPrOADWWx4zOU35UAESERGRYn3z1XRya0CzkzVo0SnK7DjlQgVIREREimX78QsArDVaY3GrHtWherwLERERqRCG3Y4tfzcAse3uNDdMOVIBEhERkSLtSkng11r5eJ6Dvv2fNDtOuVEBEhERkSIlfnt++Xvvk3WpWaeByWnKjwqQiIiIFMmWsQYAa3BPk5OULxUgERERKdTp44dZVesYANZbHjU5TflSARIREZFCffvVW+TWgCYna9Cyc6zZccqVCpCIiIgUyvbD5wBY3VtWm+XvF1WvdyMiIiLl4vzy910AWNsNNDlN+VMBEhERkQJ+2ryMfbXOXVj+XvWv/n45FSAREREpwPbNuwD0PFkHv7rBJqcpf6YXoBkzZtC0aVO8vb0JDw9nzZo1RY5dtGgRUVFR1K9fH39/fyIjI1m2bFmBcQsXLqRNmzZ4eXnRpk0bPv/884p8CyIiItVO4sXl70E9TE5SMUwtQAsWLGDs2LGMHz+eLVu20LNnT6xWK2lpaYWOX716NVFRUSQkJLB582b69u3LHXfcwZYtWxxjkpOTGTx4MEOGDGHr1q0MGTKEe++9lw0bNlyrtyUiIlKlnck8wkq/owBY+44wOU3FsBiGYZj14l27dqVTp0688847jm2tW7fmzjvvZOLEiSXaR9u2bRk8eDAvvfQSAIMHDyYrKwubzeYYExsbS506dZg3b16h+8jJySEnJ8dxPysri5CQEDIzM/H39y/LWxMREamyEua+Sv89rxB6yp39k3KrzAqwrKwsAgICSvT727R3lJuby+bNm4mOjnbaHh0dzfr160u0D7vdzsmTJ6lbt65jW3JycoF9xsTEFLvPiRMnEhAQ4LiFhISU4p2IiIhUL7ZtCwGwWm6oMuWntEx7V0eOHCE/P5+goCCn7UFBQWRkZJRoH//+9785ffo09957r2NbRkZGqfcZFxdHZmam43bgwIFSvBMREZHqxZa3EwBrNbr6++VqmB3AYrE43TcMo8C2wsybN49XXnmFxYsX06CB88XZSrtPLy8vvLy8SpFaRESketqzOYm9/ufwyIdbqtHV3y9nWgEKDAzE3d29wJGZw4cPFziCc7kFCxYwbNgwPvvsM2677Tanx4KDg8u0TxEREQHb1zMBuDmrNrXqNTI5TcUx7SswT09PwsPDSUpKctqelJRE9+7di3zevHnzGDp0KHPnzqV///4FHo+MjCywz+XLlxe7TxERETkvMf3C8vcG1fv3pqlfgY0bN44hQ4bQuXNnIiMjeffdd0lLS2PkyJHA+bk5Bw8eZM6cOcD58vPggw/y5ptv0q1bN8eRHh8fHwICAgAYM2YMvXr1YtKkSQwYMIDFixezYsUK1q5da86bFBERqSLOZh3j25p/AGDtPdzkNBXL1KndgwcPZurUqUyYMIGbbrqJ1atXk5CQQFhYGADp6elO5wSaNWsW586d44knnqBhw4aO25gxYxxjunfvzvz585k9ezbt27cnPj6eBQsW0LVr12v+/kRERKqSVQkzyPaAxqfcaRs5wOw4FcrU8wBVVqU5j4CIiEh1MSbuJqZ5b2XE6Va8O3mn2XFKrUqcB0hEREQqF1vuDgCsbf5kcpKKpwIkIiIi7E39hj3+edTIh1v7jzI7ToVTARIRERFsSecvS9UjKwD/+o1NTlPxVIBEREQE26FVAFjrR5qc5NpQARIREXFx2adO/G/5e69hJqe5NlSAREREXNzqhHc46wHXnXLjxh53mR3nmlABEhERcXG2LZ8BEMv11fbq75dzjXcpIiIiRbLlbgfA2rr6L3+/SAVIRETEhe3btprd/rnUyIfbbq/+y98vUgESERFxYbakGQB0zwogoEGoyWmuHRUgERERF2b77VsAYgNd65qZKkAiIiIuKud0Ft/4HgbA2vMRk9NcWypAIiIiLmqNbSZnPKHhaTc69LzH7DjXlAqQiIiIi7J9/ykAsUZzl1n+fpFrvVsRERFxsGX/AIC11e0mJ7n2VIBERERc0K/b17EzIBd3O0TdPsbsONecCpCIiIgLsi17G4DITH9qB4WZnObaUwESERFxQbYD55e/W+u51vL3i1SAREREXEzO6Sy+9s0AILbHQyanMYcKkIiIiItZt+w9TntC0Bk3buo92Ow4plABEhERcTG2zfMBiM1vipt7DZPTmEMFSERExMXYzl5Y/t6yv8lJzKMCJCIi4kIO7NzA9oAc3OwQ1X+02XFMowIkIiLiQmzLpgPQLbMWdRs1NzmNeVSAREREXIjt128AsNbtYnISc6kAiYiIuIjcs6dY4ZsOgLXHUHPDmEwFSERExEWsX/Y+pzyhwRkLHfv82ew4plIBEhERcRG2TfMAiHHh5e8XqQCJiIi4CNuZbQBYW/QzOYn5VIBERERcwG+7U/ghIBs3O0S78PL3i1SAREREXEBi4lsAdMnyo17jFianMZ8KkIiIiAuw/boCAGvtCJOTVA4qQCIiItVcXvYZVngfAsDa3TWv/n45FSAREZFqbv2y98jygsCzFsJvud/sOJWCCpCIiEg1l7jp/NXfY/LCXH75+0UqQCIiItWc7VQqANYWVnODVCIqQCIiItXYoT3fs7V2NhYDYvqPMTtOpaECJCIiUo0l2s5f/T0isyaBIS1NTlN5qACJiIhUY7b9SQBYAzqbnKRyUQESERGpps7lZpPkdRAAa+QQk9NULipAIiIi1VTysvfJ9IZ6Zy10vkUF6FIqQCIiItWUbeNcAKLzQnH38DQ5TeWiAiQiIlJNJV5c/t481twglZAKkIiISDWU8cs2ttQ+C0BMv1Emp6l8VIBERESqocSEaQB0PuFLgyZtTU5T+agAiYiIVEO2X5YDYPUPNzlJ5aQCJCIiUs2cy81muddvAFi7PWBymspJBUhERKSa2ZA0mxPeBnXPWuhy21Cz41RKKkAiIiLVjG3DJwBE54Vo+XsRVIBERESqmcSTWwCIbRZtcpLKSwVIRESkGvl9349srn0GgNh+uvp7UVSAREREqpFlF5a/dzrhQ1DTdianqbxML0AzZsygadOmeHt7Ex4ezpo1a4ocm56ezn333UfLli1xc3Nj7NixBcbEx8djsVgK3LKzsyvwXYiIiFQOtl+WAWCt1cnkJJWbqQVowYIFjB07lvHjx7NlyxZ69uyJ1WolLS2t0PE5OTnUr1+f8ePH06FDhyL36+/vT3p6utPN29u7ot6GiIhIpZCfl8tyjwMAWLveb3Kays3UAjRlyhSGDRvG8OHDad26NVOnTiUkJIR33nmn0PFNmjThzTff5MEHHyQgIKDI/VosFoKDg51uIiIi1d3GFfEc8zGonW2ha9TDZsep1EwrQLm5uWzevJnoaOcZ6tHR0axfv/6q9n3q1CnCwsJo3Lgxt99+O1u2bCl2fE5ODllZWU43ERGRqsb23ccAROc0poanvvkojmkF6MiRI+Tn5xMUFOS0PSgoiIyMjDLvt1WrVsTHx7NkyRLmzZuHt7c3PXr0YM+ePUU+Z+LEiQQEBDhuISEhZX59ERERs9iyNgNg1fL3KzJ9ErTFYnG6bxhGgW2l0a1bNx544AE6dOhAz549+fTTT7nhhhuYPn16kc+Ji4sjMzPTcTtw4ECZX19ERMQMh/dvZ9OF5e8x1idNTlP51TDrhQMDA3F3dy9wtOfw4cMFjgpdDTc3NyIiIoo9AuTl5YWXl1e5vaaIiMi1ttz2FgA3nfChYfObzA1TBZh2BMjT05Pw8HCSkpKcticlJdG9e/dyex3DMEhNTaVhw4bltk8REZHKxvazDQCr303mBqkiTDsCBDBu3DiGDBlC586diYyM5N133yUtLY2RI0cC57+aOnjwIHPmzHE8JzU1FTg/0fmPP/4gNTUVT09P2rRpA8Crr75Kt27daNGiBVlZWUybNo3U1FTefvvta/7+REREroX8vFyWeZw/hYy1y30mp6kaTC1AgwcP5ujRo0yYMIH09HTatWtHQkICYWFhwPkTH15+TqCOHTs6/r5582bmzp1LWFgY+/fvB+DEiRM8+uijZGRkEBAQQMeOHVm9ejVdunS5Zu9LRETkWtr0zX846mMQkA2RMcPNjlMlWAzDMMwOUdlkZWUREBBAZmYm/v7+ZscREREp1iuv9OFVyyruzryOz6b8ZnYc05Tm97fpq8BERETk6tgyNwFgbRJlcpKqQwVIRESkCjtyYDcpAacBiIl9wuQ0VYcKkIiISBW2/KtpGBZof8Kb627obHacKkMFSEREpAqz7bmw/L1m0RcJl4JUgERERKooe/45ltXYD4A14i/mhqliVIBERESqqM3ffMIfvgb+OdA9ZoTZcaqUUhWgyZMnc/bsWcf91atXk5OT47h/8uRJHn/88fJLJyIiIkWyrf8IgNuyG+Hh7WtymqqlVAUoLi6OkydPOu7ffvvtHDx40HH/zJkzzJo1q/zSiYiISJFsJ1IAsIbdZnKSqqdUBejycybqHIoiIiLmOPrbHjYEnAIgNlZXfy8tzQESERGpgpISpmNYoF2mF41bRpgdp8pRARIREamCbD99BYDVp73JSaqmUl8M9f3338fPzw+Ac+fOER8fT2BgIIDT/CARERGpGPb8cyS67wPA2vnPJqepmkp1MdQmTZpgsViuOG7fvn1XFcpsuhiqiIhUZpu//pjOa4fglwtHXziJp4+f2ZEqhdL8/i7VEaD9+/dfTS4REREpB7Z18QDcdqahyk8ZaQ6QiIhIFWM7thEAa9gtJiepukpVgDZs2IDNZnPaNmfOHJo2bUqDBg149NFHnU6MKCIiIuXr2KG9fBdwfs6tNWaUyWmqrlIVoFdeeYVt27Y57v/www8MGzaM2267jeeff54vv/ySiRMnlntIEREROW9FwlvY3aBtphchrbuaHafKKlUBSk1N5dZbb3Xcnz9/Pl27duW9995j3LhxTJs2jU8//bTcQ4qIiMh5tl1LAYj1aWdykqqtVAXo+PHjBAUFOe6vWrWK2NhYx/2IiAgOHDhQfulERETEwZ5/jkS3XwCwdhpscpqqrVQFKCgoyLHEPTc3l++//57IyEjH4ydPnsTDw6N8E4qIiAgAW9d8RkZNOzVz4ebYx8yOU6WVqgDFxsby/PPPs2bNGuLi4vD19aVnz56Ox7dt20bz5s3LPaSIiIiAbc1sAG49E4xXTZ2n7mqU6jxAf//737nrrrvo3bs3fn5+xMfH4+np6Xj8ww8/JDo6utxDioiICNiOboA6YA3pa3aUKq9UBah+/fqsWbOGzMxM/Pz8cHd3d3r8s88+o1atWuUaUERERODE77+SHJAFgDXmCZPTVH2lKkCPPPJIicZ9+OGHZQojIiIihUta+ib5btA605Owtj3MjlPllaoAxcfHExYWRseOHSnFJcRERETkKiXuWgp+EOut5e/loVQFaOTIkcyfP59ffvmFRx55hAceeIC6detWVDYREREBDLudRMteAKwd7zE5TfVQqlVgM2bMID09neeee44vv/ySkJAQ7r33XpYtW6YjQiIiIhVk29r/cqimHd9c6NXvcbPjVAulvhiql5cXf/nLX0hKSmLHjh20bduWxx9/nLCwME6dOlURGUVERFyabfX5ubW3nGmg5e/l5KquBm+xWLBYLBiGgd1uL69MIiIicgnbke8AsDbW8vfyUuoClJOTw7x584iKiqJly5b88MMPvPXWW6SlpeHn51cRGUVERFxW5uE01gVkAmCN0tdf5aVUk6Aff/xx5s+fT2hoKA8//DDz58+nXr16FZVNRETE5a1YOp18N2iZ5UnT9r3MjlNtlKoAzZw5k9DQUJo2bcqqVatYtWpVoeMWLVpULuFERERcXeLOL8EPrJ5tzY5SrZSqAD344INYLJaKyiIiIiKXMOx2bOwBIPamQSanqV5KfSJEERERuTZ+XP85B/3s+ORB7/66/EV5uqpVYCIiIlJxbKs+AKDv6fp4+9U2N0w1owIkIiJSSdn+SAbA2qi3yUmqHxUgERGRSijrj99Y638CAGvUX80NUw2pAImIiFRCX381nXPu0CLLg+Y33WJ2nGpHBUhERKQSsu1YAoDVs43JSaonFSAREZFKxrDbSTTOL3+3drjb5DTVkwqQiIhIJbPjuy854JePdx701tXfK4QKkIiISCVjW/UeAH1OB+LjX9fkNNWTCpCIiEglY/t9PQDWhrr2V0VRARIREalETh49xBr/4wBYbx1pcprqSwVIRESkEvnmq7fIc4fmWTVoER5ldpxqSwVIRESkErH9+AUAVo/W5gap5lSAREREKgnDbsdm/ASAtb2u/l6RVIBEREQqiV0pCaT55eN1Dvro6u8VSgVIRESkkrB9e375e++T9fANCDQ5TfWmAiQiIlJJ2DLWAmBt2NPkJNWfCpCIiEglcOpYBqtrHQPAesujJqep/lSAREREKoFvv3qb3BrQ9GQNbgiPMTtOtacCJCIiUgnYfvwcAKt7Kyxu+vVc0Uz/hGfMmEHTpk3x9vYmPDycNWvWFDk2PT2d++67j5YtW+Lm5sbYsWMLHbdw4ULatGmDl5cXbdq04fPPP6+g9CIiIlfPsNux5e8GwHrjQJPTuAZTC9CCBQsYO3Ys48ePZ8uWLfTs2ROr1UpaWlqh43Nycqhfvz7jx4+nQ4cOhY5JTk5m8ODBDBkyhK1btzJkyBDuvfdeNmzYUJFvRUREpMx+2ryM/bXO4XkO+vZ/0uw4LsFiGIZh1ot37dqVTp068c477zi2tW7dmjvvvJOJEycW+9w+ffpw0003MXXqVKftgwcPJisrC5vN5tgWGxtLnTp1mDdvXolyZWVlERAQQGZmJv7+/iV/QyIiImUwddJAnsr+gtuO1yVp6lGz41RZpfn9bdoRoNzcXDZv3kx0dLTT9ujoaNavX1/m/SYnJxfYZ0xMTLH7zMnJISsry+kmIiJyrdjSz0//sAbfbHIS12FaATpy5Aj5+fkEBQU5bQ8KCiIjI6PM+83IyCj1PidOnEhAQIDjFhISUubXFxERKY0zmUdYVev8UR9r3xEmp3Edpk+CtlgsTvcNwyiwraL3GRcXR2ZmpuN24MCBq3p9ERGRkvp26Vvk1ICwk+60iuhndhyXUcOsFw4MDMTd3b3AkZnDhw8XOIJTGsHBwaXep5eXF15eXmV+TRERkbKy/bAIfMDq3lLL368h0z5pT09PwsPDSUpKctqelJRE9+7dy7zfyMjIAvtcvnz5Ve1TRESkIhh2O7ZzOwGwtrvT3DAuxrQjQADjxo1jyJAhdO7cmcjISN59913S0tIYOXIkcP6rqYMHDzJnzhzHc1JTUwE4deoUf/zxB6mpqXh6etKmTRsAxowZQ69evZg0aRIDBgxg8eLFrFixgrVr117z9yciIlKcPd8n8cuF5e+39B9ldhyXYmoBGjx4MEePHmXChAmkp6fTrl07EhISCAsLA86f+PDycwJ17NjR8ffNmzczd+5cwsLC2L9/PwDdu3dn/vz5vPDCC7z44os0b96cBQsW0LVr12v2vkREREoi8Zt3Aeh5sg5+dYNNTuNaTD0PUGWl8wCJiMi1YH2qPom1j/Avz/48HbfU7DhVXpU4D5CIiIgrO5t1jJU1jwBg7a3l79eaCpCIiIgJVn71FtkeEHLKnTbd7jA7jstRARIRETGBbetCAKyWFlr+bgJ94iIiIiaw5V1Y/t72TnODuCgVIBERkWvs5y1f87N/Hh75cOvtWv5uBhUgERGRayxxxUwAbs6qTa16jUxO45pUgERERK4x26FVAFgb6CoFZlEBEhERuYayT53g25p/ABDb6xGT07guFSAREZFraNVXb3PWA6475Ua77gPNjuOyVIBERESuIVvqfwGwouXvZtInLyIicg3ZcrcDYG3zJ5OTuDYVIBERkWvkl60r+ck/jxr5cNvto82O49JUgERERK4RW9IMAHpkBeBfv7HJaVybCpCIiMg1knjwwvL3+pEmJxEVIBERkWsg+9QJvvE9DEBsz4dNTiMqQCIiItfAGttMznhCo9NutL/5brPjuDwVIBERkWvAtuUzAGKN5lr+Xgnon4CIiMg1YMv+EQBrqztMTiKgAiQiIlLh9v+4ll0Bubjbtfy9slABEhERqWC2ZW8D0D3Tn9pBYSanEVABEhERqXCJv60EwBrYzdwg4qACJCIiUoFyTmfxtW8GANaeuvp7ZaECJCIiUoHWJs7itCcEn3ajQ897zI4jF6gAiYiIVCDb9wsAiLU30/L3SkT/JERERCqQ7ezF5e+3m5xELqUCJCIiUkHSdiSzIyAHNztE9dfy98pEBUhERKSC2Ja9BUBkZi3qNGxqchq5lAqQiIhIBbGlfQOAtV5Xk5PI5VSAREREKkDu2VP/W/7eY6i5YaQAFSAREZEKsC7xXU55QtAZN27qPdjsOHIZFSAREZEKYNs0H4CY/Ca4udcwOY1cTgVIRESkAtjObgPAekN/k5NIYVSAREREytmBnRv48cLy9+jbx5gdRwqhAiQiIlLOEi9c/b1rph91GzU3OY0URgVIRESknNl+XQGAtW4Xk5NIUVSAREREylFe9hlW+KQDYO3+kMlppCgqQCIiIuVo/bL3OOkFDc5Y6NT3PrPjSBFUgERERMqRLWUeADH5TbX8vRJTARIRESlHttNbAYi9PtbkJFIcFSAREZFycvCnTWyrnY3FgGhd/b1SUwESEREpJ4mJ56/+3iWzJoEhLU1OI8VRARIRESkntv0Xlr/XjjA5iVyJCpCIiEg5yMs+Q5L3QQCskQ+anEauRAVIRESkHHyX9CFZXhB41kLnW4eYHUeuQAVIRESkHNg2zgUgJi9My9+rABUgERGRcmA7lQpo+XtVoQIkIiJyldL3ppJa+ywWA2K0/L1KUAESERG5SokJ0wDonFmT+qGtTU4jJaECJCIicpVs+5IAsAaEm5xESkoFSERE5Cqcy80myevC8vduWv1VVagAiYiIXIXvln/ICW+DemctRNyq8/9UFSpAIiIiVyHxwvL36LxQ3D08TU4jJaUCJCIichVsJ78HwNpcy9+rEtML0IwZM2jatCne3t6Eh4ezZs2aYsevWrWK8PBwvL29adasGTNnznR6PD4+HovFUuCWnZ1dkW9DRERcUMYv2/i+9lkAoq1PmpxGSsPUArRgwQLGjh3L+PHj2bJlCz179sRqtZKWllbo+H379tGvXz969uzJli1b+Nvf/sbo0aNZuHCh0zh/f3/S09Odbt7e3tfiLYmIiAtZZpsOQPgJX4KatjM5jZSGqefqnjJlCsOGDWP48OEATJ06lWXLlvHOO+8wceLEAuNnzpxJaGgoU6dOBaB169Zs2rSJ119/nUGDBjnGWSwWgoODS5wjJyeHnJwcx/2srKwyviMREXEltr3LIACs/p3MjiKlZNoRoNzcXDZv3kx0dLTT9ujoaNavX1/oc5KTkwuMj4mJYdOmTeTl5Tm2nTp1irCwMBo3bsztt9/Oli1bis0yceJEAgICHLeQkJAyvisREXEV53KzWe71GwDWrg+YnEZKy7QCdOTIEfLz8wkKCnLaHhQUREZGRqHPycjIKHT8uXPnOHLkCACtWrUiPj6eJUuWMG/ePLy9venRowd79uwpMktcXByZmZmO24EDB67y3YmISHW3ccVHHPc2qJNtoWvUw2bHkVIy/XK1FovF6b5hGAW2XWn8pdu7detGt27dHI/36NGDTp06MX36dKZNm1boPr28vPDy8ipTfhERcU2JGz4BN4jOaazl71WQaUeAAgMDcXd3L3C05/DhwwWO8lwUHBxc6PgaNWpQr169Qp/j5uZGREREsUeARERESsuWtRkAa/MYk5NIWZhWgDw9PQkPDycpKclpe1JSEt27dy/0OZGRkQXGL1++nM6dO+Ph4VHocwzDIDU1lYYNG5ZPcBERcXmH929nU+0zAMRYR5mcRsrC1GXw48aN4/333+fDDz9k586dPPXUU6SlpTFy5Ejg/NycBx/832nFR44cya+//sq4cePYuXMnH374IR988AFPP/20Y8yrr77KsmXL+OWXX0hNTWXYsGGkpqY69ikiInK1liWcX/7e8YQPwc3am5xGysLUOUCDBw/m6NGjTJgwgfT0dNq1a0dCQgJhYWEApKenO50TqGnTpiQkJPDUU0/x9ttv06hRI6ZNm+a0BP7EiRM8+uijZGRkEBAQQMeOHVm9ejVdunS55u9PRESqJ9veRPAHa62OZkeRMrIYF2cRi0NWVhYBAQFkZmbi7+9vdhwREalE8vNyafCiN8d8DNaEv83Ntz9udiS5oDS/v02/FIaIiEhVkvL1HI75GNTOttAt+hGz40gZqQCJiIiUgu27/wAQlXMdNTx1maWqSgVIRESkFBIzLyx/bxplchK5GipAIiIiJfRH2k5SAk4DENtvtMlp5GqoAImIiJTQ8oTpGBbocMKbhs1vMjuOXAUVIBERkRKy7bEBYPW7ydwgctVUgERERErAnn+OZR6/AmCNuM/kNHK1VIBERERKYNPX/+GIj4F/DkRGDzM7jlwlFSAREZESsCXPASAq+zo8vH1NTiNXSwVIRESkBBJPbALA2uQ2k5NIeVABEhERuYKjv+1hQ8ApAGJjnzQ5jZQHFSAREZErWP7VNAwLtD/hzXU3dDY7jpQDFSAREZErsO1JACC2ZnuTk0h5UQESEREphj3/HInu+wCwdv6LyWmkvKgAiYiIFOP7b+fyh69BrRzoEfuo2XGknKgAiYiIFMO2/iMAbjvbUMvfqxEVIBERkWLYjm0EwBqm5e/ViQqQiIhIEY4d2utY/m61jjI5jZQnFSAREZEiJH01DbsbtMv0onHLCLPjSDlSARIRESmCbfdXAFh9tPy9ulEBEhERKcSly99jwwebnEbKmwqQiIhIIVJXLeB3Xzt+uXCz9TGz40g5UwESEREphG1dPAC3ngnG08fP3DBS7lSARERECmE7ugEAa+gtJieRiqACJCIicpnj6ftIDjgJgDVGV3+vjlSARERELrMiYTp2N2iT6UVom0iz40gFUAESERG5jG3XUgCsPu1MTiIVRQVIRETkEobdTqJlLwDWTlr+Xl2pAImIiFxi65rPSK9pp2Yu3Byr5e/VlQqQiIjIJWxrPgTgljNBeNX0NzmNVBQVIBERkUvYjnwHgLVxX5OTSEVSARIREbngxO+/sj4gCwBrzBMmp5GKpAIkIiJywddfvUW+G7TK9KRJu5vNjiMVSAVIRETkAtvOJQBYvbX8vbpTARIREeHC8nd+BsDa8R6T00hFUwESEREBkhPf46CfHd9c6GkdaXYcqWA1zA4gIiJyrR1P38emtQtI2fUNKcd+ZKPH7xyqaQeg75kGePvVNjegVDgVIBERqdbOZB5hy9rPSPlxOSmHt5DCIfb45/1vQO3zf7jZ4cYsb+Jue8WMmHKNqQCJiEi1kZd9hu0bviRly1dsPLiRlHO/8qN/NvkXJ3xccl7D5lk1iKAREfVvoku7GDr2uJuadRqYkluuPRUgERGpkgy7nZ+3fM3GlM9J+TWZlLN7+d7vJNkeFwb4/W9s8Gk3uuQ1IKJOWyJa9qVzj3up17iFKbmlclABEhGRKuHgT5tISV7Ixp9XkXJyN5t8jnPC2zj/oPeFGxCQDZ3P1iGiVku6NO9FROTdXNciHIub1v3I/6gAiYhIpXPs0F42rf2UlN0XJykfJv3CJGVqAHXO/9XrHHQ85UcX7+ZEhEYS0flPtOgUhZu7fr1J8fQTIiIipro4SXnjD8tI+SOVFA7xcxGTlNtleRNRI5Qu10UQcVN/2nUbgIe3rym5pWpTARIRkWsmL/sMP363mJTUr0g5uImN535lezGTlLtwHRH1byKiXbQmKUu5UgESEZEKYc8/d2GS8hekpJ2fpLzF71Shk5QbnnYjIq8BXeq2I6LlLXS++V7qNmpuSm5xDSpAIiJy1Qy7nYN7NpOS/F9S9q5h48ldbPI5TuaFicmXT1KOOFuXiFotiWjeky7d7+G6GzqbFV1clAqQiIiU2rFDe0lZM5+U3d+Scnw7Gz0Ok1HIJGXvvPOTlCN8mtMlrDsRnQdwfcdbNUlZTKefQBERKdbp44fZsu6/bPzxf5OU9/qf+9+A2uf/cHdMUg4j4rrOdOl4B2273qFJylIpqQCJiIhDXvYZflj/OSlbE0g5tImN+Wlsr5WNvZBJytdneRBBI7o06Hh+kvLN9+AbEGhKbpHSUgESEXFR9vxz7Pk+iY0pi89PUs75hdSaRU9S7pLXgIi67ejS6lY63zyYOg2bmpJbpDyoAImIuADDbue33SmkfLeQjXtXk3LqJzb5HifL68IAnws3oHa2hc5n69DFvxURzXsRETlIk5Sl2lEBEhGpho7+toeUtQtI+enCJGXPP/jd98IkZQ+cJil3OlXrf5OUI+7k+o636rIRUu2ZXoBmzJjBv/71L9LT02nbti1Tp06lZ8+eRY5ftWoV48aNY/v27TRq1Ihnn32WkSNHOo1ZuHAhL774Inv37qV58+a89tprDBw4sKLfioiIKU4fP8z3az8lZXsSGw9vIcUtnV9qFT1JuYtHEyIaRRDRsb8mKYvLMrUALViwgLFjxzJjxgx69OjBrFmzsFqt7Nixg9DQ0ALj9+3bR79+/RgxYgQff/wx69at4/HHH6d+/foMGjQIgOTkZAYPHsz//d//MXDgQD7//HPuvfde1q5dS9euXa/1WxQRKVe5Z0/xw/ovzk9STj8/SXlHrZz/TVIO+N/YFhcnKQd1IqJdDDf1GKRJyiIXWAzDMMx68a5du9KpUyfeeecdx7bWrVtz5513MnHixALjn3vuOZYsWcLOnTsd20aOHMnWrVtJTk4GYPDgwWRlZWGz2RxjYmNjqVOnDvPmzStRrqysLAICAsjMzMTf3//KTyihnNNZpO/bVm77k+IZdnv57MeobPspn39ly/PzOX8zsNvPYdgNp21Of9oL2XbJ3+32/EIeL9mfdvsl++Li9kvHXPg7BbfbjfzixzjuX77vS557cYzT2Mv35zzOfvn+i/kzM/ckm3J+IdXvNDmF/K9ro9NudMkLIqJuOyJa3aJJyuKSSvP727QjQLm5uWzevJnnn3/eaXt0dDTr168v9DnJyclER0c7bYuJieGDDz4gLy8PDw8PkpOTeeqppwqMmTp1apFZcnJyyMnJcdzPysoq5bspmS1rPiVyw4gK2beIVBOWy/686LJJyhFn6xDh34ou1/cmIvJuGrXodA1DilR9phWgI0eOkJ+fT1BQkNP2oKAgMjIyCn1ORkZGoePPnTvHkSNHaNiwYZFjitonwMSJE3n11VfL+E5Kzs3NHZ+8K4+rjCymHSe8Opf/DjF9P+X0OVa+PBYsgJtxPpvl4p9YLvn7xe2WQu+7Xf6Y03OvvN3twr2C4yyXjS34p9ul2yw49lRw/GXbLJZLnu+8zek5lqLvu1ncLnltS+HPsVjwdveiQ+POmqQsUk5MnwRtsTj/p9wwjALbrjT+8u2l3WdcXBzjxo1z3M/KyiIkJOTK4UupS/TDnIl+uNz3KyIiIqVjWgEKDAzE3d29wJGZw4cPFziCc1FwcHCh42vUqEG9evWKHVPUPgG8vLzw8vIq8nERERGpXkw7hurp6Ul4eDhJSUlO25OSkujevXuhz4mMjCwwfvny5XTu3BkPD49ixxS1TxEREXE9pn4FNm7cOIYMGULnzp2JjIzk3XffJS0tzXFen7i4OA4ePMicOXOA8yu+3nrrLcaNG8eIESNITk7mgw8+cFrdNWbMGHr16sWkSZMYMGAAixcvZsWKFaxdu9aU9ygiIiKVj6kFaPDgwRw9epQJEyaQnp5Ou3btSEhIICwsDID09HTS0tIc45s2bUpCQgJPPfUUb7/9No0aNWLatGmOcwABdO/enfnz5/PCCy/w4osv0rx5cxYsWKBzAImIiIiDqecBqqwq6jxAIiIiUnFK8/tb6yhFRETE5agAiYiIiMtRARIRERGXowIkIiIiLkcFSERERFyOCpCIiIi4HBUgERERcTkqQCIiIuJyVIBERETE5Zh6KYzK6uLJsbOyskxOIiIiIiV18fd2SS5yoQJUiJMnTwIQEhJichIREREprZMnTxIQEFDsGF0LrBB2u51Dhw5Rq1YtLBZLue47KyuLkJAQDhw4oOuMXYE+q5LTZ1Vy+qxKTp9V6ejzKrmK+qwMw+DkyZM0atQIN7fiZ/noCFAh3NzcaNy4cYW+hr+/v/4FKSF9ViWnz6rk9FmVnD6r0tHnVXIV8Vld6cjPRZoELSIiIi5HBUhERERcjgrQNebl5cXLL7+Ml5eX2VEqPX1WJafPquT0WZWcPqvS0edVcpXhs9IkaBEREXE5OgIkIiIiLkcFSERERFyOCpCIiIi4HBUgERERcTkqQJVATk4ON910ExaLhdTUVLPjVEp/+tOfCA0Nxdvbm4YNGzJkyBAOHTpkdqxKZ//+/QwbNoymTZvi4+ND8+bNefnll8nNzTU7WqX12muv0b17d3x9faldu7bZcSqVGTNm0LRpU7y9vQkPD2fNmjVmR6qUVq9ezR133EGjRo2wWCx88cUXZkeqlCZOnEhERAS1atWiQYMG3Hnnnezevdu0PCpAlcCzzz5Lo0aNzI5RqfXt25dPP/2U3bt3s3DhQvbu3cvdd99tdqxKZ9euXdjtdmbNmsX27dt54403mDlzJn/729/MjlZp5ebmcs899/DXv/7V7CiVyoIFCxg7dizjx49ny5Yt9OzZE6vVSlpamtnRKp3Tp0/ToUMH3nrrLbOjVGqrVq3iiSee4LvvviMpKYlz584RHR3N6dOnzQlkiKkSEhKMVq1aGdu3bzcAY8uWLWZHqhIWL15sWCwWIzc31+wold7kyZONpk2bmh2j0ps9e7YREBBgdoxKo0uXLsbIkSOdtrVq1cp4/vnnTUpUNQDG559/bnaMKuHw4cMGYKxatcqU19cRIBP9/vvvjBgxgv/85z/4+vqaHafKOHbsGJ988gndu3fHw8PD7DiVXmZmJnXr1jU7hlQhubm5bN68mejoaKft0dHRrF+/3qRUUt1kZmYCmPbfJxUgkxiGwdChQxk5ciSdO3c2O06V8Nxzz1GzZk3q1atHWloaixcvNjtSpbd3716mT5/OyJEjzY4iVciRI0fIz88nKCjIaXtQUBAZGRkmpZLqxDAMxo0bx80330y7du1MyaACVM5eeeUVLBZLsbdNmzYxffp0srKyiIuLMzuyaUr6WV30zDPPsGXLFpYvX467uzsPPvgghoucyLy0nxXAoUOHiI2N5Z577mH48OEmJTdHWT4vKchisTjdNwyjwDaRsnjyySfZtm0b8+bNMy2DLoVRzo4cOcKRI0eKHdOkSRP+/Oc/8+WXXzr9xyQ/Px93d3fuv/9+Pvroo4qOarqSflbe3t4Ftv/222+EhISwfv16IiMjKypipVHaz+rQoUP07duXrl27Eh8fj5uba/2/Tll+tuLj4xk7diwnTpyo4HSVX25uLr6+vnz22WcMHDjQsX3MmDGkpqayatUqE9NVbhaLhc8//5w777zT7CiV1qhRo/jiiy9YvXo1TZs2NS1HDdNeuZoKDAwkMDDwiuOmTZvG3//+d8f9Q4cOERMTw4IFC+jatWtFRqw0SvpZFeZib8/JySnPSJVWaT6rgwcP0rdvX8LDw5k9e7bLlR+4up8tAU9PT8LDw0lKSnIqQElJSQwYMMDEZFKVGYbBqFGj+Pzzz1m5cqWp5QdUgEwTGhrqdN/Pzw+A5s2b07hxYzMiVVobN25k48aN3HzzzdSpU4dffvmFl156iebNm7vE0Z/SOHToEH369CE0NJTXX3+dP/74w/FYcHCwickqr7S0NI4dO0ZaWhr5+fmOc3Fdf/31jn8vXdG4ceMYMmQInTt3JjIyknfffZe0tDTNJyvEqVOn+Pnnnx339+3bR2pqKnXr1i3w33pX9sQTTzB37lwWL15MrVq1HPPJAgIC8PHxufaBTFl7JgXs27dPy+CLsG3bNqNv375G3bp1DS8vL6NJkybGyJEjjd9++83saJXO7NmzDaDQmxTuoYceKvTz+vbbb82OZrq3337bCAsLMzw9PY1OnTqZtly5svv2228L/Rl66KGHzI5WqRT136bZs2ebkkdzgERERMTluN7kABEREXF5KkAiIiLiclSARERExOWoAImIiIjLUQESERERl6MCJCIiIi5HBUhERERcjgqQiIiIuBwVIBEpsT59+jB27FizYxTq6NGjNGjQgP379wOwcuVKLBZLhV/ctKyvEx8fT+3atUv1nIiICBYtWlSq54hI4VSARMQ06enp3HfffbRs2RI3N7ciy9XChQtp06YNXl5etGnThs8//7zAmIkTJ3LHHXfQpEmTig1tohdffJHnn38eu91udhSRKk8FSERMk5OTQ/369Rk/fjwdOnQodExycjKDBw9myJAhbN26lSFDhnDvvfeyYcMGx5izZ8/ywQcfMHz48GsV3RT9+/cnMzOTZcuWmR1FpMpTARKRMjl+/DgPPvggderUwdfXF6vVyp49e5zGvPfee4SEhODr68vAgQOZMmWK09c+TZo04c033+TBBx8kICCg0NeZOnUqUVFRxMXF0apVK+Li4rj11luZOnWqY4zNZqNGjRpERkYWmffo0aP85S9/oXHjxvj6+nLjjTcyb948pzF9+vRh1KhRjB07ljp16hAUFMS7777L6dOnefjhh6lVqxbNmzfHZrMV2P+6devo0KED3t7edO3alR9++MHp8fj4eEJDQx2fxdGjR50e37t3LwMGDCAoKAg/Pz8iIiJYsWKF0xh3d3f69etXILeIlJ4KkIiUydChQ9m0aRNLliwhOTkZwzDo168feXl5wPlCMHLkSMaMGUNqaipRUVG89tprpX6d5ORkoqOjnbbFxMSwfv16x/3Vq1fTuXPnYveTnZ1NeHg4S5cu5ccff+TRRx9lyJAhTkeSAD766CMCAwPZuHEjo0aN4q9//Sv33HMP3bt35/vvvycmJoYhQ4Zw5swZp+c988wzvP7666SkpNCgQQP+9Kc/OT6LDRs28Mgjj/D444+TmppK3759+fvf/+70/FOnTtGvXz9WrFjBli1biImJ4Y477iAtLc1pXJcuXVizZk3JPjwRKZop16AXkSqpd+/expgxY4yffvrJAIx169Y5Hjty5Ijh4+NjfPrpp4ZhGMbgwYON/v37Oz3//vvvNwICAord9+U8PDyMTz75xGnbJ598Ynh6ejruDxgwwHjkkUecxnz77bcGYBw/frzI99OvXz/j//2//+eU4eabb3bcP3funFGzZk1jyJAhjm3p6ekGYCQnJzu9zvz58x1jjh49avj4+BgLFiwwDMMw/vKXvxixsbFOrz148OAiP4uL2rRpY0yfPt1p2+LFiw03NzcjPz+/2OeKSPF0BEhESm3nzp3UqFGDrl27OrbVq1ePli1bsnPnTgB2795Nly5dnJ53+f2SslgsTvcNw3DadvbsWby9vYvdR35+Pq+99hrt27enXr16+Pn5sXz58gJHWNq3b+/4u7u7O/Xq1ePGG290bAsKCgLg8OHDTs+79Ou3unXrOn0WO3fuLPD13OX3T58+zbPPPkubNm2oXbs2fn5+7Nq1q0A+Hx8f7HY7OTk5xb5fESleDbMDiEjVYxhGkdsvFpPLS0pxzytOcHAwGRkZTtsOHz7sKCIAgYGBHD9+vNj9/Pvf/+aNN95g6tSp3HjjjdSsWZOxY8eSm5vrNM7Dw8PpvsVicdp28T2VZCXWpZ/FlTzzzDMsW7aM119/neuvvx4fHx/uvvvuAvmOHTuGr68vPj4+V9yniBRNR4BEpNTatGnDuXPnnObPHD16lJ9++onWrVsD0KpVKzZu3Oj0vE2bNpX6tSIjI0lKSnLatnz5crp37+6437FjR3bs2FHsftasWcOAAQN44IEH6NChA82aNSswaftqfPfdd46/Hz9+nJ9++olWrVoB5z+vSx+/fPzFfEOHDmXgwIHceOONBAcHO85pdKkff/yRTp06lVtuEVelAiQipdaiRQsGDBjAiBEjWLt2LVu3buWBBx7guuuuY8CAAQCMGjWKhIQEpkyZwp49e5g1axY2m63AUaHU1FRSU1M5deoUf/zxB6mpqU5lZsyYMSxfvpxJkyaxa9cuJk2axIoVK5zOGRQTE8P27duLPQp0/fXXk5SUxPr169m5cyePPfZYgSNLV2PChAl8/fXX/PjjjwwdOpTAwEDuvPNOAEaPHk1iYiKTJ0/mp59+4q233iIxMbFAvkWLFpGamsrWrVu57777Cj3KtGbNmgKTwkWk9FSARKRMZs+eTXh4OLfffjuRkZEYhkFCQoLj66IePXowc+ZMpkyZQocOHUhMTOSpp54qMFenY8eOdOzYkc2bNzN37lw6duxIv379HI93796d+fPnM3v2bNq3b098fDwLFixwmn9044030rlzZz799NMi87744ot06tSJmJgY+vTpQ3BwsKOglId//vOfjBkzhvDwcNLT01myZAmenp4AdOvWjffff5/p06dz0003sXz5cl544QWn57/xxhvUqVOH7t27c8cddxATE1PgSM/BgwdZv349Dz/8cLnlFnFVFqMsX8qLiJTBiBEj2LVrV4Us405ISODpp5/mxx9/xM2tev6/3TPPPENmZibvvvuu2VFEqjxNghaRCvP6668TFRVFzZo1sdlsfPTRR8yYMaNCXqtfv37s2bOHgwcPEhISUiGvYbYGDRrw9NNPmx1DpFrQESARqTD33nsvK1eu5OTJkzRr1oxRo0YxcuRIs2OJiKgAiYiIiOupnl+Ui4iIiBRDBUhERERcjgqQiIiIuBwVIBEREXE5KkAiIiLiclSARERExOWoAImIiIjLUQESERERl/P/AZaP27Xvhj1uAAAAAElFTkSuQmCC",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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_72209/4162706317.py:7: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.\n",
|
||
" cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 2000x1400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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_72209/3777801602.py:7: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.\n",
|
||
" cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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|
||
"text/plain": [
|
||
"<Figure size 2000x1400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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_72209/438060758.py:10: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.\n",
|
||
" cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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|
||
"text/plain": [
|
||
"<Figure size 2000x1400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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_72209/3544313922.py:9: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.\n",
|
||
" cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 2000x1400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"clf_lasso = skl.Lasso(alpha=_lambda).fit(X_train, y_train)\n",
|
||
"J_lasso_sk = clf_lasso.coef_.reshape(L, L)\n",
|
||
"fig = plt.figure(figsize=(20, 14))\n",
|
||
"im = plt.imshow(J_lasso_sk, **cmap_args)\n",
|
||
"plt.title(\"Lasso from Scikit-learn\", fontsize=18)\n",
|
||
"plt.xticks(fontsize=18)\n",
|
||
"plt.yticks(fontsize=18)\n",
|
||
"cb = fig.colorbar(im)\n",
|
||
"cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "57839941",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"It is quite striking how LASSO breaks the symmetry of the coupling\n",
|
||
"constant as opposed to ridge and OLS. We get a sparse solution with\n",
|
||
"$J_{j, j + 1} = -1$.\n",
|
||
"\n",
|
||
"We see how the different models perform for a different set of values for $\\lambda$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 28,
|
||
"id": "0e3bbb4e",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
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"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_coordinate_descent.py:695: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 3.924e+00, tolerance: 1.797e+00\n",
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|
||
"text/plain": [
|
||
"<Figure size 3200x5400 with 30 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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": {
|
||
"image/png": 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|
||
"text/plain": [
|
||
"<Figure size 2000x1400 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"fig = plt.figure(figsize=(20, 14))\n",
|
||
"\n",
|
||
"colors = {\n",
|
||
" \"ols_sk\": \"r\",\n",
|
||
" \"ridge_sk\": \"y\",\n",
|
||
" \"lasso_sk\": \"c\"\n",
|
||
"}\n",
|
||
"\n",
|
||
"for key in train_errors:\n",
|
||
" plt.semilogx(\n",
|
||
" lambdas,\n",
|
||
" train_errors[key],\n",
|
||
" colors[key],\n",
|
||
" label=\"Train {0}\".format(key),\n",
|
||
" linewidth=4.0\n",
|
||
" )\n",
|
||
"\n",
|
||
"for key in test_errors:\n",
|
||
" plt.semilogx(\n",
|
||
" lambdas,\n",
|
||
" test_errors[key],\n",
|
||
" colors[key] + \"--\",\n",
|
||
" label=\"Test {0}\".format(key),\n",
|
||
" linewidth=4.0\n",
|
||
" )\n",
|
||
"plt.legend(loc=\"best\", fontsize=18)\n",
|
||
"plt.xlabel(r\"$\\lambda$\", fontsize=18)\n",
|
||
"plt.ylabel(r\"$R^2$\", fontsize=18)\n",
|
||
"plt.tick_params(labelsize=18)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9c10be56",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"From the above figure we can see that LASSO with $\\lambda = 10^{-2}$\n",
|
||
"achieves a very good accuracy on the test set. This by far surpasses the\n",
|
||
"other models for all values of $\\lambda$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "efce3b63",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Exercises and Projects\n",
|
||
"\n",
|
||
"The main aim of this project is to study in more detail various\n",
|
||
"regression methods, including the Ordinary Least Squares (OLS) method,\n",
|
||
"The total score is **100** points. Each subtask has its own final score.\n",
|
||
"\n",
|
||
"We will first study how to fit polynomials to a specific\n",
|
||
"two-dimensional function called [Franke's\n",
|
||
"function](http://www.dtic.mil/dtic/tr/fulltext/u2/a081688.pdf). This\n",
|
||
"is a function which has been widely used when testing various\n",
|
||
"interpolation and fitting algorithms. Furthermore, after having\n",
|
||
"established the model and the method, we will employ resamling\n",
|
||
"techniques such as cross-validation and/or bootstrap in order to perform a\n",
|
||
"proper assessment of our models. We will also study in detail the\n",
|
||
"so-called Bias-Variance trade off.\n",
|
||
"\n",
|
||
"The Franke function, which is a weighted sum of four exponentials reads as follows"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ef5a4df0",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\begin{align*}\n",
|
||
"f(x,y) &= \\frac{3}{4}\\exp{\\left(-\\frac{(9x-2)^2}{4} - \\frac{(9y-2)^2}{4}\\right)}+\\frac{3}{4}\\exp{\\left(-\\frac{(9x+1)^2}{49}- \\frac{(9y+1)}{10}\\right)} \\\\\n",
|
||
"&+\\frac{1}{2}\\exp{\\left(-\\frac{(9x-7)^2}{4} - \\frac{(9y-3)^2}{4}\\right)} -\\frac{1}{5}\\exp{\\left(-(9x-4)^2 - (9y-7)^2\\right) }.\n",
|
||
"\\end{align*}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b085eff4",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The function will be defined for $x,y\\in [0,1]$. Our first step will\n",
|
||
"be to perform an OLS regression analysis of this function, trying out\n",
|
||
"a polynomial fit with an $x$ and $y$ dependence of the form $[x, y,\n",
|
||
"x^2, y^2, xy, \\dots]$. We will also include bootstrap first as\n",
|
||
"a resampling technique. After that we will include the cross-validation technique. As in homeworks 1 and 2, we can use a uniform\n",
|
||
"distribution to set up the arrays of values for $x$ and $y$, or as in\n",
|
||
"the example below just a set of fixed \n",
|
||
"values for $x$ and $y$ with a given step\n",
|
||
"size. We will fit a\n",
|
||
"function (for example a polynomial) of $x$ and $y$. Thereafter we\n",
|
||
"will repeat much of the same procedure using the Ridge and Lasso\n",
|
||
"regression methods, introducing thus a dependence on the bias\n",
|
||
"(penalty) $\\lambda$.\n",
|
||
"\n",
|
||
"Finally we are going to use (real) digital terrain data and try to\n",
|
||
"reproduce these data using the same methods. We will also try to go\n",
|
||
"beyond the second-order polynomials metioned above and explore \n",
|
||
"which polynomial fits the data best.\n",
|
||
"\n",
|
||
"The Python code for the Franke function is included here (it performs also a three-dimensional plot of it)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 30,
|
||
"id": "5056dccb",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"ename": "TypeError",
|
||
"evalue": "gca() got an unexpected keyword argument 'projection'",
|
||
"output_type": "error",
|
||
"traceback": [
|
||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||
"\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
|
||
"Cell \u001b[0;32mIn[30], line 9\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mrandom\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m random, seed\n\u001b[1;32m 8\u001b[0m fig \u001b[38;5;241m=\u001b[39m plt\u001b[38;5;241m.\u001b[39mfigure()\n\u001b[0;32m----> 9\u001b[0m ax \u001b[38;5;241m=\u001b[39m \u001b[43mfig\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgca\u001b[49m\u001b[43m(\u001b[49m\u001b[43mprojection\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43m3d\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m 11\u001b[0m \u001b[38;5;66;03m# Make data.\u001b[39;00m\n\u001b[1;32m 12\u001b[0m x \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marange(\u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m0.05\u001b[39m)\n",
|
||
"\u001b[0;31mTypeError\u001b[0m: gca() got an unexpected keyword argument 'projection'"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 0 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"from mpl_toolkits.mplot3d import Axes3D\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from matplotlib import cm\n",
|
||
"from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
|
||
"import numpy as np\n",
|
||
"from random import random, seed\n",
|
||
"\n",
|
||
"fig = plt.figure()\n",
|
||
"ax = fig.gca(projection='3d')\n",
|
||
"\n",
|
||
"# Make data.\n",
|
||
"x = np.arange(0, 1, 0.05)\n",
|
||
"y = np.arange(0, 1, 0.05)\n",
|
||
"x, y = np.meshgrid(x,y)\n",
|
||
"\n",
|
||
"\n",
|
||
"def FrankeFunction(x,y):\n",
|
||
" term1 = 0.75*np.exp(-(0.25*(9*x-2)**2) - 0.25*((9*y-2)**2))\n",
|
||
" term2 = 0.75*np.exp(-((9*x+1)**2)/49.0 - 0.1*(9*y+1))\n",
|
||
" term3 = 0.5*np.exp(-(9*x-7)**2/4.0 - 0.25*((9*y-3)**2))\n",
|
||
" term4 = -0.2*np.exp(-(9*x-4)**2 - (9*y-7)**2)\n",
|
||
" return term1 + term2 + term3 + term4\n",
|
||
"\n",
|
||
"\n",
|
||
"z = FrankeFunction(x, y)\n",
|
||
"\n",
|
||
"# Plot the surface.\n",
|
||
"surf = ax.plot_surface(x, y, z, cmap=cm.coolwarm,\n",
|
||
" linewidth=0, antialiased=False)\n",
|
||
"\n",
|
||
"# Customize the z axis.\n",
|
||
"ax.set_zlim(-0.10, 1.40)\n",
|
||
"ax.zaxis.set_major_locator(LinearLocator(10))\n",
|
||
"ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))\n",
|
||
"\n",
|
||
"# Add a color bar which maps values to colors.\n",
|
||
"fig.colorbar(surf, shrink=0.5, aspect=5)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f5e72aef",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"### Exercise: Ordinary Least Square (OLS) on the Franke function\n",
|
||
"\n",
|
||
"We will generate our own dataset for a function\n",
|
||
"$\\mathrm{FrankeFunction}(x,y)$ with $x,y \\in [0,1]$. The function\n",
|
||
"$f(x,y)$ is the Franke function. You should explore also the addition\n",
|
||
"of an added stochastic noise to this function using the normal\n",
|
||
"distribution $N(0,1)$.\n",
|
||
"\n",
|
||
"*Write your own code* (using either a matrix inversion or a singular\n",
|
||
"value decomposition from e.g., **numpy** ) or use your code from\n",
|
||
"homeworks 1 and 2 and perform a standard least square regression\n",
|
||
"analysis using polynomials in $x$ and $y$ up to fifth order. Find the\n",
|
||
"[confidence intervals](https://en.wikipedia.org/wiki/Confidence_interval) of the parameters (estimators) $\\beta$ by computing their\n",
|
||
"variances, evaluate the Mean Squared error (MSE)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0ba33237",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"MSE(\\hat{y},\\hat{\\tilde{y}}) = \\frac{1}{n}\n",
|
||
"\\sum_{i=0}^{n-1}(y_i-\\tilde{y}_i)^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1f9af2ef",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and the $R^2$ score function. If $\\tilde{\\hat{y}}_i$ is the predicted\n",
|
||
"value of the $i-th$ sample and $y_i$ is the corresponding true value,\n",
|
||
"then the score $R^2$ is defined as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "77d5b0f2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"R^2(\\hat{y}, \\tilde{\\hat{y}}) = 1 - \\frac{\\sum_{i=0}^{n - 1} (y_i - \\tilde{y}_i)^2}{\\sum_{i=0}^{n - 1} (y_i - \\bar{y})^2},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6c1f9df9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where we have defined the mean value of $\\hat{y}$ as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1d06102c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\bar{y} = \\frac{1}{n} \\sum_{i=0}^{n - 1} y_i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8fb40b08",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Your code has to include a scaling of the data (for example by\n",
|
||
"subtracting the mean value), and\n",
|
||
"a split of the data in training and test data. For this exercise you can\n",
|
||
"either write your own code or use for example the function for\n",
|
||
"splitting training data provided by the library **Scikit-Learn** (make\n",
|
||
"sure you have installed it). This function is called\n",
|
||
"$train\\_test\\_split$. **You should present a critical discussion of why and how you have scaled or not scaled the data**.\n",
|
||
"\n",
|
||
"It is normal in essentially all Machine Learning studies to split the\n",
|
||
"data in a training set and a test set (eventually also an additional\n",
|
||
"validation set). There\n",
|
||
"is no explicit recipe for how much data should be included as training\n",
|
||
"data and say test data. An accepted rule of thumb is to use\n",
|
||
"approximately $2/3$ to $4/5$ of the data as training data.\n",
|
||
"\n",
|
||
"You can easily reuse the solutions to your exercises from week 35 and week 36."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1701de47",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"### Exercise: Bias-variance trade-off and resampling techniques\n",
|
||
"\n",
|
||
"Our aim here is to study the bias-variance trade-off by implementing the **bootstrap** resampling technique.\n",
|
||
"\n",
|
||
"With a code which does OLS and includes resampling techniques, \n",
|
||
"we will now discuss the bias-variance trade-off in the context of\n",
|
||
"continuous predictions such as regression. However, many of the\n",
|
||
"intuitions and ideas discussed here also carry over to classification\n",
|
||
"tasks and basically all Machine Learning algorithms. \n",
|
||
"\n",
|
||
"Before you perform an analysis of the bias-variance trade-off on your test data, make\n",
|
||
"first a figure similar to Fig. 2.11 of Hastie, Tibshirani, and\n",
|
||
"Friedman. Figure 2.11 of this reference displays only the test and training MSEs. The test MSE can be used to \n",
|
||
"indicate possible regions of low/high bias and variance. You will most likely not get an\n",
|
||
"equally smooth curve!\n",
|
||
"\n",
|
||
"With this result we move on to the bias-variance trade-off analysis.\n",
|
||
"\n",
|
||
"Consider a\n",
|
||
"dataset $\\mathcal{L}$ consisting of the data\n",
|
||
"$\\mathbf{X}_\\mathcal{L}=\\{(y_j, \\boldsymbol{x}_j), j=0\\ldots n-1\\}$.\n",
|
||
"\n",
|
||
"Let us assume that the true data is generated from a noisy model"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "15110cdf",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{y}=f(\\boldsymbol{x}) + \\boldsymbol{\\epsilon}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "33046595",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Here $\\epsilon$ is normally distributed with mean zero and standard\n",
|
||
"deviation $\\sigma^2$.\n",
|
||
"\n",
|
||
"In our derivation of the ordinary least squares method we defined then\n",
|
||
"an approximation to the function $f$ in terms of the parameters\n",
|
||
"$\\boldsymbol{\\beta}$ and the design matrix $\\boldsymbol{X}$ which embody our model,\n",
|
||
"that is $\\boldsymbol{\\tilde{y}}=\\boldsymbol{X}\\boldsymbol{\\beta}$.\n",
|
||
"\n",
|
||
"The parameters $\\boldsymbol{\\beta}$ are in turn found by optimizing the means\n",
|
||
"squared error via the so-called cost function"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "84527747",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\boldsymbol{X},\\boldsymbol{\\beta}) =\\frac{1}{n}\\sum_{i=0}^{n-1}(y_i-\\tilde{y}_i)^2=\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right].\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "da2f876d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Here the expected value $\\mathbb{E}$ is the sample value. \n",
|
||
"\n",
|
||
"Show that you can rewrite this as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1845a7dc",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\frac{1}{n}\\sum_i(f_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\frac{1}{n}\\sum_i(\\tilde{y}_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\sigma^2.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d2f1d7d7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Explain what the terms mean, which one is the bias and which one is\n",
|
||
"the variance and discuss their interpretations.\n",
|
||
"\n",
|
||
"Perform then a bias-variance analysis of the Franke function by\n",
|
||
"studying the MSE value as function of the complexity of your model.\n",
|
||
"\n",
|
||
"Discuss the bias and variance trade-off as function\n",
|
||
"of your model complexity (the degree of the polynomial) and the number\n",
|
||
"of data points, and possibly also your training and test data using the **bootstrap** resampling method.\n",
|
||
"\n",
|
||
"Note also that when you calculate the bias, in all applications you don't know the function values $f_i$. You would hence replace them with the actual data points $y_i$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e898c902",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"### Exercise: Cross-validation as resampling techniques, adding more complexity\n",
|
||
"\n",
|
||
"The aim here is to write your own code for another widely popular\n",
|
||
"resampling technique, the so-called cross-validation method. Again,\n",
|
||
"before you start with cross-validation approach, you should scale your\n",
|
||
"data.\n",
|
||
"\n",
|
||
"Implement the $k$-fold cross-validation algorithm (write your own\n",
|
||
"code) and evaluate again the MSE function resulting\n",
|
||
"from the test folds. You can compare your own code with that from\n",
|
||
"**Scikit-Learn** if needed. \n",
|
||
"\n",
|
||
"Compare the MSE you get from your cross-validation code with the one\n",
|
||
"you got from your **bootstrap** code. Comment your results. Try $5-10$\n",
|
||
"folds. You can also compare your own cross-validation code with the\n",
|
||
"one provided by **Scikit-Learn**."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d23dc734",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"### Exercise: Ridge Regression on the Franke function with resampling\n",
|
||
"\n",
|
||
"Write your own code for the Ridge method, either using matrix\n",
|
||
"inversion or the singular value decomposition as done in the previous\n",
|
||
"exercise. Perform the same bootstrap analysis as in the\n",
|
||
"Exercise 2 (for the same polynomials) and the cross-validation in exercise 3 but now for different values of $\\lambda$. Compare and\n",
|
||
"analyze your results with those obtained in exercises 1-3. Study the\n",
|
||
"dependence on $\\lambda$.\n",
|
||
"\n",
|
||
"Study also the bias-variance trade-off as function of various values of\n",
|
||
"the parameter $\\lambda$. For the bias-variance trade-off, use the **bootstrap** resampling method. Comment your results."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "39a35330",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"### Exercise: Lasso Regression on the Franke function with resampling\n",
|
||
"\n",
|
||
"This exercise is essentially a repeat of the previous two ones, but now\n",
|
||
"with Lasso regression. Write either your own code (difficult and optional) or, in this case,\n",
|
||
"you can also use the functionalities of **Scikit-Learn** (recommended). \n",
|
||
"Give a\n",
|
||
"critical discussion of the three methods and a judgement of which\n",
|
||
"model fits the data best. Perform here as well an analysis of the bias-variance trade-off using the **bootstrap** resampling technique and an analysis of the mean squared error using cross-validation."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "44d9e821",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"### Exercise: Analysis of real data\n",
|
||
"\n",
|
||
"With our codes functioning and having been tested properly on a\n",
|
||
"simpler function we are now ready to look at real data. We will\n",
|
||
"essentially repeat in this exercise what was done in exercises 1-5. However, we\n",
|
||
"need first to download the data and prepare properly the inputs to our\n",
|
||
"codes. We are going to download digital terrain data from the website\n",
|
||
"<https://earthexplorer.usgs.gov/>,\n",
|
||
"\n",
|
||
"Or, if you prefer, we have placed selected datafiles at <https://github.com/CompPhysics/MachineLearning/tree/master/doc/Projects/2021/Project1/DataFiles>\n",
|
||
"\n",
|
||
"In order to obtain data for a specific region, you need to register as\n",
|
||
"a user (free) at this website and then decide upon which area you want\n",
|
||
"to fetch the digital terrain data from. In order to be able to read\n",
|
||
"the data properly, you need to specify that the format should be **SRTM\n",
|
||
"Arc-Second Global** and download the data as a **GeoTIF** file. The\n",
|
||
"files are then stored in *tif* format which can be imported into a\n",
|
||
"Python program using"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 31,
|
||
"id": "0a4e6d7e",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"scipy.misc.imread"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "16a73292",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Here is a simple part of a Python code which reads and plots the data\n",
|
||
"from such files"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 32,
|
||
"id": "168356a4",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"\"\"\"\n",
|
||
"import numpy as np\n",
|
||
"from imageio import imread\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from mpl_toolkits.mplot3d import Axes3D\n",
|
||
"from matplotlib import cm\n",
|
||
"\n",
|
||
"# Load the terrain\n",
|
||
"terrain1 = imread('SRTM_data_Norway_1.tif')\n",
|
||
"# Show the terrain\n",
|
||
"plt.figure()\n",
|
||
"plt.title('Terrain over Norway 1')\n",
|
||
"plt.imshow(terrain1, cmap='gray')\n",
|
||
"plt.xlabel('X')\n",
|
||
"plt.ylabel('Y')\n",
|
||
"plt.show()\n",
|
||
"\"\"\""
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e9ec3e68",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"If you should have problems in downloading the digital terrain data,\n",
|
||
"we provide two examples under the data folder of project 1. One is\n",
|
||
"from a region close to Stavanger in Norway and the other Møsvatn\n",
|
||
"Austfjell, again in Norway.\n",
|
||
"Feel free to produce your own terrain data.\n",
|
||
"\n",
|
||
"Alternatively, if you would like to use another data set, feel free to do so. This could be data close to your reseach area or simply a data set you found interesting. See for example [kaggle.com](https://www.kaggle.com/datasets) for examples.\n",
|
||
"\n",
|
||
"Our final part deals with the parameterization of your digital terrain\n",
|
||
"data (or your own data). We will apply all three methods for linear regression, the same type (or higher order) of polynomial\n",
|
||
"approximation and cross-validation as resampling technique to evaluate which\n",
|
||
"model fits the data best.\n",
|
||
"\n",
|
||
"At the end, you should present a critical evaluation of your results\n",
|
||
"and discuss the applicability of these regression methods to the type\n",
|
||
"of data presented here (either the terrain data we propose or other data sets)."
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.9.15"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
} |