{ "cells": [ { "cell_type": "markdown", "id": "5eb8c31b", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Classification II: Discriminative models\n", "\n", "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/git/https%3A%2F%2Fgitlab.in2p3.fr%2Fenergy4climate%2Fpublic%2Feducation%2Fmachine_learning_for_climate_and_energy/master?filepath=book%2Fnotebooks%2F06_classification_discriminative.ipynb)" ] }, { "cell_type": "markdown", "id": "3a485dc1", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "
\n", " Prerequisites\n", " \n", "- Generative models\n", "- Vector and matrix derivative\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "8790b2ae", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "
\n", " Learning Outcomes\n", " \n", "- Define a discriminative model.\n", "- Apply a logistic regression.\n", "- Perform a Fisher Linear discriminant analysis (F-LDA) for dimension reduction.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "fcd4e485", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Case study: Rain prediction\n", "\n", "We apply the following methods to the prediction of whether it rains ($C = 1$) or not ($C = 0$) from climate variables, as in the notebook [Classification I: Generative models](06_classification_generative.ipynb)." ] }, { "cell_type": "code", "execution_count": 46, "id": "dc7520d5", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "# Import data analysis modules\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "plt.rc('font', size=14)\n", "RC_COLORS = [d['color'] for d in plt.rcParams['axes.prop_cycle']]\n", "\n", "# Load data\n", "df = pd.read_csv(\"data/era5_paris_sf_2000_2009.csv\",\n", " index_col='time', parse_dates=True)\n", "\n", "# Normalize the variables\n", "df_norm = (df - df.mean()) /df.std()\n", "\n", "# Select variables and resample to daily values\n", "df_day = df_norm[['tp', 'sp', 't2m']].resample(\"D\").mean()\n", "\n", "# Assign tag to precipitation\n", "PRECIP_TH = -0.2 # normalized threshold\n", "df_day['tag'] = df_day['tp'].where(df_day['tp'] > PRECIP_TH, 0)\n", "df_day['tag'] = df_day['tag'].where(df_day['tp'] <= PRECIP_TH, 1)" ] }, { "cell_type": "markdown", "id": "2ed5ab39", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Discriminative models\n", "\n", "In the notebook [Classification I: Generative models](06_classification_generative.ipynb), the *Bayes' theorem* is applied to invert the classification problem: the focus is on class densities $\\boldsymbol x \\mapsto f_{\\boldsymbol X|C}(\\boldsymbol x | k)$ or the likelihood functions $k \\mapsto f_{\\boldsymbol X|C}(\\boldsymbol x | k)$.\n", "\n", "Here, we instead directly estimate the probability $P(C = k | \\boldsymbol X = \\boldsymbol x)$ to observe a class $k$ given an input $\\boldsymbol x$.\n", "\n", "If we know this probability for all classes, we can then assign an observation to the class that has the maximum probability according to the *Bayes classifier*." ] }, { "cell_type": "markdown", "id": "fe33e9e8", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Discriminative models based on regression\n", "\n", "We first consider to classification models that are based on regression:\n", "- linear regression and\n", "- logistic regression.\n", "\n", "Both are linear models (in the generalized sense)." ] }, { "cell_type": "markdown", "id": "54d14ee8", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Two-classes problem\n", "\n", "Let us consider a simple problem with only 2 classes: $C = 0$ or 1. We must have,\n", "\n", "$$ P(C = 0 | \\boldsymbol X = \\boldsymbol x) = 1 - P(C = 1 | \\boldsymbol X = \\boldsymbol x).$$\n", "\n", "Thus, setting $y(\\boldsymbol x) = P(C = 1 | \\boldsymbol X = \\boldsymbol x)$, we can assign a real number to the probability of the class $C = 1$ for each input.\n", "\n", "We can then apply the indicator function $I_{(0.5, +\\infty)}(y) = 1$ if $y > 0.5$, 0 otherwise, to assign points to the two classes.\n", "\n", "The *classification* problem thus translates into a *regression* problem." ] }, { "cell_type": "markdown", "id": "c738a3ca", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Linear regression for classification\n", "\n", "In linear regression for classification, the regression method is that of the Ordinary Least Square (OLS) applied to a target given by the indicator response, i.e. such that $y = 1$ if $k = 1$ else 0.\n", "\n", "The decision boundary is the set of $\\boldsymbol x$ such that $y(\\boldsymbol x) = \\beta_0 + \\boldsymbol \\beta^\\top \\boldsymbol x = 0.5$.\n", "\n", "For $p = 1$, the decision point is given by $x = (0.5 - \\beta) / \\alpha$.\n", "\n", "The figure below illustrates this approach for our case study." ] }, { "cell_type": "markdown", "id": "efec9bbe", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "
\n", " Warning\n", " \n", "Here, $y$ does not represent some quantity of rain, but the probability that it rains.\n", "
" ] }, { "cell_type": "code", "execution_count": 2, "id": "9db2f20c", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Import the linear regression class\n", "from sklearn.linear_model import LinearRegression\n", "\n", "# Fit linear regression model\n", "ols = LinearRegression()\n", "_ = ols.fit(df_day[['sp']], df_day['tag'])\n", "\n", "# Get decision boundary\n", "boundary = (.5 - ols.intercept_) / ols.coef_[0]\n", "\n", "# Plot targets and predictions\n", "fig, ax = plt.subplots()\n", "sp_test = np.linspace(-4, 3, 300)\n", "ax.plot(sp_test, ols.coef_ * sp_test + ols.intercept_, 'r',\n", " label=\"OLS prediction\")\n", "ax.axvline(boundary, linestyle='--', color='.5',\n", " label=\"Decision boundary\")\n", "ax.scatter(df_day['sp'], df_day['tag'], s=4, alpha=0.1,\n", " label=\"Target\")\n", "ax.set_xlabel('x: Normalized pressure')\n", "ax.set_ylabel('y: Rain tag')\n", "ax.set_xlim(-4, 3.)\n", "ax.set_ylim(-0.5, 2.)\n", "ax2 = ax.twiny()\n", "ax2.set_xlim(ax.get_xlim())\n", "ax2.set_xticks([boundary.round(2)])\n", "_ = ax.legend(loc='upper left')" ] }, { "cell_type": "markdown", "id": "8828abf0", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "**Interpretation:**\n", "- The fit that we obtain is not too bad: there seem to be a tendency for low pressure days to be rainy and high pressure days to be dry, with a decision boundary given by $x \\approx -0.29$.\n", "- This is not fully satisfactory however because $y(x)$ is not restricted to take values between 0 and 1 and so $y$ is not a probability." ] }, { "cell_type": "markdown", "id": "a8f3c140", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "
\n", " Warning\n", " \n", "- For $K = 2$, linear regression of the indicator response(s) provides coefficients that correspond to those of linear discriminant analysis but for the intercept (Chap. 4 in Hastie *et al.* 2009).\n", "- Linear regression for classification easily generalizes to multiple classes. However, for $K > 2$, classes can be masked by others due to the rigid nature of the linear regression model (Chap. 4 in Hastie *et al.* 2009).\n", " \n", "
" ] }, { "cell_type": "markdown", "id": "7222bbdb", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Logistic regression\n", "\n", "### Logistic regression for two classes and one input\n", "\n", "In order to address the above problem, we are going to fit a non-linear function of $x$ called the sigmoid:\n", "\n", "\\begin{equation}\n", "y(x) = \\frac{1}{1 + e^{-x}}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "93ec2ebf", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "> ***Question***\n", "> - Check that for any $x$, $0 < y(x) < 1$.\n", "> - For which value of $x$ do we have $y(x) = 0.5$.\n", "> - Introduce a parameter in the function in order to control that threshold.\n", "> - Introduce a second parameter to control the speed of the transition from $y\\simeq 0$ to $y\\simeq 1$." ] }, { "cell_type": "markdown", "id": "ba1544e4", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Hence, $y(x)$ can be interpreted as a probability conditioned on the observation $x$.\n", "- In order to adjust this conditional probability, we introduce the parameters $\\beta_0$ and $\\beta_1$ and maximize the probability $y(\\beta_0 + \\beta_1 x)$, so that the decision boundary is at $x = -\\beta_0 / \\beta_1$.\n", "- Because this function is non-linear, we no longer have an analytical solution and we instead need a non-linear solver to find $\\beta_0$ and $\\beta_1$.\n", "\n", "Below is an example for the same data set as above using the `linear_model.LogisticRegression` model implemented in Scikit-Learn." ] }, { "cell_type": "code", "execution_count": 3, "id": "08127934", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Import the logistic regression class\n", "from sklearn.linear_model import LogisticRegression\n", "\n", "# Define sigmoid function\n", "def sigmoid(x): \n", " return 1 / (1 + np.exp(-x))\n", "\n", "# Fit logistic regression model using scikit-learn\n", "clf = LogisticRegression()\n", "clf.fit(df_day[['sp']], df_day['tag'])\n", "\n", "# Get decision boundary\n", "boundary = -clf.intercept_[0] / clf.coef_[0, 0]\n", "\n", "# Plot target and predictions\n", "fig, ax = plt.subplots()\n", "loss = sigmoid(sp_test * clf.coef_[0, :] + clf.intercept_)\n", "ax.plot(sp_test, loss, color='red', label=\"Logistic prediction\")\n", "ax.axvline(boundary, linestyle='--', color='.5',\n", " label=\"Decision boundary\")\n", "ax.scatter(df_day['sp'], df_day['tag'], s=4, alpha=0.1,\n", " label=\"Target\")\n", "ax.set_xlabel('x: Normalized pressure')\n", "ax.set_ylabel('y: Rain tag')\n", "ax.set_xlim(-4, 3.)\n", "ax.set_ylim(-0.5, 2.)\n", "ax2 = ax.twiny()\n", "ax2.set_xlim(ax.get_xlim())\n", "ax2.set_xticks([boundary.round(2)])\n", "_ = ax.legend(loc='upper left')" ] }, { "cell_type": "markdown", "id": "127ee6e7", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "**Interpretation:**\n", "\n", "- The decision boundary for logistic regression ($x \\approx -0.25$) is close to that for linear regression ($x \\approx -0.29$).\n", "- However we can now assign an estimate of the probability for the \"rain\" event given an observation of the pressure.\n", "- That probability depends on the distance of the observed pressure to the pressure at the decision boundary, i.e. on both $\\beta_0$ and $\\beta_1$, while its rate of change with the input is controled by $\\beta_1$." ] }, { "cell_type": "markdown", "id": "45e6c937", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Note that the sigmoid function has many interesting properties. For instance we can invert this function to get\n", "\n", "\\begin{equation}\n", "x = \\ln\\frac{y}{1 -y}\n", "\\end{equation}\n", "\n", "where $x$ is now the logarithm of the odds. This function $x(y)$ is called the *logit* function." ] }, { "cell_type": "markdown", "id": "54c2b539", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Another property is that the derivative of the sigmoid is easy to compute:\n", "\n", "\\begin{equation}\n", "\\frac{dy}{dx} = y(1-y)\n", "\\end{equation}\n", "\n", "We will use this property when we will study neural networks." ] }, { "cell_type": "markdown", "id": "454b9a4f", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Generalization to multiple classes and inputs\n", "\n", "- The example above is relatively straightforward because there are only two classes.\n", "- We took advantage of this when we identified the class identifier with the probability of one of the two classes given the input.\n", "- We can no longer do that when we consider more than two classes." ] }, { "cell_type": "markdown", "id": "9ce40622", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "In the multiple class problem the logistic function can be generalized to,\n", "\n", "\\begin{equation}\n", "P(C = k | \\boldsymbol X = \\boldsymbol x) := y_k(\\boldsymbol x) = \\frac{\\exp(\\beta_{k 0} + \\boldsymbol \\beta_k^\\top \\boldsymbol x) }{\\sum_{l = 1}^{K - 1} \\exp (\\beta_{l0} + \\boldsymbol \\beta_l^\\top \\boldsymbol x)},\n", "\\end{equation}\n", "\n", "where $\\beta_{k0}$ in $\\mathbb{R}$ and $\\boldsymbol \\beta_k$ in $\\mathbb{R}^p$ for $1 \\le k \\le K - 1$.\n", "\n", "As before we can use a non linear solver to find the numerical values of the $\\beta_{k0}$ and $\\boldsymbol \\beta_k$." ] }, { "cell_type": "markdown", "id": "51133f96", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Link to Linear Discriminant Analysis (LDA)\n", "\n", "In the case of LDA ([Classification I: Generative models](06_classification_generative.ipynb)), the log-posterior odds between class $k$ and $K$ are linear functions of $\\boldsymbol x$:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\log \\frac{P(C = k | \\boldsymbol X = \\boldsymbol x)}{P(C = K | \\boldsymbol X = \\boldsymbol x)}\n", "&= - \\frac{1}{2} (\\boldsymbol \\mu_k + \\boldsymbol \\mu_K)^\\top \\boldsymbol \\Sigma^{-1} (\\boldsymbol \\mu_k - \\boldsymbol \\mu_K) \\\\\n", "&+\\log \\frac{P_k}{P_K}\n", "+ (\\boldsymbol \\mu_k - \\boldsymbol \\mu_K)^\\top \\boldsymbol \\Sigma^{-1} \\boldsymbol x \\\\\n", "&= \\alpha_{k 0} + \\boldsymbol \\alpha_{k}^\\top \\boldsymbol x\n", "\\end{aligned}\n", "$$\n", "\n", "This linearity is a consequence of the Gaussian assumption for the class\n", "densities, as well as the assumption of a common covariance matrix." ] }, { "cell_type": "markdown", "id": "c3a8753c", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The linear logistic model by construction has linear logits:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\log \\frac{P(C = k | \\boldsymbol X = \\boldsymbol x)}{P(C = K | \\boldsymbol X = \\boldsymbol x)}\n", "&= \\beta_{k 0} + \\boldsymbol \\beta_{k}^\\top \\boldsymbol x\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "id": "611cd490", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- It seems that the models are the same.\n", "- However, LDA assumes that $P(\\boldsymbol X = \\boldsymbol x)$ is a Gaussian mixture, while we can think of it as being estimated in a fully nonparametric and unrestricted fashion in logistic regression.\n", "- It is generally felt that logistic regression is a safer, more robust bet than the LDA model, relying on fewer assumptions, even though results may be similar in practice (Chap. 4 in Hastie *et al.* 2009)." ] }, { "cell_type": "markdown", "id": "115f1405", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Conclusion on logistic regression\n", "\n", "- Logistic regression is a powerful strategy that does not make any assumption about the distribution of the data in the input space.\n", "- It provides a probability of belonging to a class given an input.\n", "- The major drawback of the logistic regression is that, by design, we suppose that there is a linear relationship between the log odds of the output variable and the input variables.\n", "- This is problematic of course when this relation does not hold in which case nonlinear models may be needed." ] }, { "cell_type": "markdown", "id": "c046dcdb", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Optimal dimension reduction for classification: Fisher Linear Discriminant Analysis" ] }, { "cell_type": "markdown", "id": "77b6c852", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- So far, we have not considered problems with a high number of features.\n", "- However, the feature space is often high-dimensional, thus prohibiting visualizing the classes and making overfitting more likely. \n", "- Fisher Linear Discriminant Analysis (F-LDA) is a method to tackle this problem: it relies on projecting the data set onto a reduced number of dimensions that are best suited to separate the classes.\n", "- (Another other popular tool for dimension reduction is *Principal Component Analysis*, see [Introduction to Unsupervised Learning with a Focus on PCA](08_unsupervised_learning_pca.ipynb).)" ] }, { "cell_type": "markdown", "id": "e988b60f", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "To present this method, let us use a 2-dimensional dataset $(\\boldsymbol x_i, k_i), 1 \\le i \\le N$ with two classes $C = 0$ and $C = 1$ (e.g. pressure and temperature and no rain/rain)." ] }, { "cell_type": "code", "execution_count": 68, "id": "277fee0d", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "CLASS_LABELS = [r'$C = 0$', r'$C = 1$']\n", "DIM_LABELS = [r'$x_1$', r'$x_2$']\n", "\n", "N = 1000\n", "THETA = np.pi / 6\n", "MU_1 = np.array([-10, 0])\n", "MU_2 = np.array([10, 0])\n", "SIGMA_V = np.array([10, 1])\n", "\n", "Rw = np.array([[np.cos(THETA), -np.sin(THETA)],\n", " [np.sin(THETA), np.cos(THETA)]])\n", "Cv = np.diag(SIGMA_V**2)\n", "Cw = Rw @ Cv @ Rw.T\n", "\n", "z1 = np.random.multivariate_normal(MU_1, Cw, N)\n", "z2 = np.random.multivariate_normal(MU_2, Cw, N)\n", "\n", "fig, ax = plt.subplots(1)\n", "s = 2\n", "alpha_scatter = 0.2\n", "ax.scatter(z1[:, 0], z1[:, 1], s=s, alpha=alpha_scatter,\n", " label=CLASS_LABELS[0])\n", "ax.scatter(z2[:, 0], z2[:, 1], s=s, alpha=alpha_scatter,\n", " label=CLASS_LABELS[1])\n", "ax.set_xlabel(DIM_LABELS[0])\n", "ax.set_ylabel(DIM_LABELS[1])\n", "_ = ax.legend()" ] }, { "cell_type": "markdown", "id": "84a062a0", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "In the example above, we have observations from two distinct and well separated classes: a boundary separating these classes can be drawn.\n", "\n", "The plots below represent the histograms of the data along the dimensions $x_1$ and $x_2$ in order to study whether or not the classes can be separated in each of these dimensions." ] }, { "cell_type": "code", "execution_count": 69, "id": "468bcb52", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ztot = np.concatenate((z1, z2), 0)\n", "\n", "alpha_hist = 0.3\n", "density = True\n", "bins = 20\n", "\n", "fig, ax = plt.subplots(1, 2, sharey=True, figsize=(10, 4))\n", "ax[0].hist(z1[:, 0], bins, density=density, alpha=alpha_hist,\n", " label=CLASS_LABELS[0])\n", "ax[0].hist(z2[:, 0], bins, density=density, alpha=alpha_hist,\n", " label=CLASS_LABELS[1])\n", "ax[0].set_xlabel(DIM_LABELS[0])\n", "ax[0].legend()\n", "\n", "ax[1].hist(z1[:, 1], bins, density=density, alpha=alpha_hist,\n", " label=CLASS_LABELS[0])\n", "ax[1].hist(z2[:, 1], bins, density=density, alpha=alpha_hist,\n", " label=CLASS_LABELS[1])\n", "ax[1].set_xlabel(DIM_LABELS[1])\n", "_ = ax[1].legend()" ] }, { "cell_type": "markdown", "id": "2774cf4b", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "**Interpretation:**\n", "\n", "The projection of the data from the original parameter space $(x_1, x_2)$ to each dimension mixes the two classes: they can no longer be separated by a boundary.\n", "\n", "**Problem:**\n", "\n", "Can we find a vector given by the linear combination of $\\boldsymbol e_1$ and $\\boldsymbol e_2$ so that the two classes are best separated for the data projected on this vector?" ] }, { "cell_type": "markdown", "id": "7031ffff", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We look for a vector $\\boldsymbol \\beta$ that best *discriminate* between the two classes.\n", "\n", "Given $\\boldsymbol \\beta$, the projection of an input vector on this vector is given by \n", "\n", "\\begin{equation}\n", "z = \\boldsymbol \\beta^\\top \\boldsymbol x.\n", "\\end{equation}\n", "\n", "We can then propose a threshold $z_0$ such that if $z > z_0$ we assign a point to class $C = 0$ and if $ z \\le z_0$ we assign this point to $C = 1$. " ] }, { "cell_type": "markdown", "id": "035d1825", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "> ***Question***\n", "> - In the example above, do you have an idea of which axis you could use to project the data and get maximum class separability?" ] }, { "cell_type": "markdown", "id": "94100bfa", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### A first attempt: maximizing the distance between the conditional means\n", "\n", "In order to find a direction that best separates each class, a first approach could to maximize the distance between the sample means of the input data for each class.\n", "\n", "In the original coordinate system, these means are given by,\n", "\n", "\\begin{equation}\n", "\\begin{aligned}\n", "\\hat{\\boldsymbol \\mu}_0 &= \\frac{1}{N_0} \\sum_{i, k_i = 0} \\boldsymbol x_i\\\\\n", "\\hat{\\boldsymbol \\mu}_1 &= \\frac{1}{N_1} \\sum_{i, k_i = 1} \\boldsymbol x_i.\n", "\\end{aligned}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "7ace0305", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The projection of these means onto the vector $\\boldsymbol \\beta$ is given by,\n", "\n", "\\begin{equation}\n", "\\begin{aligned}\n", " \\nu_0^{\\boldsymbol \\beta} &= \\boldsymbol \\beta^\\top \\hat{\\boldsymbol \\mu}_0\\\\\n", " \\nu_1^{\\boldsymbol \\beta} &= \\boldsymbol \\beta^\\top \\hat{\\boldsymbol \\mu}_1 .\n", "\\end{aligned}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "89d9ae58", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "**Objective:** Find the vector $\\boldsymbol \\beta$ that maximizes\n", "\n", "\\begin{equation}\n", "J(\\boldsymbol \\beta) = \\left(\\nu_1^{\\boldsymbol \\beta} - \\nu_0^{\\boldsymbol \\beta}\\right)^2.\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "9b521b4d", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "> ***Question (optional)***\n", "> - Show that \n", "\\begin{equation}\n", "\\left(\\nu_1^{\\boldsymbol \\beta} - \\nu_0^{\\boldsymbol \\beta}\\right)^2\n", "= \\boldsymbol \\beta^\\top \\boldsymbol S_b \\boldsymbol \\beta,\n", "\\end{equation}\n", "> with \n", "\\begin{equation}\n", "\\boldsymbol S_b :=\n", "\\left(\\hat{\\boldsymbol\\mu}_1^{\\boldsymbol \\beta} - \\hat{\\boldsymbol\\mu}_0^{\\boldsymbol \\beta}\\right)\n", "\\left(\\hat{\\boldsymbol\\mu}_1^{\\boldsymbol \\beta} - \\hat{\\boldsymbol\\mu}_0^{\\boldsymbol \\beta}\\right)^\\top,\n", "\\end{equation}\n", "> the *between* class scatter matrix." ] }, { "cell_type": "markdown", "id": "4a85d826", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The cost function can be arbitrarily big if we take $\\boldsymbol \\beta$ as big as we want.\n", "\n", "In order to find the direction $\\boldsymbol \\beta$, we need to add a constraint on the norm $\\lVert \\boldsymbol \\beta \\lVert$ to the cost function.\n", "\n", "The new cost function is,\n", "\n", "\\begin{equation}\n", "J(\\boldsymbol \\beta) = \\left(\\hat{\\nu}_1^{\\boldsymbol \\beta} - \\hat{\\nu}_0^{\\boldsymbol \\beta}\\right)^2\n", "- \\lambda (\\boldsymbol \\beta^\\top \\boldsymbol \\beta - 1),\n", "\\end{equation}\n", "\n", "with $\\lambda \\ge 0$ a Lagrange multiplier." ] }, { "cell_type": "markdown", "id": "67164461", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "> ***Question (optional)***\n", "> - Differentiate the cost function $J(\\boldsymbol \\beta)$ with respect to $\\boldsymbol \\beta$ and show that $\\nabla J = 0$ when \n", "\\begin{equation}\n", " \\boldsymbol S_b \\boldsymbol \\beta = \\lambda \\boldsymbol \\beta,\n", "\\end{equation}\n", "> for some $\\lambda \\ge 0$." ] }, { "cell_type": "markdown", "id": "e7d42dcb", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "However, \n", "\\begin{equation}\n", "\\begin{aligned}\n", "\\boldsymbol S_b \\boldsymbol \\beta\n", "&= \\left(\\hat{\\boldsymbol\\mu}_1^{\\boldsymbol \\beta} - \\hat{\\boldsymbol\\mu}_0^{\\boldsymbol \\beta}\\right)\n", "\\left[\\left(\\hat{\\boldsymbol\\mu}_1^{\\boldsymbol \\beta} - \\hat{\\boldsymbol\\mu}_0^{\\boldsymbol \\beta}\\right)^\\top \\boldsymbol \\beta\\right] \\\\\n", "& \\propto \\left(\\hat{\\boldsymbol\\mu}_1^{\\boldsymbol \\beta} - \\hat{\\boldsymbol\\mu}_0^{\\boldsymbol \\beta}\\right).\n", "\\end{aligned}\n", "\\end{equation}\n", "In other words, $\\boldsymbol S_b$ is a matrix that projects on $\\hat{\\boldsymbol\\mu}_1^{\\boldsymbol \\beta} - \\hat{\\boldsymbol\\mu}_0^{\\boldsymbol \\beta}$." ] }, { "cell_type": "markdown", "id": "2a8b9dd8", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Thus, $J$ is maximum when \n", "\\begin{equation}\n", "\\boldsymbol \\beta \\propto \\left(\\hat{\\boldsymbol\\mu}_1^{\\boldsymbol \\beta} - \\hat{\\boldsymbol\\mu}_0^{\\boldsymbol \\beta}\\right).\n", "\\end{equation}\n", "\n", "That is $\\boldsymbol \\beta$ is the direction that joins the two sample means." ] }, { "cell_type": "markdown", "id": "4bb3c41a", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Unfortunately, this does not necessarily ensures that the classes are well separated when projected onto $\\boldsymbol \\beta$.\n", "\n", "For instance, the line spanned by this vector is represented below for our example." ] }, { "cell_type": "code", "execution_count": 85, "id": "09939da0", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mu_0_hat = z1.mean(0)\n", "mu_1_hat = z2.mean(0)\n", "beta = (mu_1_hat - mu_0_hat)\n", "\n", "fig, ax = plt.subplots(1)\n", "s_mu = s * 1000\n", "marker_mu = 'x'\n", "ax.scatter(z1[:, 0], z1[:, 1], s=s, alpha=alpha_scatter,\n", " label=CLASS_LABELS[0])\n", "ax.scatter(z2[:, 0], z2[:, 1], s=s, alpha=alpha_scatter,\n", " label=CLASS_LABELS[1])\n", "ax.scatter(*mu_0_hat, s=s_mu, marker=marker_mu, c=RC_COLORS[0])\n", "ax.scatter(*mu_1_hat, s=s_mu, marker=marker_mu, c=RC_COLORS[1])\n", "xlim = ax.get_xlim()\n", "ylim = ax.get_ylim()\n", "x = np.linspace(*xlim, 1000)\n", "y_line = mu_0_hat[1] + beta[1] / beta[0] * (x - mu_0_hat[0])\n", "ax.plot(x, y_line, '--k', label=r'$\\beta^\\top x = 0$')\n", "ax.set_xlim(xlim)\n", "ax.set_ylim(ylim)\n", "ax.set_xlabel(DIM_LABELS[0])\n", "ax.set_ylabel(DIM_LABELS[1])\n", "_ = plt.legend()" ] }, { "cell_type": "markdown", "id": "72b5a2c6", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Second attempt: maximizing the means relatively to the variances\n", "\n", "We introduce for each class a quantity that is proportional to the sample variance of the data projected on $\\beta$:\n", "\n", "\\begin{equation}\n", "\\begin{aligned}\n", "\\left(s_0^{\\boldsymbol \\beta}\\right)^2\n", "&= \\sum_{i, k_i = 0} \\left(\\boldsymbol \\beta^\\top \\boldsymbol x_i - \\nu_0^{\\boldsymbol \\beta}\\right)^2\\\\\n", "\\left(s_1^{\\boldsymbol \\beta}\\right)^2\n", "&= \\sum_{i, k_i = 1} \\left(\\boldsymbol \\beta^\\top \\boldsymbol x_i - \\nu_1^{\\boldsymbol \\beta}\\right)^2,\n", "\\end{aligned}\n", "\\end{equation}\n", "\n", "Then, we want $(s_0^{\\boldsymbol \\beta})^2 + (s_1^{\\boldsymbol \\beta})^2$ to be as small as possible. " ] }, { "cell_type": "markdown", "id": "67c55add", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "In a similar way as before, we can show that\n", "\n", "\\begin{equation}\n", "\\left(s_0^{\\boldsymbol \\beta}\\right)^2 + \\left(s_1^{\\boldsymbol \\beta}\\right)^2\n", "= \\boldsymbol \\beta^\\top \\boldsymbol S_w \\boldsymbol \\beta\n", "\\end{equation}\n", "\n", "with $\\boldsymbol S_w$ the *within* class scatter matrix,\n", "\n", "\\begin{equation}\n", "\\boldsymbol S_w\n", ":= \\sum_{i, k_i = 0} (\\boldsymbol x_i - \\hat{\\boldsymbol\\mu}_0^{\\boldsymbol \\beta})\n", "(\\boldsymbol x_i - \\hat{\\boldsymbol\\mu}_0^{\\boldsymbol \\beta})^\\top\n", "+ \\sum_{i, k_i = 1} (\\boldsymbol x_i - \\hat{\\boldsymbol\\mu}_1^{\\boldsymbol \\beta})\n", "(\\boldsymbol x_i - \\hat{\\boldsymbol\\mu}_1^{\\boldsymbol \\beta})^\\top.\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "4cdb9c93", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We define a new cost function that combines these two metrics:\n", "\n", "\\begin{equation}\n", "J(\\mathbf w) = \\frac{\\left(\\hat{\\nu}_1^{\\boldsymbol \\beta} - \\hat{\\nu}_0^{\\boldsymbol \\beta}\\right)^2}{\\left(s_0^{\\boldsymbol \\beta}\\right)^2 + \\left(s_1^{\\boldsymbol \\beta}\\right)^2}\n", "\\end{equation}\n", "\n", "The maximum of this cost function corresponds to the maximum separation of the sample means relative to the sample variances. " ] }, { "cell_type": "markdown", "id": "d3e9c51a", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We can write the cost function explicitly with the vector $\\boldsymbol \\beta$:\n", "\n", "\\begin{equation}\n", "J(\\boldsymbol \\beta) = \\frac{\\boldsymbol \\beta^\\top \\boldsymbol S_b \\boldsymbol \\beta}{\\boldsymbol \\beta^\\top \\boldsymbol S_w \\boldsymbol \\beta}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "0caee2f1", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Once again, to find the maximum of this cost function we can differenciate it with respect to $\\boldsymbol \\beta$.\n", "\n", "> ***Question (optional)***\n", "> - Show that for $\\boldsymbol \\beta$ to maximize $J$, it must be such that,\n", "\\begin{equation}\n", "\\left(\\boldsymbol \\beta^\\top \\boldsymbol S_b \\boldsymbol \\beta\\right) \\boldsymbol S_w \\boldsymbol \\beta\n", "= \\left(\\boldsymbol \\beta^\\top \\boldsymbol S_w \\boldsymbol \\beta\\right) \\boldsymbol S_b \\boldsymbol \\beta.\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "203bf2e5", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Both quantities in parenthesis are scalars.\n", "They affect the norm of $\\boldsymbol \\beta$ but not its direction (what we are actually looking for).\n", "\n", "We can then formulate this problem as a generalized eigenvalue problem:\n", "\n", "\\begin{equation}\n", "\\boldsymbol S_w \\boldsymbol \\beta = \\lambda \\boldsymbol S_b \\boldsymbol \\beta.\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "a222b576", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "For the two-classes case considered here, we saw above that $\\boldsymbol S_b$ is the projection matrix on $\\hat{\\boldsymbol\\mu}_1^{\\boldsymbol \\beta} - \\hat{\\boldsymbol\\mu}_0^{\\boldsymbol \\beta}$.\n", "\n", "Thus, we have\n", "\n", "\\begin{equation}\n", "\\boldsymbol \\beta \\propto \\boldsymbol S_w^{-1} (\\hat{\\boldsymbol\\mu}_1^{\\boldsymbol \\beta} - \\hat{\\boldsymbol\\mu}_0^{\\boldsymbol \\beta}).\n", "\\end{equation}\n", "\n", "Note that this equation requires that $\\boldsymbol S_w$ be invertible.\n", "\n", "This condition is satisfied when the features are not colinear." ] }, { "cell_type": "markdown", "id": "12eefe46", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Below, we use `np.linalg.solve` to solve the above generalized eigenvalue problem for our example." ] }, { "cell_type": "code", "execution_count": 87, "id": "e28b0814", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "beta = np.linalg.solve(Cw, mu_1_hat - mu_0_hat) # we use C_w instead of S_w\n", "\n", "fig, ax = plt.subplots(1)\n", "mu_avg_hat = (mu_0_hat + mu_1_hat) / 2\n", "ax.scatter(z1[:, 0], z1[:, 1], s=s, alpha=alpha_scatter,\n", " label=CLASS_LABELS[0])\n", "ax.scatter(z2[:, 0], z2[:, 1], s=s, alpha=alpha_scatter,\n", " label=CLASS_LABELS[1])\n", "ax.scatter(*mu_0_hat, s=s_mu, marker=marker_mu, c=RC_COLORS[0])\n", "ax.scatter(*mu_1_hat, s=s_mu, marker=marker_mu, c=RC_COLORS[1])\n", "xlim = ax.get_xlim()\n", "ylim = ax.get_ylim()\n", "y_line = mu_avg_hat[1] + beta[1] / beta[0] * (x - mu_avg_hat[0])\n", "ax.plot(x, y_line, '--k', label=r'$\\beta^\\top x = 0$')\n", "ax.set_xlim(xlim)\n", "ax.set_ylim(ylim)\n", "ax.set_xlabel(DIM_LABELS[0])\n", "ax.set_ylabel(DIM_LABELS[1])\n", "_ = plt.legend()" ] }, { "cell_type": "markdown", "id": "fe830eb6", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Once we have determined $\\boldsymbol \\beta$, we can project the dataset onto it.\n", "\n", "Doing so, the feature space is reduced to a single dimension.\n", "\n", "This is illustrated below for our example." ] }, { "cell_type": "code", "execution_count": 91, "id": "e436582b", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Project inputs on beta\n", "z1_proj = z1 @ beta\n", "z2_proj = z2 @ beta\n", "\n", "fig, ax = plt.subplots(1)\n", "ax.hist(z1_proj, bins, density=density, alpha=alpha_hist,\n", " label=CLASS_LABELS[0])\n", "ax.hist(z2_proj, bins, density=density, alpha=alpha_hist,\n", " label=CLASS_LABELS[1])\n", "ax.set_xlabel(r'$\\beta^\\top x$')\n", "_ = ax.legend()" ] }, { "cell_type": "markdown", "id": "114fa0c7", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "**Interpretation:**\n", "\n", "- The inputs associated with the two classes are clearly separated in the one-dimensional space defined by $\\boldsymbol \\beta$.\n", "\n", "**Remark:**\n", "- Fisher's linear discriminant, although strictly it is not a discriminant but rather a speciļ¬c choice of direction for projection of the data down to one dimension.\n", "- However, the projected data can subsequently be used to construct a discriminant, by choosing a threshold for $\\boldsymbol \\beta^\\top \\boldsymbol x$, for instance using standard linear discriminant analysis [Classification I: Generative models](06_classification_generative.ipynb)." ] }, { "cell_type": "markdown", "id": "36bb977f", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## To go further\n", "\n", "- Fisher's linear discriminant can be generalized to any number $K$ of classes and for $p$ dimensions provided that $K \\le p$ and that $q \\le K - 1$, with $q$ the dimension of the reduced space. (Chap. 4 in Bishop 2006)." ] }, { "cell_type": "markdown", "id": "00851f30", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## References\n", "\n", "- [Bishop, C., 2006. Pattern Recognition and Machine Learning, Information Science and Statistics. Springer-Verlag, New York](//www.springer.com/us/book/9780387310732).\n", "- [Hastie, T., Tibshirani, R., Friedman, J., 2009. The Elements of Statistical Learning, 2nd ed. Springer, New York](https://doi.org/10.1007/978-0-387-84858-7)." ] }, { "cell_type": "markdown", "id": "5e186998", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "***\n", "## Credit\n", "\n", "[//]: # \"This notebook is part of [E4C Interdisciplinary Center - Education](https://gitlab.in2p3.fr/energy4climate/public/education).\"\n", "Contributors include Bruno Deremble and Alexis Tantet.\n", "\n", "
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This work is licensed under a   Creative Commons Attribution-ShareAlike 4.0 International License.\n", "
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