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"# Logistic Regression\n",
"\n",
"\n",
"\n",
"## Logistic Regression\n",
"\n",
"In linear regression our main interest was centered on learning the\n",
"coefficients of a functional fit (say a polynomial) in order to be\n",
"able to predict the response of a continuous variable on some unseen\n",
"data. The fit to the continuous variable $y_i$ is based on some\n",
"independent variables $x_i$. Linear regression resulted in\n",
"analytical expressions for standard ordinary Least Squares or Ridge\n",
"regression (in terms of matrices to invert) for several quantities,\n",
"ranging from the variance and thereby the confidence intervals of the\n",
"optimal parameters $\\hat{\\beta}$ to the mean squared error. If we can invert\n",
"the product of the design matrices, linear regression gives then a\n",
"simple recipe for fitting our data.\n",
"\n",
"\n",
"Classification problems, however, are concerned with outcomes taking\n",
"the form of discrete variables (i.e. categories). We may for example,\n",
"on the basis of DNA sequencing for a number of patients, like to find\n",
"out which mutations are important for a certain disease; or based on\n",
"scans of various patients' brains, figure out if there is a tumor or\n",
"not; or given a specific physical system, we'd like to identify its\n",
"state, say whether it is an ordered or disordered system (typical\n",
"situation in solid state physics); or classify the status of a\n",
"patient, whether she/he has a stroke or not and many other similar\n",
"situations.\n",
"\n",
"The most common situation we encounter when we apply logistic\n",
"regression is that of two possible outcomes, normally denoted as a\n",
"binary outcome, true or false, positive or negative, success or\n",
"failure etc.\n",
"\n",
"\n",
"Logistic regression will also serve as our stepping stone towards\n",
"neural network algorithms and supervised deep learning. For logistic\n",
"learning, the minimization of the cost function leads to a non-linear\n",
"equation in the parameters $\\hat{\\beta}$. The optimization of the\n",
"problem calls therefore for minimization algorithms. This forms the\n",
"bottle neck of all machine learning algorithms, namely how to find\n",
"reliable minima of a multi-variable function. This leads us to the\n",
"family of gradient descent methods. The latter are the working horses\n",
"of basically all modern machine learning algorithms.\n",
"\n",
"We note also that many of the topics discussed here on logistic \n",
"regression are also commonly used in modern supervised Deep Learning\n",
"models, as we will see later.\n",
"\n",
"\n",
"\n",
"## Basics\n",
"\n",
"We consider the case where the dependent variables, also called the\n",
"responses or the outcomes, $y_i$ are discrete and only take values\n",
"from $k=0,\\dots,K-1$ (i.e. $K$ classes).\n",
"\n",
"The goal is to predict the\n",
"output classes from the design matrix $\\boldsymbol{X}\\in\\mathbb{R}^{n\\times p}$\n",
"made of $n$ samples, each of which carries $p$ features or predictors. The\n",
"primary goal is to identify the classes to which new unseen samples\n",
"belong.\n",
"\n",
"Let us specialize to the case of two classes only, with outputs\n",
"$y_i=0$ and $y_i=1$. Our outcomes could represent the status of a\n",
"credit card user that could default or not on her/his credit card\n",
"debt. That is"
]
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"$$\n",
"y_i = \\begin{bmatrix} 0 & \\mathrm{no}\\\\ 1 & \\mathrm{yes} \\end{bmatrix}.\n",
"$$"
]
},
{
"cell_type": "markdown",
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"Before moving to the logistic model, let us try to use our linear\n",
"regression model to classify these two outcomes. We could for example\n",
"fit a linear model to the default case if $y_i > 0.5$ and the no\n",
"default case $y_i \\leq 0.5$.\n",
"\n",
"We would then have our \n",
"weighted linear combination, namely"
]
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"<!-- Equation labels as ordinary links -->\n",
"<div id=\"_auto1\"></div>\n",
"\n",
"$$\n",
"\\begin{equation}\n",
"\\boldsymbol{y} = \\boldsymbol{X}^T\\boldsymbol{\\beta} + \\boldsymbol{\\epsilon},\n",
"\\label{_auto1} \\tag{1}\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"where $\\boldsymbol{y}$ is a vector representing the possible outcomes, $\\boldsymbol{X}$ is our\n",
"$n\\times p$ design matrix and $\\boldsymbol{\\beta}$ represents our estimators/predictors.\n",
"\n",
"\n",
"The main problem with our function is that it takes values on the\n",
"entire real axis. In the case of logistic regression, however, the\n",
"labels $y_i$ are discrete variables. A typical example is the credit\n",
"card data discussed below here, where we can set the state of\n",
"defaulting the debt to $y_i=1$ and not to $y_i=0$ for one the persons\n",
"in the data set (see the full example below).\n",
"\n",
"One simple way to get a discrete output is to have sign\n",
"functions that map the output of a linear regressor to values $\\{0,1\\}$,\n",
"$f(s_i)=sign(s_i)=1$ if $s_i\\ge 0$ and 0 if otherwise. \n",
"We will encounter this model in our first demonstration of neural networks. Historically it is called the ``perceptron\" model in the machine learning\n",
"literature. This model is extremely simple. However, in many cases it is more\n",
"favorable to use a ``soft\" classifier that outputs\n",
"the probability of a given category. This leads us to the logistic function.\n",
"\n",
"\n",
"The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot whether a person has had CHD (output = 1) or not (output = 0). This ouput is plotted the person's against age. Clearly, the figure shows that attempting to make a standard linear regression fit may not be very meaningful."
]
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"<div>\n",
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" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
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" .dataframe thead th {\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>ID</th>\n",
" <th>Age</th>\n",
" <th>Agegroup</th>\n",
" <th>CHD</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1</td>\n",
" <td>21</td>\n",
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" <td>23</td>\n",
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" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>3</td>\n",
" <td>25</td>\n",
" <td>1</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>4</td>\n",
" <td>29</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>5</td>\n",
" <td>21</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" </tr>\n",
" <tr>\n",
" <th>95</th>\n",
" <td>96</td>\n",
" <td>61</td>\n",
" <td>8</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>96</th>\n",
" <td>97</td>\n",
" <td>69</td>\n",
" <td>8</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>97</th>\n",
" <td>98</td>\n",
" <td>65</td>\n",
" <td>8</td>\n",
" <td>1</td>\n",
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" <tr>\n",
" <th>98</th>\n",
" <td>99</td>\n",
" <td>64</td>\n",
" <td>8</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>99</th>\n",
" <td>100</td>\n",
" <td>63</td>\n",
" <td>8</td>\n",
" <td>0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>100 rows × 4 columns</p>\n",
"</div>"
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"text/plain": [
" ID Age Agegroup CHD\n",
"0 1 21 1 0\n",
"1 2 23 1 0\n",
"2 3 25 1 1\n",
"3 4 29 1 0\n",
"4 5 21 1 0\n",
".. ... ... ... ...\n",
"95 96 61 8 1\n",
"96 97 69 8 1\n",
"97 98 65 8 1\n",
"98 99 64 8 1\n",
"99 100 63 8 0\n",
"\n",
"[100 rows x 4 columns]"
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\n",
"text/plain": [
"<Figure size 576x396 with 1 Axes>"
]
},
"metadata": {
"filenames": {
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_5_1.png"
}
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"\n",
"# 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",
"from IPython.display import display\n",
"from pylab import plt, mpl\n",
"plt.style.use('seaborn')\n",
"mpl.rcParams['font.family'] = 'serif'\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(\"chddata.csv\"),'r')\n",
"\n",
"# Read the chd data as csv file and organize the data into arrays with age group, age, and chd\n",
"chd = pd.read_csv(infile, names=('ID', 'Age', 'Agegroup', 'CHD'))\n",
"chd.columns = ['ID', 'Age', 'Agegroup', 'CHD']\n",
"output = chd['CHD']\n",
"age = chd['Age']\n",
"agegroup = chd['Agegroup']\n",
"numberID = chd['ID'] \n",
"display(chd)\n",
"\n",
"plt.scatter(age, output, marker='o')\n",
"plt.axis([18,70.0,-0.1, 1.2])\n",
"plt.xlabel(r'Age')\n",
"plt.ylabel(r'CHD')\n",
"plt.title(r'Age distribution and Coronary heart disease')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What we could attempt however is to plot the mean value for each group."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false,
"editable": true
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x396 with 1 Axes>"
]
},
"metadata": {
"filenames": {
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_7_0.png"
}
},
"output_type": "display_data"
}
],
"source": [
"agegroupmean = np.array([0.1, 0.133, 0.250, 0.333, 0.462, 0.625, 0.765, 0.800])\n",
"group = np.array([1, 2, 3, 4, 5, 6, 7, 8])\n",
"plt.plot(group, agegroupmean, \"r-\")\n",
"plt.axis([0,9,0, 1.0])\n",
"plt.xlabel(r'Age group')\n",
"plt.ylabel(r'CHD mean values')\n",
"plt.title(r'Mean values for each age group')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are now trying to find a function $f(y\\vert x)$, that is a function which gives us an expected value for the output $y$ with a given input $x$.\n",
"In standard linear regression with a linear dependence on $x$, we would write this in terms of our model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"f(y_i\\vert x_i)=\\beta_0+\\beta_1 x_i.\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This expression implies however that $f(y_i\\vert x_i)$ could take any\n",
"value from minus infinity to plus infinity. If we however let\n",
"$f(y\\vert y)$ be represented by the mean value, the above example\n",
"shows us that we can constrain the function to take values between\n",
"zero and one, that is we have $0 \\le f(y_i\\vert x_i) \\le 1$. Looking\n",
"at our last curve we see also that it has an S-shaped form. This leads\n",
"us to a very popular model for the function $f$, namely the so-called\n",
"Sigmoid function or logistic model. We will consider this function as\n",
"representing the probability for finding a value of $y_i$ with a given\n",
"$x_i$.\n",
"\n",
"\n",
"## The logistic function\n",
"\n",
"Another widely studied model, is the so-called \n",
"perceptron model, which is an example of a \"hard classification\" model. We\n",
"will encounter this model when we discuss neural networks as\n",
"well. Each datapoint is deterministically assigned to a category (i.e\n",
"$y_i=0$ or $y_i=1$). In many cases, and the coronary heart disease data forms one of many such examples, it is favorable to have a \"soft\"\n",
"classifier that outputs the probability of a given category rather\n",
"than a single value. For example, given $x_i$, the classifier\n",
"outputs the probability of being in a category $k$. Logistic regression\n",
"is the most common example of a so-called soft classifier. In logistic\n",
"regression, the probability that a data point $x_i$\n",
"belongs to a category $y_i=\\{0,1\\}$ is given by the so-called logit function (or Sigmoid) which is meant to represent the likelihood for a given event,"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"p(t) = \\frac{1}{1+\\mathrm \\exp{-t}}=\\frac{\\exp{t}}{1+\\mathrm \\exp{t}}.\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that $1-p(t)= p(-t)$.\n",
"\n",
"## Examples of likelihood functions used in logistic regression and nueral networks\n",
"\n",
"\n",
"The following code plots the logistic function, the step function and other functions we will encounter from here and on."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false,
"editable": true
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 576x396 with 1 Axes>"
]
},
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"filenames": {
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_13_0.png"
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},
{
"data": {
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\n",
"text/plain": [
"<Figure size 576x396 with 1 Axes>"
]
},
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"filenames": {
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_13_1.png"
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},
{
"data": {
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\n",
"text/plain": [
"<Figure size 576x396 with 1 Axes>"
]
},
"metadata": {
"filenames": {
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_13_2.png"
}
},
"output_type": "display_data"
}
],
"source": [
"\"\"\"The sigmoid function (or the logistic curve) is a\n",
"function that takes any real number, z, and outputs a number (0,1).\n",
"It is useful in neural networks for assigning weights on a relative scale.\n",
"The value z is the weighted sum of parameters involved in the learning algorithm.\"\"\"\n",
"\n",
"import numpy\n",
"import matplotlib.pyplot as plt\n",
"import math as mt\n",
"\n",
"z = numpy.arange(-5, 5, .1)\n",
"sigma_fn = numpy.vectorize(lambda z: 1/(1+numpy.exp(-z)))\n",
"sigma = sigma_fn(z)\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111)\n",
"ax.plot(z, sigma)\n",
"ax.set_ylim([-0.1, 1.1])\n",
"ax.set_xlim([-5,5])\n",
"ax.grid(True)\n",
"ax.set_xlabel('z')\n",
"ax.set_title('sigmoid function')\n",
"\n",
"plt.show()\n",
"\n",
"\"\"\"Step Function\"\"\"\n",
"z = numpy.arange(-5, 5, .02)\n",
"step_fn = numpy.vectorize(lambda z: 1.0 if z >= 0.0 else 0.0)\n",
"step = step_fn(z)\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111)\n",
"ax.plot(z, step)\n",
"ax.set_ylim([-0.5, 1.5])\n",
"ax.set_xlim([-5,5])\n",
"ax.grid(True)\n",
"ax.set_xlabel('z')\n",
"ax.set_title('step function')\n",
"\n",
"plt.show()\n",
"\n",
"\"\"\"tanh Function\"\"\"\n",
"z = numpy.arange(-2*mt.pi, 2*mt.pi, 0.1)\n",
"t = numpy.tanh(z)\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111)\n",
"ax.plot(z, t)\n",
"ax.set_ylim([-1.0, 1.0])\n",
"ax.set_xlim([-2*mt.pi,2*mt.pi])\n",
"ax.grid(True)\n",
"ax.set_xlabel('z')\n",
"ax.set_title('tanh function')\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We assume now that we have two classes with $y_i$ either $0$ or $1$. Furthermore we assume also that we have only two parameters $\\beta$ in our fitting of the Sigmoid function, that is we define probabilities"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\begin{align*}\n",
"p(y_i=1|x_i,\\boldsymbol{\\beta}) &= \\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}},\\nonumber\\\\\n",
"p(y_i=0|x_i,\\boldsymbol{\\beta}) &= 1 - p(y_i=1|x_i,\\boldsymbol{\\beta}),\n",
"\\end{align*}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"where $\\boldsymbol{\\beta}$ are the weights we wish to extract from data, in our case $\\beta_0$ and $\\beta_1$. \n",
"\n",
"Note that we used"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"p(y_i=0\\vert x_i, \\boldsymbol{\\beta}) = 1-p(y_i=1\\vert x_i, \\boldsymbol{\\beta}).\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to define the total likelihood for all possible outcomes from a \n",
"dataset $\\mathcal{D}=\\{(y_i,x_i)\\}$, with the binary labels\n",
"$y_i\\in\\{0,1\\}$ and where the data points are drawn independently, we use the so-called [Maximum Likelihood Estimation](https://en.wikipedia.org/wiki/Maximum_likelihood_estimation) (MLE) principle. \n",
"We aim thus at maximizing \n",
"the probability of seeing the observed data. We can then approximate the \n",
"likelihood in terms of the product of the individual probabilities of a specific outcome $y_i$, that is"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\begin{align*}\n",
"P(\\mathcal{D}|\\boldsymbol{\\beta})& = \\prod_{i=1}^n \\left[p(y_i=1|x_i,\\boldsymbol{\\beta})\\right]^{y_i}\\left[1-p(y_i=1|x_i,\\boldsymbol{\\beta}))\\right]^{1-y_i}\\nonumber \\\\\n",
"\\end{align*}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"from which we obtain the log-likelihood and our **cost/loss** function"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\mathcal{C}(\\boldsymbol{\\beta}) = \\sum_{i=1}^n \\left( y_i\\log{p(y_i=1|x_i,\\boldsymbol{\\beta})} + (1-y_i)\\log\\left[1-p(y_i=1|x_i,\\boldsymbol{\\beta}))\\right]\\right).\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Reordering the logarithms, we can rewrite the **cost/loss** function as"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\mathcal{C}(\\boldsymbol{\\beta}) = \\sum_{i=1}^n \\left(y_i(\\beta_0+\\beta_1x_i) -\\log{(1+\\exp{(\\beta_0+\\beta_1x_i)})}\\right).\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The maximum likelihood estimator is defined as the set of parameters that maximize the log-likelihood where we maximize with respect to $\\beta$.\n",
"Since the cost (error) function is just the negative log-likelihood, for logistic regression we have that"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\mathcal{C}(\\boldsymbol{\\beta})=-\\sum_{i=1}^n \\left(y_i(\\beta_0+\\beta_1x_i) -\\log{(1+\\exp{(\\beta_0+\\beta_1x_i)})}\\right).\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This equation is known in statistics as the **cross entropy**. Finally, we note that just as in linear regression, \n",
"in practice we often supplement the cross-entropy with additional regularization terms, usually $L_1$ and $L_2$ regularization as we did for Ridge and Lasso regression.\n",
"\n",
"\n",
"The cross entropy is a convex function of the weights $\\boldsymbol{\\beta}$ and,\n",
"therefore, any local minimizer is a global minimizer. \n",
"\n",
"\n",
"Minimizing this\n",
"cost function with respect to the two parameters $\\beta_0$ and $\\beta_1$ we obtain"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\beta_0} = -\\sum_{i=1}^n \\left(y_i -\\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}}\\right),\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"and"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\beta_1} = -\\sum_{i=1}^n \\left(y_ix_i -x_i\\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}}\\right).\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us now define a vector $\\boldsymbol{y}$ with $n$ elements $y_i$, an\n",
"$n\\times p$ matrix $\\boldsymbol{X}$ which contains the $x_i$ values and a\n",
"vector $\\boldsymbol{p}$ of fitted probabilities $p(y_i\\vert x_i,\\boldsymbol{\\beta})$. We can rewrite in a more compact form the first\n",
"derivative of cost function as"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = -\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{p}\\right).\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we in addition define a diagonal matrix $\\boldsymbol{W}$ with elements \n",
"$p(y_i\\vert x_i,\\boldsymbol{\\beta})(1-p(y_i\\vert x_i,\\boldsymbol{\\beta})$, we can obtain a compact expression of the second derivative as"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T} = \\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X}.\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Within a binary classification problem, we can easily expand our model to include multiple predictors. Our ratio between likelihoods is then with $p$ predictors"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\log{ \\frac{p(\\boldsymbol{\\beta}\\boldsymbol{x})}{1-p(\\boldsymbol{\\beta}\\boldsymbol{x})}} = \\beta_0+\\beta_1x_1+\\beta_2x_2+\\dots+\\beta_px_p.\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we defined $\\boldsymbol{x}=[1,x_1,x_2,\\dots,x_p]$ and $\\boldsymbol{\\beta}=[\\beta_0, \\beta_1, \\dots, \\beta_p]$ leading to"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"p(\\boldsymbol{\\beta}\\boldsymbol{x})=\\frac{ \\exp{(\\beta_0+\\beta_1x_1+\\beta_2x_2+\\dots+\\beta_px_p)}}{1+\\exp{(\\beta_0+\\beta_1x_1+\\beta_2x_2+\\dots+\\beta_px_p)}}.\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Till now we have mainly focused on two classes, the so-called binary\n",
"system. Suppose we wish to extend to $K$ classes. Let us for the sake\n",
"of simplicity assume we have only two predictors. We have then following model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\log{\\frac{p(C=1\\vert x)}{p(K\\vert x)}} = \\beta_{10}+\\beta_{11}x_1,\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"and"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\log{\\frac{p(C=2\\vert x)}{p(K\\vert x)}} = \\beta_{20}+\\beta_{21}x_1,\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"and so on till the class $C=K-1$ class"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\log{\\frac{p(C=K-1\\vert x)}{p(K\\vert x)}} = \\beta_{(K-1)0}+\\beta_{(K-1)1}x_1,\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"and the model is specified in term of $K-1$ so-called log-odds or\n",
"**logit** transformations.\n",
"\n",
"\n",
"\n",
"In our discussion of neural networks we will encounter the above again\n",
"in terms of a slightly modified function, the so-called **Softmax** function.\n",
"\n",
"The softmax function is used in various multiclass classification\n",
"methods, such as multinomial logistic regression (also known as\n",
"softmax regression), multiclass linear discriminant analysis, naive\n",
"Bayes classifiers, and artificial neural networks. Specifically, in\n",
"multinomial logistic regression and linear discriminant analysis, the\n",
"input to the function is the result of $K$ distinct linear functions,\n",
"and the predicted probability for the $k$-th class given a sample\n",
"vector $\\boldsymbol{x}$ and a weighting vector $\\boldsymbol{\\beta}$ is (with two\n",
"predictors):"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"p(C=k\\vert \\mathbf {x} )=\\frac{\\exp{(\\beta_{k0}+\\beta_{k1}x_1)}}{1+\\sum_{l=1}^{K-1}\\exp{(\\beta_{l0}+\\beta_{l1}x_1)}}.\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is easy to extend to more predictors. The final class is"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"p(C=K\\vert \\mathbf {x} )=\\frac{1}{1+\\sum_{l=1}^{K-1}\\exp{(\\beta_{l0}+\\beta_{l1}x_1)}},\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"and they sum to one. Our earlier discussions were all specialized to\n",
"the case with two classes only. It is easy to see from the above that\n",
"what we derived earlier is compatible with these equations.\n",
"\n",
"To find the optimal parameters we would typically use a gradient\n",
"descent method. Newton's method and gradient descent methods are\n",
"discussed in the material on [optimization\n",
"methods](https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html).\n",
"\n",
"## Wisconsin Cancer Data\n",
"\n",
"We show here how we can use a simple regression case on the breast\n",
"cancer data using Logistic regression as our algorithm for\n",
"classification."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"editable": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(426, 30)\n",
"(143, 30)\n",
"Test set accuracy with Logistic Regression: 0.94\n",
"Test set accuracy Logistic Regression with scaled data: 0.96\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/mhjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/linear_model/_logistic.py:762: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
"STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
"\n",
"Increase the number of iterations (max_iter) or scale the data as shown in:\n",
" https://scikit-learn.org/stable/modules/preprocessing.html\n",
"Please also refer to the documentation for alternative solver options:\n",
" https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
" n_iter_i = _check_optimize_result(\n"
]
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from sklearn.model_selection import train_test_split \n",
"from sklearn.datasets import load_breast_cancer\n",
"from sklearn.linear_model import LogisticRegression\n",
"\n",
"# Load the data\n",
"cancer = load_breast_cancer()\n",
"\n",
"X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
"print(X_train.shape)\n",
"print(X_test.shape)\n",
"# Logistic Regression\n",
"logreg = LogisticRegression(solver='lbfgs')\n",
"logreg.fit(X_train, y_train)\n",
"print(\"Test set accuracy with Logistic Regression: {:.2f}\".format(logreg.score(X_test,y_test)))\n",
"#now scale the data\n",
"from sklearn.preprocessing import StandardScaler\n",
"scaler = StandardScaler()\n",
"scaler.fit(X_train)\n",
"X_train_scaled = scaler.transform(X_train)\n",
"X_test_scaled = scaler.transform(X_test)\n",
"# Logistic Regression\n",
"logreg.fit(X_train_scaled, y_train)\n",
"print(\"Test set accuracy Logistic Regression with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In addition to the above scores, we could also study the covariance (and the correlation matrix).\n",
"We use **Pandas** to compute the correlation matrix."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false,
"editable": true
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 720x1440 with 30 Axes>"
]
},
"metadata": {
"filenames": {
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_51_0.png"
}
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 1080x576 with 2 Axes>"
]
},
"metadata": {
"filenames": {
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_51_1.png"
}
},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from sklearn.model_selection import train_test_split \n",
"from sklearn.datasets import load_breast_cancer\n",
"from sklearn.linear_model import LogisticRegression\n",
"cancer = load_breast_cancer()\n",
"import pandas as pd\n",
"# Making a data frame\n",
"cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)\n",
"\n",
"fig, axes = plt.subplots(15,2,figsize=(10,20))\n",
"malignant = cancer.data[cancer.target == 0]\n",
"benign = cancer.data[cancer.target == 1]\n",
"ax = axes.ravel()\n",
"\n",
"for i in range(30):\n",
" _, bins = np.histogram(cancer.data[:,i], bins =50)\n",
" ax[i].hist(malignant[:,i], bins = bins, alpha = 0.5)\n",
" ax[i].hist(benign[:,i], bins = bins, alpha = 0.5)\n",
" ax[i].set_title(cancer.feature_names[i])\n",
" ax[i].set_yticks(())\n",
"ax[0].set_xlabel(\"Feature magnitude\")\n",
"ax[0].set_ylabel(\"Frequency\")\n",
"ax[0].legend([\"Malignant\", \"Benign\"], loc =\"best\")\n",
"fig.tight_layout()\n",
"plt.show()\n",
"\n",
"import seaborn as sns\n",
"correlation_matrix = cancerpd.corr().round(1)\n",
"# use the heatmap function from seaborn to plot the correlation matrix\n",
"# annot = True to print the values inside the square\n",
"plt.figure(figsize=(15,8))\n",
"sns.heatmap(data=correlation_matrix, annot=True)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the above example we note two things. In the first plot we display\n",
"the overlap of benign and malignant tumors as functions of the various\n",
"features in the Wisconsing breast cancer data set. We see that for\n",
"some of the features we can distinguish clearly the benign and\n",
"malignant cases while for other features we cannot. This can point to\n",
"us which features may be of greater interest when we wish to classify\n",
"a benign or not benign tumour.\n",
"\n",
"In the second figure we have computed the so-called correlation\n",
"matrix, which in our case with thirty features becomes a $30\\times 30$\n",
"matrix.\n",
"\n",
"We constructed this matrix using **pandas** via the statements"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"editable": true
},
"outputs": [],
"source": [
"cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"and then"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false,
"editable": true
},
"outputs": [],
"source": [
"correlation_matrix = cancerpd.corr().round(1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Diagonalizing this matrix we can in turn say something about which\n",
"features are of relevance and which are not. This leads us to\n",
"the classical Principal Component Analysis (PCA) theorem with\n",
"applications. This will be discussed later this semester ([week 43](https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43-bs.html))."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false,
"editable": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(426, 30)\n",
"(143, 30)\n",
"Test set accuracy with Logistic Regression: 0.94\n",
"Test set accuracy Logistic Regression with scaled data: 0.96\n",
"[1. 1. 1. 1. 1. 1.\n",
" 1. 1. 0.92857143 0.92857143]\n",
"Test set accuracy with Logistic Regression and scaled data: 0.96\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/mhjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/linear_model/_logistic.py:762: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
"STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
"\n",
"Increase the number of iterations (max_iter) or scale the data as shown in:\n",
" https://scikit-learn.org/stable/modules/preprocessing.html\n",
"Please also refer to the documentation for alternative solver options:\n",
" https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
" n_iter_i = _check_optimize_result(\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x396 with 2 Axes>"
]
},
"metadata": {
"filenames": {
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_57_2.png"
}
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x396 with 1 Axes>"
]
},
"metadata": {
"filenames": {
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_57_3.png"
}
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 576x396 with 1 Axes>"
]
},
"metadata": {
"filenames": {
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_57_4.png"
}
},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from sklearn.model_selection import train_test_split \n",
"from sklearn.datasets import load_breast_cancer\n",
"from sklearn.linear_model import LogisticRegression\n",
"\n",
"# Load the data\n",
"cancer = load_breast_cancer()\n",
"\n",
"X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
"print(X_train.shape)\n",
"print(X_test.shape)\n",
"# Logistic Regression\n",
"logreg = LogisticRegression(solver='lbfgs')\n",
"logreg.fit(X_train, y_train)\n",
"print(\"Test set accuracy with Logistic Regression: {:.2f}\".format(logreg.score(X_test,y_test)))\n",
"#now scale the data\n",
"from sklearn.preprocessing import StandardScaler\n",
"scaler = StandardScaler()\n",
"scaler.fit(X_train)\n",
"X_train_scaled = scaler.transform(X_train)\n",
"X_test_scaled = scaler.transform(X_test)\n",
"# Logistic Regression\n",
"logreg.fit(X_train_scaled, y_train)\n",
"print(\"Test set accuracy Logistic Regression with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
"\n",
"\n",
"from sklearn.preprocessing import LabelEncoder\n",
"from sklearn.model_selection import cross_validate\n",
"#Cross validation\n",
"accuracy = cross_validate(logreg,X_test_scaled,y_test,cv=10)['test_score']\n",
"print(accuracy)\n",
"print(\"Test set accuracy with Logistic Regression and scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
"\n",
"\n",
"import scikitplot as skplt\n",
"y_pred = logreg.predict(X_test_scaled)\n",
"skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)\n",
"plt.show()\n",
"y_probas = logreg.predict_proba(X_test_scaled)\n",
"skplt.metrics.plot_roc(y_test, y_probas)\n",
"plt.show()\n",
"skplt.metrics.plot_cumulative_gain(y_test, y_probas)\n",
"plt.show()"
]
}
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