diff --git a/mec-12.4.2-logistic-regression-mini-project/Mini_Project_Logistic_Regression.ipynb b/mec-12.4.2-logistic-regression-mini-project/Mini_Project_Logistic_Regression.ipynb
index e43193ac6..f0c250f38 100755
--- a/mec-12.4.2-logistic-regression-mini-project/Mini_Project_Logistic_Regression.ipynb
+++ b/mec-12.4.2-logistic-regression-mini-project/Mini_Project_Logistic_Regression.ipynb
@@ -1,7 +1,11 @@
{
"cells": [
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {
+ "hide": true
+ },
"source": [
"# Classification\n",
"$$\n",
@@ -14,30 +18,32 @@
"\\renewcommand{\\x}{{\\mathbf x}}\n",
"\\renewcommand{\\v}[1]{{\\mathbf #1}}\n",
"$$"
- ],
- "metadata": {
- "hide": true
- }
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
- "source": [],
- "metadata": {}
+ "metadata": {},
+ "source": []
},
{
+ "attachments": {},
"cell_type": "markdown",
- "source": [],
- "metadata": {}
+ "metadata": {},
+ "source": []
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"**Note:** We've adapted this Mini Project from [Lab 5 in the CS109](https://github.com/cs109/2015lab5) course. Please feel free to check out the original lab, both for more exercises, as well as solutions."
- ],
- "metadata": {}
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"We turn our attention to **classification**. Classification tries to predict, which of a small set of classes, an observation belongs to. Mathematically, the aim is to find $y$, a **label** based on knowing a feature vector $\\x$. For instance, consider predicting gender from seeing a person's face, something we do fairly well as humans. To have a machine do this well, we would typically feed the machine a bunch of images of people which have been labelled \"male\" or \"female\" (the training set), and have it learn the gender of the person in the image from the labels and the *features* used to determine gender. Then, given a new photo, the trained algorithm returns us the gender of the person in the photo.\n",
"\n",
@@ -45,12 +51,16 @@
"\n",
"\n",
"\n"
- ],
- "metadata": {}
+ ]
},
{
"cell_type": "code",
"execution_count": 1,
+ "metadata": {
+ "collapsed": false,
+ "hide": true
+ },
+ "outputs": [],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
@@ -122,37 +132,32 @@
" cs2 = plt.contour(xx, yy, Z, cmap=ccolor, alpha=.6, axes=ax)\n",
" plt.clabel(cs2, fmt = '%2.1f', colors = 'k', fontsize=14)\n",
" return ax "
- ],
- "outputs": [],
- "metadata": {
- "collapsed": false,
- "hide": true
- }
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"## A Motivating Example Using `sklearn`: Heights and Weights"
- ],
- "metadata": {}
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"We'll use a dataset of heights and weights of males and females to hone our understanding of classifiers. We load the data into a dataframe and plot it."
- ],
- "metadata": {}
+ ]
},
{
"cell_type": "code",
"execution_count": 2,
- "source": [
- "dflog = pd.read_csv(\"data/01_heights_weights_genders.csv.zip\")\n",
- "dflog.head()"
- ],
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [
{
- "output_type": "execute_result",
"data": {
"text/html": [
"
\n",
@@ -222,16 +227,20 @@
"4 Male 69.881796 206.349801"
]
},
+ "execution_count": 2,
"metadata": {},
- "execution_count": 2
+ "output_type": "execute_result"
}
],
- "metadata": {
- "collapsed": false
- }
+ "source": [
+ "dflog = pd.read_csv(\"data/01_heights_weights_genders.csv.zip\")\n",
+ "dflog.head()"
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"Remember that the form of data we will use always is\n",
"\n",
@@ -240,11 +249,12 @@
"with the \"response\" or \"label\" $y$ as a plain array of 0s and 1s for binary classification. Sometimes we will also see -1 and +1 instead. There are also *multiclass* classifiers that can assign an observation to one of $K > 2$ classes and the labe may then be an integer, but we will not be discussing those here.\n",
"\n",
"`y = [1,1,0,0,0,1,0,1,0....]`."
- ],
- "metadata": {}
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"
\n",
"
Checkup Exercise Set I
\n",
@@ -254,22 +264,23 @@
"
Exercise: Color the points differently by Gender\n",
"\n",
"
This also leads directly to the idea of cross-validation, next section.
\n",
"\n",
"
"
- ],
- "metadata": {}
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"First, we try a basic Logistic Regression:\n",
"\n",
"* Split the data into a training and test (hold-out) set\n",
"* Train on the training set, and test for accuracy on the testing set"
- ],
- "metadata": {}
+ ]
},
{
"cell_type": "code",
"execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0.9252\n"
+ ]
+ }
+ ],
"source": [
"from sklearn.model_selection import train_test_split\n",
"from sklearn.linear_model import LogisticRegression\n",
@@ -321,48 +344,43 @@
"clf.fit(Xlr, ylr)\n",
"# Print the accuracy from the testing data.\n",
"print(accuracy_score(clf.predict(Xtestlr), ytestlr))"
- ],
- "outputs": [
- {
- "output_type": "stream",
- "name": "stdout",
- "text": [
- "0.9252\n"
- ]
- }
- ],
- "metadata": {
- "collapsed": false
- }
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"### Tuning the Model"
- ],
- "metadata": {}
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"The model has some hyperparameters we can tune for hopefully better performance. For tuning the parameters of your model, you will use a mix of *cross-validation* and *grid search*. In Logistic Regression, the most important parameter to tune is the *regularization parameter* `C`. Note that the regularization parameter is not always part of the logistic regression model. \n",
"\n",
"The regularization parameter is used to control for unlikely high regression coefficients, and in other cases can be used when data is sparse, as a method of feature selection.\n",
"\n",
"You will now implement some code to perform model tuning and selecting the regularization parameter $C$."
- ],
- "metadata": {}
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"We use the following `cv_score` function to perform K-fold cross-validation and apply a scoring function to each test fold. In this incarnation we use accuracy score as the default scoring function."
- ],
- "metadata": {}
+ ]
},
{
"cell_type": "code",
"execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"from sklearn.model_selection import KFold\n",
"from sklearn.metrics import accuracy_score\n",
@@ -374,42 +392,41 @@
" clf.fit(x[train], y[train]) # fit\n",
" result += score_func(clf.predict(x[test]), y[test]) # evaluate score function on held-out data\n",
" return result / nfold # average"
- ],
- "outputs": [],
- "metadata": {
- "collapsed": false
- }
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"Below is an example of using the `cv_score` function for a basic logistic regression model without regularization."
- ],
- "metadata": {}
+ ]
},
{
"cell_type": "code",
"execution_count": 6,
- "source": [
- "clf = LogisticRegression()\n",
- "score = cv_score(clf, Xlr, ylr)\n",
- "print(score)"
- ],
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [
{
- "output_type": "stream",
"name": "stdout",
+ "output_type": "stream",
"text": [
"0.917066666667\n"
]
}
],
- "metadata": {
- "collapsed": false
- }
+ "source": [
+ "clf = LogisticRegression()\n",
+ "score = cv_score(clf, Xlr, ylr)\n",
+ "print(score)"
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"
\n",
"
Checkup Exercise Set II
\n",
@@ -426,25 +443,26 @@
"\n",
"Your goal is to find the best model parameters based *only* on the training set, without showing the model test set at all (which is why the test set is also called a *hold-out* set).\n",
"
"
- ],
- "metadata": {}
+ ]
},
{
"cell_type": "code",
"execution_count": 8,
- "source": [
- "# your turn\n"
- ],
- "outputs": [],
"metadata": {
"collapsed": true
- }
+ },
+ "outputs": [],
+ "source": [
+ "# your turn\n"
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"### Black Box Grid Search in `sklearn`"
- ],
- "metadata": {}
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"Scikit-learn, as with many other Python packages, provides utilities to perform common operations so you do not have to do it manually. It is important to understand the mechanics of each operation, but at a certain point, you will want to use the utility instead to save time..."
- ],
- "metadata": {}
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"
\n",
"
Checkup Exercise Set IV
\n",
"\n",
- "Exercise: Use scikit-learn's [GridSearchCV](http://scikit-learn.org/stable/modules/generated/sklearn.grid_search.GridSearchCV.html) tool to perform cross validation and grid search. \n",
+ "Exercise: Use scikit-learn's [GridSearchCV](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html) tool to perform cross validation and grid search. \n",
"\n",
"* Instead of writing your own loops above to iterate over the model parameters, can you use GridSearchCV to find the best model over the training set? \n",
"* Does it give you the same best value of `C`?\n",
"* How does this model you've obtained perform on the test set?
"
- ],
- "metadata": {}
+ ]
},
{
"cell_type": "code",
"execution_count": 9,
- "source": [
- "# your turn\n"
- ],
- "outputs": [],
"metadata": {
"collapsed": true
- }
+ },
+ "outputs": [],
+ "source": [
+ "# your turn\n"
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"## A Walkthrough of the Math Behind Logistic Regression"
- ],
- "metadata": {}
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"### Setting up Some Demo Code"
- ],
- "metadata": {}
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"Let's first set some code up for classification that we will need for further discussion on the math. We first set up a function `cv_optimize` which takes a classifier `clf`, a grid of hyperparameters (such as a complexity parameter or regularization parameter) implemented as a dictionary `parameters`, a training set (as a samples x features array) `Xtrain`, and a set of labels `ytrain`. The code takes the traning set, splits it into `n_folds` parts, sets up `n_folds` folds, and carries out a cross-validation by splitting the training set into a training and validation section for each foldfor us. It prints the best value of the parameters, and retuens the best classifier to us."
- ],
- "metadata": {}
+ ]
},
{
"cell_type": "code",
"execution_count": 10,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
"source": [
"def cv_optimize(clf, parameters, Xtrain, ytrain, n_folds=5):\n",
" gs = sklearn.model_selection.GridSearchCV(clf, param_grid=parameters, cv=n_folds)\n",
@@ -546,22 +573,24 @@
" print(\"BEST PARAMS\", gs.best_params_)\n",
" best = gs.best_estimator_\n",
" return best"
- ],
- "outputs": [],
- "metadata": {
- "collapsed": true
- }
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"We then use this best classifier to fit the entire training set. This is done inside the `do_classify` function which takes a dataframe `indf` as input. It takes the columns in the list `featurenames` as the features used to train the classifier. The column `targetname` sets the target. The classification is done by setting those samples for which `targetname` has value `target1val` to the value 1, and all others to 0. We split the dataframe into 80% training and 20% testing by default, standardizing the dataset if desired. (Standardizing a data set involves scaling the data so that it has 0 mean and is described in units of its standard deviation. We then train the model on the training set using cross-validation. Having obtained the best classifier using `cv_optimize`, we retrain on the entire training set and calculate the training and testing accuracy, which we print. We return the split data and the trained classifier."
- ],
- "metadata": {}
+ ]
},
{
"cell_type": "code",
"execution_count": 11,
+ "metadata": {
+ "collapsed": false,
+ "hide": true
+ },
+ "outputs": [],
"source": [
"from sklearn.model_selection import train_test_split\n",
"\n",
@@ -581,22 +610,20 @@
" print(\"Accuracy on training data: {:0.2f}\".format(training_accuracy))\n",
" print(\"Accuracy on test data: {:0.2f}\".format(test_accuracy))\n",
" return clf, Xtrain, ytrain, Xtest, ytest"
- ],
- "outputs": [],
- "metadata": {
- "collapsed": false,
- "hide": true
- }
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"## Logistic Regression: The Math"
- ],
- "metadata": {}
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"We could approach classification as linear regression, there the class, 0 or 1, is the target variable $y$. But this ignores the fact that our output $y$ is discrete valued, and futhermore, the $y$ predicted by linear regression will in general take on values less than 0 and greater than 1. Additionally, the residuals from the linear regression model will *not* be normally distributed. This violation means we should not use linear regression.\n",
"\n",
@@ -626,35 +653,36 @@
"Notice that at $z=0$ this function has the value 0.5. If $z > 0$, $h > 0.5$ and as $z \\to \\infty$, $h \\to 1$. If $z < 0$, $h < 0.5$ and as $z \\to -\\infty$, $h \\to 0$. As long as we identify any value of $y > 0.5$ as 1, and any $y < 0.5$ as 0, we can achieve what we wished above.\n",
"\n",
"This function is plotted below:"
- ],
- "metadata": {}
+ ]
},
{
"cell_type": "code",
"execution_count": 12,
- "source": [
- "h = lambda z: 1. / (1 + np.exp(-z))\n",
- "zs=np.arange(-5, 5, 0.1)\n",
- "plt.plot(zs, h(zs), alpha=0.5);"
- ],
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [
{
- "output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAECCAYAAAAYfWtSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzt3Xl002W+P/B3kiZNkzYpXdO0tSyhG6tF1h8u1JkfjoyM3nHgerxTBjl3ZDooMjo49nr1zoxDhaMOHfAI6ngvcMcR5p6rgiLzk3ZUFEEF2dtCCpRutKWlSZc06/f3RyAltjRdkn6b5P06p6cnT/NNPg8teX+X53m+EkEQBBARUViSil0AERGJhyFARBTGGAJERGGMIUBEFMYYAkREYYwhQEQUxiLELmCwjhw5InYJRERBacaMGb3agi4EgL47MpqVl5cDAHJyckSuZOSEY5+B8Ox3OPYZCL5+32wHmqeDiIjC2IBC4PLly/j973+PpUuXYtq0acjKykJtbe2A3sDlcmHr1q3Iz8/HlClTsHjxYvz9738fVtFEROQfAwqB6upqfPTRR9BoNLjtttsG9QYlJSXYtGkTHn74YbzxxhuYPn06Vq9ejU8//XRIBRMRkf8M6JrAzJkzcfDgQQDA3/72N3z++ecDevGWlhb8+c9/xs9//nOsWLECADBnzhxUV1fjpZdewp133jnEsomIyB8GdCQglQ7t0sGBAwdgt9uxePFir/bFixfj7NmzqKmpGdLrEhGRfwT0wrDRaIRCoUBGRoZX+8SJEwEAVVVVgXx7IiLyIaBDRE0mEzQaDSQSiVe7VqsFALS1tQ3pda8PzQoWFosFQPDVPRzh2GcgPPsdjn0GAtNvQRDgcAF2lwC789qXS4DDJUACICVGDplU4vN1BiMo5wkQEY12TpeAboeAbocL1hu/OwXYHC7YnAKsTgE2pwCbw/1hb3MK6O8WLxmxCtw+NtqvdQY0BDQaDcxmMwRB8DoaMJlMAIDY2NghvW6wTM64LtgmlfhDOPYZCM9+h1ufBUGAxe7EkRPl6LK7kJSgQ4fVgU6rAx1WJzqtDnTaHLDaXTd/EQncn74R7nPyymtfviQnqpGTkzqkum82WSygITBx4kTYbDZcunTJ67qA0WgEAEyYMCGQb09ENCROlwCTxY62LhuudtlhtthhuvbV3m2H3SngyhUzACCho3nY76eIkCIyQopIuQyRMiki5VIoZFLIZVIoItzf1ZEyZCbHDPu9viugIXD77bdDLpdjz549WLVqlad99+7dyMzMRHp6eiDfnoioX06XgKtdNlzpsKKlw4aWThtaO6wwWRxwDfHOuzKpBCqFDOrICKgUMkTJZVApIhClkEIpdz+OUsigjJBBKZchMkIKqZ/P8w/GgENg3759AIBTp04BAD777DPExcUhLi4Os2bNAgDk5ubi/vvvx7p16wAA8fHx+NnPfoatW7dCrVYjNzcXe/fuxaFDh/Daa6/5uy9ERDflcLrQ3GFFo9mKJnM3mtqtaO20weka+Ie9TCpBjDICMUo5tK5IqBVSTMpMRnRkBNSREYiOjIBSLu01GGY0G3AIrF692uvxb3/7WwDArFmzsGPHDgCA0+mEy+V9HmzNmjVQqVTYvn07mpubMW7cOGzcuBELFiwYbu1ERDfVaXWgvs2CujYLGkzdaG63DugDXyaVIFYlxxiVwvNdGyWHViVHtCLCs9deXt4OAMhJ1Qa0H4E24BCorKwc0nNkMhkKCwtRWFg4uMqIiAahy+ZA7VULalq7UNPahatddp/bxKrkSIyJRLw6EokxCsSpIxEbJRf19MxI4xBRIgpKgiCgwdSNiy2dqG7pQqO5G/2dxtdGyaHTKpGsUSJZE4nEmEhERshGruBRiiFAREHD6RJQ3dKJquZOXLjSgU6rs8/nSSRAskYJfWwUUmOjoI9VQqXgx11f+K9CRKOayyXgUmsXKhvbUdXccdPx9/HRCtwSp8ItcSroY6OglHMvfyAYAkQ0KjW3W1HeYEbFZXOfe/wyqQS3xKkwPlGNjHg1tFFyEaoMfgwBIho1bA4Xzja241SdCQ2m7l4/l8skGJcQjYnJ0ciIV/Gcvh8wBIhIdKYuO47VtuF0vanX6R6pRIKxCSpk6zQYl6CGIoJ3xfUnhgARiabBZME3F6+iqrmj18ie+GgFJum1yNbFQB3Jj6pA4b8sEY0oQRBQe9WCry604lJrl9fPZFIJMpOjMTlVi9TYqKCaeRusGAJENGJqr3bhYFUL6q5avNpVChmmpGkxNS0W0dzrH1H81yaigGsyd+Nz4xVUt3jv+Wui5LgtYwxy9RrIZTzXLwaGABEFTHu3HQerWlDeYPY656+NkmP2+Dhk6zR+v1MWDQ5DgIj8zuF04Zvqq/jmYivszp5P/xhlBGaPi0eunh/+owVDgIj8qrqlE/+oaPJawE0RIcXscXGYnh6LCJ72GVUYAkTkFxabE59UNqHicrunTSIBpqRqMXdCPNfuGaX4WyGiYREEAZfa7Pjsy4vosvUs76DTKnF3dhKSNAO5ey6JhSFARENmsTlxoLoTl9psSEiIAgBEyqWYb0jAZL02rNblD1YMASIakkstXfj76cu41GbztI1PVCM/OwkxSi7mFiwYAkQ0KE6XgINVV3Ck+qpn2KdCJsXCSTrkpMRwlm+QYQgQ0YC1d9vx0cnLqGvrmfGbpJZjXoYKuXqNiJXRUDEEiGhAalq7sPdkg+fir1QiwdwJ8VBbHJBy7z9oMQSIqF+CIODbmjZ8drbZc/onOjICP5iiQ9oYFcrLG8UtkIaFIUBEN+VwulBW0YTT9WZPW3qcCj+YrOPyziGCv0Ui6pPF5sSe4/Ve5/9nZIzBfEMCh36GEIYAEfVi6rLj3W9rPUs/yKQS3J2ThEl6rciVkb8xBIjIy2VTN94/Vue5AKxSyHDfND30sVEiV0aBwBAgIo/qlk7sOV7vWflzjEqO+29NRaxKIXJlFCgMASICABib2rH35GU4Xe4A0McqsXhaKqIUMpEro0AaUAg0NDSguLgYX3zxBQRBwLx581BUVAS9Xu9z2/r6epSUlODw4cNobW1FSkoK7rnnHjz66KNQqVTD7gARDd/pehM+PtPoGQI6PlGNe6ek8G5fYcBnCFgsFixbtgwKhQLr168HAJSUlKCgoAC7d+/u94O8q6sLy5cvh91ux+rVq5GSkoKTJ09i06ZNqK6uxsaNG/3XEyIakpO1Juy/Yax/li4GCyfpeNOXMOEzBHbt2oWamhrs27cPGRkZAICsrCwsXLgQO3fuxPLly2+67dGjR3Hx4kX8+c9/xvz58wEAc+bMgclkwltvvQWLxYKoKF5sIhLLdwNgSqoW+dlJHAIaRnwe65WVlWHatGmeAACA9PR05OXlobS0tN9t7Xb38LLo6Givdo1GA5fLBeHGm44S0Yj6bgBMvyUWd+cwAMKNzxAwGo3IzMzs1W4wGGA0Gvvddt68eRg7dixeeuklGI1GdHZ24ssvv8T27dvxz//8z7wmQCSS0/W9A+CuzESuABqGfJ4OMplM0Gh6rw6o1WphNpv72KJHZGQk3n77bTz22GNYtGiRp/0nP/kJnnvuuSGU61ZeXj7kbcVgsbhnXAZb3cMRjn0GgqPfl9psOHCxEwLcR+KZCUokOx2oqGgZ0usFQ58DIVT6HdAholarFU888QRaWlqwYcMG6PV6nDhxAq+++ipkMhl++9vfBvLtieg76s12fF7dEwCG+EjMTI3iEUAY8xkCGo2mzz3+mx0h3Oh//ud/8NVXX+Hjjz/GLbfcAgCYOXMmYmJi8O///u946KGHkJ2dPeiic3JyBr2NmK7vKQRb3cMRjn0GRne/G0wWlDbUIi7efc/fLF0M7pmkG/Y1gNHc50AKtn4fOXKkz3af1wQMBgPOnTvXq72qqgoGg6HfbSsrK6HVaj0BcN3UqVM9r0FEgXe104b3j/XMBB6fqMZCPwQABT+fIZCfn4/jx4+jpqbG01ZbW4ujR48iPz+/320TExNhMplQXV3t1X78+HEAQHJy8lBqJqJB6LQ68O63dbBcWwsoNTYK905J4TwAAjCAEFiyZAlSU1NRWFiI/fv3o7S0FIWFhdDpdFi6dKnneXV1dcjNzcXmzZs9bQ888ADUajV+/vOf491338WhQ4fw5ptvYv369Zg0aRLy8vIC0ysiAgDYHC68f6weJot7uHZ8tAKLp+s5E5g8fF4TUKlU2LZtG4qLi7F27VoIgoC5c+eiqKgIarXa8zxBEOB0Or3G/qelpWHXrl3YtGkTNm7ciKtXryIlJQVLly7FypUrIZXyD5EoUFwuAR+dakCjuRuA+25gP5qeCqWcawFRjwGNDtLr9di0aVO/z0lLS0NlZWWvdoPBgJKSkqFVR0RD9rnxCs43dwIAFBFS/OhWPbRRcpGrotGGu+JEIehUnQlHqq8CACQS4N4pKUiKUYpcFY1GDAGiEFPT2oXS8ibP4zsyEzEuQd3PFhTOGAJEIcRksePDkw1wXbs2NzVNi1vTY0WuikYzhgBRiLA7XfjgRL1nKGh6nAp3ZSVxNjD1iyFAFAIEQUBpeROazFYAgCZKjkWcC0ADwBAgCgHHatpQ3uBe3iVCKsF9U1N4W0gaEIYAUZCrb7Pgs7NXPI+/l5uMJA1HAtHAMASIgpjF5sTeGy4ET78lFjkp/S/sSHQjhgBRkBIEAftON6C92wEASNEqccfERJGromDDECAKUl9daMXFK10AAKVchnun8kIwDR5DgCgI1bVZ8OX5njuB3TNZB42SS0LQ4DEEiIJMt92Jj0424PpajbPGxXFGMA0ZQ4AoiAiCgP93ptFzHUAfq8Sc8fEiV0XBjCFAFERO1JpQ1dQBAIiUS3HPZF4HoOFhCBAFiZYOKz472+x5/P2cZC4NTcPGECAKAg6nCx+dugyHy30hYEqqFhOTY0SuikIBQ4AoCHx5vgXN7e51gcao5Lgjk/MByD8YAkSjXE1rl+cGMVKJBPdMToEigv91yT/4l0Q0inXbnfj76cue4aBzxsdBp+W6QOQ/DAGiUeyzs81ew0Fnjo0TuSIKNQwBolGqqrkDp+vdy0PLZRIsnKSDlMNByc8YAkSjkMXmRGl5o+fx7RMTEatSiFgRhSqGANEo9I/KJnRa3beJzIhXYWqaVuSKKFQxBIhGmXON7ai83A7APSv4e7nJvE8wBQxDgGgUsdicKKto8jy+MzORq4NSQDEEiEaRTyqb0GVznwYal6BGLu8SRgHGECAaJYxNHai4dhpIESHF3TlJPA1EATegEGhoaMDjjz+OGTNmIC8vD6tWrUJ9ff2A36SqqgqPP/44Zs+ejalTp2LhwoXYtm3bkIsmCjXddifKKnpGA92ZmYgYngaiERDh6wkWiwXLli2DQqHA+vXrAQAlJSUoKCjA7t27oVKp+t3+5MmTWLZsGWbNmoU//OEPiI6ORnV1Nbq6uvzTA6IQ8NnZZq/RQJP0PA1EI8NnCOzatQs1NTXYt28fMjIyAABZWVlYuHAhdu7cieXLl990W5fLhaeffhpz587Fq6++6mmfM2eOH0onCg3VLZ2eSWHu00AcDUQjx+fpoLKyMkybNs0TAACQnp6OvLw8lJaW9rvt4cOHUVVV1W9QEIUzm8OF/eU9o4HmTYjnPQJoRPkMAaPRiMzMzF7tBoMBRqOx322PHDkCALBarViyZAkmTZqEuXPn4oUXXkB3d/cQSyYKHV+eb4HZYgcApGiVmJYWK3JFFG58ng4ymUzQaHqfn9RqtTCbzf1u29Tk3sNZs2YNHn74YTz55JM4deoU/vSnP6GhocHrFNFglJeXD2k7sVgsFgDBV/dwhGOfgcH1+0qnAx+fa4cAAVKJBHPiNaisrAh0iX7H33Vw99tnCAyHcG3928WLF2P16tUAgNmzZ8PpdOLll19GVVUVJkyYEMgSiEYlp0vA4douCHD/H5mcrERslEzkqigc+QwBjUbT5x7/zY4QbhQb6z60nTdvnlf7/Pnz8fLLL+PMmTNDCoGcnJxBbyOm63sKwVb3cIRjn4GB9/ubi62QqSOQoAbioxV4cHZG0N4wnr/r4Oj39dPz3+XzmoDBYMC5c+d6tVdVVcFgMPjctj9SKeeqUfgxddlx6HyL5/HdOclBGwAU/Hx+Cufn5+P48eOoqanxtNXW1uLo0aPIz8/vd9s77rgDCoUCn3/+uVf7gQMHAACTJ08eSs1EQUsQBJRWNMLudJ8GmpqmRWpslMhVUTjzGQJLlixBamoqCgsLsX//fpSWlqKwsBA6nQ5Lly71PK+urg65ubnYvHmzp23MmDF49NFH8c477+CVV17BwYMH8frrr+PVV1/FAw884DXslCgcVDa2o7rFPVEyOjIC/8eQIHJFFO58XhNQqVTYtm0biouLsXbtWgiCgLlz56KoqAhqtdrzPEEQ4HQ6PReDr/vlL38JtVqNt99+G2+99RYSExOxYsUKFBYW+r83RKNYt92JTyubPY/vykqEUs6LwSSuAY0O0uv12LRpU7/PSUtLQ2VlZa92iUSC5cuXc8IYhb3Pz13xrBA6PlENQ1K0yBURcRVRohFR32bByToTAPf9gu/K4gqhNDowBIgCzOkSvO4XPGc8l4ag0YMhQBRgRy9dxZUOGwAgISYSt94yRuSKiHowBIgCyGSx4/C1OQESCfC9nCTOCaBRhSFAFCCCIOCTyibPnIApqVqkaDkngEYXhgBRgFQ1d+B8cycAQKWQcU4AjUoMAaIAsDqc+OSGOQF3ZHJOAI1ODAGiADh0vhXt3Q4AQHqcCtm6GJErIupbQJeSJgpHVy0OHGttAwDIpBLkZ3NOAI1ePBIg8iNBEPBVbRdc15ZPuS1jDOLUCpGrIro5hgCRH1W12tDc6T4NpI2SY+a4OJErIuofQ4DIT7psDhytt3geL8hOglzG/2I0uvEvlMhPDpy7ApvTBQCYmByNcQlqH1sQiY8hQOQHtVe7cKbefRvWCKkEd2YmilwR0cAwBIiGyekS8I+KJs/jabooxCi5QBwFB4YA0TB9e8MCcWOiIpCVGClyRUQDxxAgGgaTxfum8bPSVJByTgAFEYYA0TB8erbZa4G4RDXnX1JwYQgQDZGxqQNVTR0AgCiFDPMncoE4Cj4MAaIhsDlc+KSy52Lw7RMTuEAcBSWGANEQHL7Q4lkgLm1MFHJTNCJXRDQ0DAGiQWput+JoNReIo9DAECAaBEEQUFbR6FkgbkbGGMRHc0goBS+GANEgnKozo76tG4B7gbhZXCCOghxDgGiAOq0OHDD23C0snwvEUQjgXzDRAH12thlWu3uBuCxdDMZygTgKAQwBogGobulExeV2AIAiQoo7uEAchYgBhUBDQwMef/xxzJgxA3l5eVi1ahXq6+sH/Wavv/46srKy8NBDDw16WyKx2J0ulJb3zAmYb0hAdCRnBlNo8BkCFosFy5Ytw/nz57F+/Xps2LAB1dXVKCgoQFdX14DfqKamBq+99hri4+OHVTDRSDt8vhUmix0AkKJVYmqaVuSKiPzH5+7Mrl27UFNTg3379iEjIwMAkJWVhYULF2Lnzp1Yvnz5gN7oP/7jP3DffffhwoULcDgcw6uaaIQ0t1txpPoqAEAqkeDunGTOCaCQ4vNIoKysDNOmTfMEAACkp6cjLy8PpaWlA3qTPXv24PTp0/jVr3419EqJRpjLJWB/ec+cgNvGjkFiDOcEUGjxGQJGoxGZmZm92g0GA4xGo883MJlMKC4uxq9//WvExsYOrUoiERyvbcNlk3tOQKyKcwIoNPk8HWQymaDR9F4XRavVwmw2+3yDDRs2YOzYsfinf/qnoVXYh/Lycr+91kiwWNw3Hw+2uocj2PvcaXNhT4UJDpf7KGD6hBgYz1b63C7Y+z0U4dhnIHT6HdAhDt988w3ef/99/O///i/Po1LQEAQBh2s7PQEwPi4SuhjeLpJCk88Q0Gg0fe7x3+wI4UbPPfccfvzjH0On03lew+FwwOVywWw2Q6lUQqFQDLronJycQW8jput7CsFW93AEc5/LG8yw1V1GQgKgjpTh4bljB7xMdDD3e6jCsc9A8PX7yJEjfbb7DAGDwYBz5871aq+qqoLBYOh326qqKlRVVeGdd97p9bOZM2fimWeewc9+9jNfJRCNmC6bA5+e7Vka4q6sJN4ngEKazxDIz8/Hhg0bUFNTg/T0dABAbW0tjh49iieffLLfbbdv396rbd26dXC5XHj22We9RhwRjQafVjbDYnMCACYkRWNiUrTIFREFls8QWLJkCf7yl7+gsLAQq1evhkQiQUlJCXQ6HZYuXep5Xl1dHb7//e+jsLAQq1atAgDMnj271+tpNBo4HI4+f0YkJmNTh9fSEAuyEnkti0KezyGiKpUK27Ztw9ixY7F27Vo89dRTSEtLw7Zt26BW9yygJQgCnE4nhGtjqomCSbfdibKKRs/jOzMTEaPkxWAKfQMaHaTX67Fp06Z+n5OWlobKSt9D6Hbs2DGwyohG0CeVzei0uk8DZcSrMEnP20VSeOAqohT2zjd3oLzBPXpNESHl0hAUVhgCFNa67c5eK4Rqo3gaiMIHQ4DC2ieVTeiwuhc0TBsTxRVCKewwBChsGZvaUd7QMxro/07S8TQQhR2GAIWlLpvD6zTQnZmJPA1EYYkhQGFHEASUljeh69qksHEJao4GorDFEKCwc6bBDGNTBwBAKZfhe7kcDUThiyFAYaWty4ZPKnvWBlqQncj7BVNYYwhQ2HC5BPz99GXYHC4AQE5KDLJ1PA1E4Y0hQGHjq4utqG9z3yksRhmBu7KSRK6ISHwMAQoL9W0WHD7fCgCQSICFk3RcIpoIDAEKA912Jz46dbnnhvEZcUiPU4lcFdHowBCgkHZ9OKjZYgcA6LRKzJ0QL3JVRKMHQ4BC2qk6M8429swKvndyCmRSDgcluo4hQCGrud2KT8/2zAr+Xk4ytCrOCia6EUOAQpLV4cSHJ+phd7qvA0zSa5ClixG5KqLRhyFAIUcQBOw/04SrXe7rAAnRCizI5nBQor4wBCjkHKtp87oOsGiqHnIZ/9SJ+sL/GRRS6tssOHDuiufx93OTEadWiFgR0ejGEKCQ0WF14MMTDXC63NcBpqfHIjOZ1wGI+sMQoJDgdAn48ES95y5h+lgl7shMFLkqotGPIUAh4ZPKJs+6QNGREVg0Vc/5AEQDwBCgoHeitg0nak0AAJlUgkVTU7g8NNEAMQQoqF1q6cI/KnruD3BXViL0sVEiVkQUXBgCFLRaO2344GS9Z2G46emxmJoWK3JVRMGFIUBByWJz4v1jdbDa3TeIyYhX4U5eCCYaNIYABR2704Xdx+vQdm1GcHy0AvdOSYGUF4KJBm1AV88aGhpQXFyML774AoIgYN68eSgqKoJer+93u5MnT2LXrl34+uuv0dDQgDFjxmDGjBl44oknkJ6e7pcOUHhxuQTsO3XZMxIoSiHD4ml63iCGaIh8HglYLBYsW7YM58+fx/r167FhwwZUV1ejoKAAXV1d/W67d+9enDt3Dj/96U/xxhtv4Mknn8SZM2fw4IMPoqGhwW+doPAgCAI+PdcMY1MHAEAuk+BH0/WIVXFGMNFQ+TwS2LVrF2pqarBv3z5kZGQAALKysrBw4ULs3LkTy5cvv+m2//qv/4q4uDivtry8PNx9993YtWsXVq9ePczyKZx8ffEqjl1qA+C+ReQPpqQgRcuRQETD4fNIoKysDNOmTfMEAACkp6cjLy8PpaWl/W773QAAgNTUVMTFxaGxsXEI5VK4Ol7Thi+MPWsC5WcnYUJitIgVEYUGnyFgNBqRmZnZq91gMMBoNA76DauqqtDS0oIJEyYMelsKT+UNZpRV9NwcZs74eA4FJfITn6eDTCYTNBpNr3atVguz2TyoN3M4HHj++ecRFxeHBx98cFDb3qi8vHzI24rBYrEACL66h8Nffb7UZsOB6k4I1+YC5CQqobU6UF7e5GNLcfB3HT5Cpd8jOrf+d7/7Hb799lts3boVWq12JN+aglCNyTsAJsRFIk8fBYmEQ0GJ/MVnCGg0mj73+G92hHAzL730Enbt2oUXX3wR8+fPH1yV35GTkzOs7Ufa9T2FYKt7OIbb56rmDlTUNyA+3n3hN0sXg3sm6Ub9XAD+rsNHsPX7yJEjfbb7vCZgMBhw7ty5Xu1VVVUwGAwDevPXXnsNb7zxBp599lncf//9A9qGwpexqcPrvgCZycERAETByGcI5Ofn4/jx46ipqfG01dbW4ujRo8jPz/f5Btu3b8fGjRuxZs0a/Mu//MvwqqWQV95g9gqAicnRuGcyA4AoUHyGwJIlS5CamorCwkLs378fpaWlKCwshE6nw9KlSz3Pq6urQ25uLjZv3uxp+/DDD7Fu3TrcfvvtmDNnDo4dO+b5GsrIIgptx2vasO/UZc+CcJnJMfjB5BTeF4AogHxeE1CpVNi2bRuKi4uxdu1aCIKAuXPnoqioCGq12vM8QRDgdDo9F/EA4MCBAxAEAQcOHMCBAwe8XnfWrFnYsWOHH7tCwUoQBHx1oRUHq1o8bZNTtbg7O4lHAEQBNqDRQXq9Hps2ber3OWlpaaisrPRqe/HFF/Hiiy8OvToKeS6XgLKKJpysM3na8jLG4I6JCRwFRDQCePslEo3N4cJHpxpwvrnT0zZ3Qjxmj4tjABCNEIYAicLcbcee4/VoMlsBAFKJBN/LTcIkPeePEI0khgCNuPo2C/Ycr0eXzQkAUERIsWhKCsYmqH1sSUT+xhCgEXWqzoSyiibPENAYZQQWT9cjKUYpcmVE4YkhQCPC7nThHxVNOF3fM/s8NTYKP5yWApWCf4ZEYuH/Pgq4q502fHCyAVfarZ62KalaLMhO4hwAIpExBChgBEHAqToTPj3bDJvDfUP4CKkEC7KTMDmVF4CJRgOGAAWE1eHC4doudEX03DwoViXHoqkpPP9PNIowBMjvqpo78EGlGRa7CwkJ7racFA0WZCciMoI3hCcaTRgC5DcWmxOfVDah4nI7LHb36Z9IuRT52UnI1g182XEiGjkMARo2QRBwpsGMz89d8Yz9BwBdjBwPz86ANkouYnVE1B+GAA1Lc7sV/6hoQl2bxdOmiJBiTroaE+Kun98IAAAMKklEQVQUDACiUY4hQEPSaXXg0PkWnKwz4YaFYzEhKRp3ZSWi7gKXCicKBgwBGhSbw4VjNW34+mKrZ9gnAGii5FiQlYjxidEAgDqxCiSiQWEI0IA4nC6cqDPh6wutXuf95TIJZmTE4baxYyCX+bxHERGNMgwB6pfd6cKpOhOOVF9Fe7fD0y6RALkpGswzJCA6kn9GRMGK/3upTxabEydq2/BtTRssN+z5A8D4RDXmTUhAYkykSNURkb8wBMhLS4cV315qQ3mDGQ6X4PWzsQkqzB2fAJ2WM36JQgVDgOBwumBs7sCJWhPqrlq8fiaRAIakaMwcG4dkDT/8iUINQyBMCYKApnYrztSbUdnY3uuUj1wmQa5eg+npYxCnVohUJREFGkMgzLR22nC2sR1nG9vR0mHr9XNtlBxT07SYnKqFUs51fohCHUMgxAmCgOZ2K4zNHahq7vRa0/86mVSC8YlqTEnV4pY4FW/yThRGGAIhyOpwoqa1C9UtXbhwpdNraOeNdFolclM0yEyOQZSCe/1E4YghEALsThcum7pRc7ULta0WNJi64RKEPp+bpIlEZnIMMpNioFVxXR+icMcQCELt3XY0mrtR39aN+jYLmtqtnhu3f5dUIkHqmChMSFRjfGI0F3QjIi8MgVFMEAS0Wx1obreiud2KpnYrGk3d6LD2fXrnOm2UHBnxKmTEq5EeF8UbuRDRTTEERoHrH/ZXO21ovfbV0mHDlU4rrHaXz+21UXLoY5VIG6NCepyKe/tENGADCoGGhgYUFxfjiy++gCAImDdvHoqKiqDX631ua7VasXHjRuzZswdmsxk5OTl46qmnMHPmzGEXH0wcLgEtHVa0dztgstg9X20WO0xdNtidfZ/O+S65TIIkjRI6jRI6rRIpWiVilPzQJ6Kh8RkCFosFy5Ytg0KhwPr16wEAJSUlKCgowO7du6FSqfrdvqioCJ9++inWrl2L9PR0/OUvf8GKFSuwc+dO5OTk+KcXInK6BHTaHLDYnOi0OtBlc6LD6kCn1YEOqwPt3Q6cr2mD1eFCQn31oF5bpZAhIToSCTGRSLr2NUalgFTKIZxE5B8+Q2DXrl2oqanBvn37kJGRAQDIysrCwoULsXPnTixfvvym21ZUVOCDDz7AunXr8OMf/xgAMHPmTCxatAglJSXYsmWLn7oxPIIgwOZ0weZwwero+W51ONFtd8Fqd6Lb4YLF5oTV4YTF5oTF7kSXzem1pv7NWPt5jkQCaJRyxKrkGKNSIE7t/oqPVkCl4Nk6Igosn58yZWVlmDZtmicAACA9PR15eXkoLS3tNwRKS0shl8tx77339rxhRAQWLVqE119/HTabDQrFyCxJcKymDRevdMLudMHuFGC/9qFvc7pgd7pwkxGVwyaRAFFyKVRyKTKTYxCjjIAmSo7YKDm0UXLEKCMQwXX4iUgkPkPAaDTi7rvv7tVuMBiwb98+n9umpqYiKiqq17Z2ux3V1dWYOHHiIEsevJYO931w/UkRIYVSLoNKcf0rAiqFDOrICKivf4+MQHRkBM5WutflyclJ8WsNRETD5TMETCYTNBpNr3atVguz2exzW61W26s9NjbW8/OhKC8vH9TzHS4BtnYzzNaeRdJkEgnkMgkipO7v8uvfZYBCJoVcJoFCJkGkzN0eKZNAESFBpEyKyAj3doDd+43s7i8HANO1L8B9XWUodQezcOwzEJ79Dsc+A6HT77A46RwhleC+bA26HQJkUgkipO5JVERE4c5nCGg0mj73+G92hPDdbevqet9yvK2tDQD6PEoYiGAbVXR9TyHY6h6OcOwzEJ79Dsc+A8HX7yNHjvTZ7vOKpMFgwLlz53q1V1VVwWAw+Ny2rq7Oc9h047ZyudzrYjMREY08nyGQn5+P48ePo6amxtNWW1uLo0ePIj8/3+e2drvd6wKyw+HA3r17MX/+/BEbGURERH3zGQJLlixBamoqCgsLsX//fpSWlqKwsBA6nQ5Lly71PK+urg65ubnYvHmzpy03Nxf33nsv1q1bh7/97W/48ssv8atf/Qq1tbV47LHHAtMjIiIaMJ/XBFQqFbZt24bi4mKsXbsWgiBg7ty5KCoqglqt9jxPEAQ4nU4I3xlwX1xcjD/+8Y/YuHEjzGYzsrOz8eabb2LSpEn+7w0REQ3KgEYH6fV6bNq0qd/npKWlobKysle7UqnEM888g2eeeWZoFRIRUcBwqioRURhjCBARhTGJ8N2T+KPczca6EhFR/2bMmNGrLehCgIiI/Ieng4iIwhhDgIgojDEEiIjCGEOAiCiMMQSIiMIYQ4CIKIwxBIiIwhhDgIgojDEEiIjCGENAZB9++CGysrJwxx13iF1KwFy4cAEvvPAC7rvvPtx6662YP38+Vq5ciYqKCrFL85uGhgY8/vjjmDFjBvLy8rBq1SrU19eLXVbA7Nu3D4899hgWLFiAqVOnYuHChXj55ZfR0dEhdmkjasWKFcjKysIf//hHsUsZsrC40fxoZTabsW7dOiQmJopdSkB98cUXOHz4MB544AHk5uaivb0db775JpYsWYK3334bkydPFrvEYbFYLFi2bBkUCgXWr18PACgpKUFBQQF2794NlUolcoX+99ZbbyElJQVr1qyBTqfDmTNnsHnzZhw+fBjvvPMOpNLQ37/84IMP+lw+P+gIJJpnn31WeOSRR4Snn35auP3228UuJ2BaWloEl8vl1WY2m4XbbrtN+PWvfy1SVf7zX//1X0J2drZw8eJFT9ulS5eEnJwc4a233hKxssBpaWnp1fbuu+8KmZmZwsGDB0WoaGS1tbUJ8+bNE/bs2SNkZmYKr7zyitglDVnox/UodeTIEezevRvPPfec2KUEXFxcHCQSiVdbTEwMxo4di8bGRpGq8p+ysjJMmzYNGRkZnrb09HTk5eWhtLRUxMoCJy4urlfblClTACAkfqe+vPTSS5g4cSJ++MMfil3KsDEERGC32/Hcc89hxYoVXh8c4aStrQ3nzp3DhAkTxC5l2IxGIzIzM3u1GwwGGI1GESoSx1dffQUAIfE77c8333yD9957L2R24BgCInjjjTdgs9nw6KOPil2KaH7/+99DEAQsW7ZM7FKGzWQyQaPR9GrXarUwm80iVDTyGhsb8ac//Qnz5s3zHBGEIpvNhueffx6PPPIIxo8fL3Y5fsELw8N08OBBLF++3OfzZs2ahR07dqC6uhpbtmzB5s2bERkZOQIV+t9g+/xdW7duxQcffIA//OEPYXskFEo6Ozvxi1/8AjKZDMXFxWKXE1Bvvvkmuru78Ytf/ELsUvyGITBMt956K/bu3evzeVFRUQCAF154AXPmzMH06dM9e4l2ux2CIMBsNkOhUECpVAa05uEabJ9v9Ne//hWvvPIKnnjiCTz44IOBKG/EaTSaPvf4b3aEEEq6u7uxcuVK1NbWYseOHdDpdGKXFDD19fXYsmULXnjhBdhsNthsNs/PbDYbzGYz1Go1ZDKZiFUOHu8sNsLy8/NRV1d3058XFBTg3/7t30awopHz3nvv4Te/+Q2WL1+Op59+Wuxy/KagoAB2ux1//etfvdp/+tOfQhAE/Pd//7dIlQWW3W7HL3/5S3z99df4z//8T0yfPl3skgLq8OHDKCgo6Pc57733HnJyckaoIv/gkcAIe+WVV2C1Wr3aXn/9dZw+fRolJSUhuyf18ccfo6ioCD/5yU9CKgAAd7Bv2LABNTU1SE9PBwDU1tbi6NGjePLJJ0WuLjBcLheeeuopHDp0CFu3bg35AACAnJwcbN++vVd7QUEBFi9ejAcffBC33HKLCJUND48ERoHf/OY3OHjwID777DOxSwmIr7/+Go888ggmTpyIZ5991msikUKhQG5urojVDV9XVxd+9KMfQalUYvXq1ZBIJCgpKUFnZyd2794NtVotdol+9/zzz+Odd97BypUrsWDBAq+f6XS6kN2Z6UtWVhZWrlyJNWvWiF3KkPBIgALu0KFDsNlsOH36NB566CGvn6WmpqKsrEykyvxDpVJh27ZtKC4uxtq1ayEIAubOnYuioqKQDAAAOHDgAABgy5Yt2LJli9fPVq1ahccee0yMsmgIeCRARBTGOE+AiCiMMQSIiMIYQ4CIKIwxBIiIwhhDgIgojDEEiIjCGEOAiCiMMQSIiMIYQ4CIKIz9fxz/TWE8nXeSAAAAAElFTkSuQmCC",
"text/plain": [
""
]
},
- "metadata": {}
+ "metadata": {},
+ "output_type": "display_data"
}
],
- "metadata": {
- "collapsed": false
- }
+ "source": [
+ "h = lambda z: 1. / (1 + np.exp(-z))\n",
+ "zs=np.arange(-5, 5, 0.1)\n",
+ "plt.plot(zs, h(zs), alpha=0.5);"
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"So we then come up with our rule by identifying:\n",
"\n",
@@ -678,18 +706,16 @@
"where $C$ is the regularization strength (equivalent to $1/\\alpha$ from the Ridge case), and smaller values of $C$ mean stronger regularization. As before, the regularization tries to prevent features from having terribly high weights, thus implementing a form of feature selection. \n",
"\n",
"How did we come up with this loss? We'll come back to that, but let us see how logistic regression works out. \n"
- ],
- "metadata": {}
+ ]
},
{
"cell_type": "code",
"execution_count": 13,
- "source": [
- "dflog.head()"
- ],
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [
{
- "output_type": "execute_result",
"data": {
"text/html": [
"
\n",
@@ -759,34 +785,33 @@
"4 Male 69.881796 206.349801"
]
},
+ "execution_count": 13,
"metadata": {},
- "execution_count": 13
+ "output_type": "execute_result"
}
],
- "metadata": {
- "collapsed": false
- }
+ "source": [
+ "dflog.head()"
+ ]
},
{
"cell_type": "code",
"execution_count": 14,
- "source": [
- "clf_l, Xtrain_l, ytrain_l, Xtest_l, ytest_l = do_classify(LogisticRegression(), \n",
- " {\"C\": [0.01, 0.1, 1, 10, 100]}, \n",
- " dflog, ['Weight', 'Height'], 'Gender','Male')"
- ],
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [
{
- "output_type": "stream",
"name": "stderr",
+ "output_type": "stream",
"text": [
"/usr/local/anaconda/lib/python3.6/site-packages/sklearn/model_selection/_split.py:2026: FutureWarning: From version 0.21, test_size will always complement train_size unless both are specified.\n",
" FutureWarning)\n"
]
},
{
- "output_type": "stream",
"name": "stdout",
+ "output_type": "stream",
"text": [
"BEST PARAMS {'C': 0.01}\n",
"Accuracy on training data: 0.92\n",
@@ -794,50 +819,56 @@
]
}
],
- "metadata": {
- "collapsed": false
- }
+ "source": [
+ "clf_l, Xtrain_l, ytrain_l, Xtest_l, ytest_l = do_classify(LogisticRegression(), \n",
+ " {\"C\": [0.01, 0.1, 1, 10, 100]}, \n",
+ " dflog, ['Weight', 'Height'], 'Gender','Male')"
+ ]
},
{
"cell_type": "code",
"execution_count": 15,
- "source": [
- "plt.figure()\n",
- "ax=plt.gca()\n",
- "points_plot(ax, Xtrain_l, Xtest_l, ytrain_l, ytest_l, clf_l, alpha=0.2);"
- ],
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [
{
- "output_type": "display_data",
"data": {
"image/png": "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",
"text/plain": [
""
]
},
- "metadata": {}
+ "metadata": {},
+ "output_type": "display_data"
}
],
- "metadata": {
- "collapsed": false
- }
+ "source": [
+ "plt.figure()\n",
+ "ax=plt.gca()\n",
+ "points_plot(ax, Xtrain_l, Xtest_l, ytrain_l, ytest_l, clf_l, alpha=0.2);"
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"In the figure here showing the results of the logistic regression, we plot the actual labels of both the training(circles) and test(squares) samples. The 0's (females) are plotted in red, the 1's (males) in blue. We also show the classification boundary, a line (to the resolution of a grid square). Every sample on the red background side of the line will be classified female, and every sample on the blue side, male. Notice that most of the samples are classified well, but there are misclassified people on both sides, as evidenced by leakage of dots or squares of one color ontothe side of the other color. Both test and traing accuracy are about 92%."
- ],
- "metadata": {}
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"### The Probabilistic Interpretaion"
- ],
- "metadata": {}
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"Remember we said earlier that if $h > 0.5$ we ought to identify the sample with $y=1$? One way of thinking about this is to identify $h(\\v{w}\\cdot\\v{x})$ with the probability that the sample is a '1' ($y=1$). Then we have the intuitive notion that lets identify a sample as 1 if we find that the probabilty of being a '1' is $\\ge 0.5$.\n",
"\n",
@@ -869,18 +900,20 @@
"Indeed its important to realize that a particular training set can be thought of as a draw from some \"true\" probability distribution (just as we did when showing the hairy variance diagram). If for example the probability of classifying a test sample as a '0' was 0.1, and it turns out that the test sample was a '0', it does not mean that this model was necessarily wrong. After all, in roughly a 10th of the draws, this new sample would be classified as a '0'! But, of-course its more unlikely than its likely, and having good probabilities means that we'll be likely right most of the time, which is what we want to achieve in classification. And furthermore, we can quantify this accuracy.\n",
"\n",
"Thus its desirable to have probabilistic, or at the very least, ranked models of classification where you can tell which sample is more likely to be classified as a '1'. There are business reasons for this too. Consider the example of customer \"churn\": you are a cell-phone company and want to know, based on some of my purchasing habit and characteristic \"features\" if I am a likely defector. If so, you'll offer me an incentive not to defect. In this scenario, you might want to know which customers are most likely to defect, or even more precisely, which are most likely to respond to incentives. Based on these probabilities, you could then spend a finite marketing budget wisely."
- ],
- "metadata": {}
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"### Maximizing the Probability of the Training Set"
- ],
- "metadata": {}
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"Now if we maximize $P(y|\\v{x},\\v{w})$, we will maximize the chance that each point is classified correctly, which is what we want to do. While this is not exactly the same thing as maximizing the 1-0 training risk, it is a principled way of obtaining the highest probability classification. This process is called **maximum likelihood** estimation since we are maximising the **likelihood of the training data y**, \n",
"\n",
@@ -911,18 +944,16 @@
"Notice that this little process we carried out above tells us something very interesting: **Probabilistic estimation using maximum likelihood is equivalent to Empiricial Risk Minimization using the negative log-likelihood**, since all we did was to minimize the negative log-likelihood over the training samples.\n",
"\n",
"`sklearn` will return the probabilities for our samples, or for that matter, for any input vector set $\\{\\v{x}_i\\}$, i.e. $P(y_i | \\v{x}_i, \\v{w})$:"
- ],
- "metadata": {}
+ ]
},
{
"cell_type": "code",
"execution_count": 16,
- "source": [
- "clf_l.predict_proba(Xtest_l)"
- ],
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [
{
- "output_type": "execute_result",
"data": {
"text/plain": [
"array([[ 0.99749979, 0.00250021],\n",
@@ -934,85 +965,92 @@
" [ 0.52371562, 0.47628438]])"
]
},
+ "execution_count": 16,
"metadata": {},
- "execution_count": 16
+ "output_type": "execute_result"
}
],
- "metadata": {
- "collapsed": false
- }
+ "source": [
+ "clf_l.predict_proba(Xtest_l)"
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"### Discriminative vs Generative Classifier"
- ],
- "metadata": {}
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"Logistic regression is what is known as a **discriminative classifier** as we learn a soft boundary between/among classes. Another paradigm is the **generative classifier** where we learn the distribution of each class. For more examples of generative classifiers, look [here](https://en.wikipedia.org/wiki/Generative_model). \n",
"\n",
"Let us plot the probabilities obtained from `predict_proba`, overlayed on the samples with their true labels:"
- ],
- "metadata": {}
+ ]
},
{
"cell_type": "code",
"execution_count": 17,
- "source": [
- "plt.figure()\n",
- "ax = plt.gca()\n",
- "points_plot_prob(ax, Xtrain_l, Xtest_l, ytrain_l, ytest_l, clf_l, psize=20, alpha=0.1);"
- ],
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [
{
- "output_type": "stream",
"name": "stderr",
+ "output_type": "stream",
"text": [
"/usr/local/anaconda/lib/python3.6/site-packages/matplotlib/contour.py:960: UserWarning: The following kwargs were not used by contour: 'axes'\n",
" s)\n"
]
},
{
- "output_type": "display_data",
"data": {
"image/png": "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",
"text/plain": [
""
]
},
- "metadata": {}
+ "metadata": {},
+ "output_type": "display_data"
}
],
- "metadata": {
- "collapsed": false
- }
+ "source": [
+ "plt.figure()\n",
+ "ax = plt.gca()\n",
+ "points_plot_prob(ax, Xtrain_l, Xtest_l, ytrain_l, ytest_l, clf_l, psize=20, alpha=0.1);"
+ ]
},
{
+ "attachments": {},
"cell_type": "markdown",
+ "metadata": {},
"source": [
"Notice that lines of equal probability, as might be expected are stright lines. What the classifier does is very intuitive: if the probability is greater than 0.5, it classifies the sample as type '1' (male), otherwise it classifies the sample to be class '0'. Thus in the diagram above, where we have plotted predicted values rather than actual labels of samples, there is a clear demarcation at the 0.5 probability line.\n",
"\n",
"Again, this notion of trying to obtain the line or boundary of demarcation is what is called a **discriminative** classifier. The algorithm tries to find a decision boundary that separates the males from the females. To classify a new sample as male or female, it checks on which side of the decision boundary the sample falls, and makes a prediction. In other words we are asking, given $\\v{x}$, what is the probability of a given $y$, or, what is the likelihood $P(y|\\v{x},\\v{w})$?"
- ],
- "metadata": {}
+ ]
},
{
"cell_type": "code",
"execution_count": 18,
- "source": [],
- "outputs": [],
"metadata": {
"collapsed": true
- }
+ },
+ "outputs": [],
+ "source": []
}
],
"metadata": {
+ "interpreter": {
+ "hash": "4885f37acae9217c235118400878352aafa7b76e66df698a1f601374f86939a7"
+ },
"kernelspec": {
- "name": "python3",
- "display_name": "Python 3.7.9 64-bit ('springboard': conda)"
+ "display_name": "Python 3.7.9 64-bit ('springboard': conda)",
+ "name": "python3"
},
"language_info": {
"codemirror_mode": {
@@ -1024,12 +1062,9 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.7.9"
- },
- "interpreter": {
- "hash": "4885f37acae9217c235118400878352aafa7b76e66df698a1f601374f86939a7"
+ "version": "3.10.10"
}
},
"nbformat": 4,
"nbformat_minor": 2
-}
\ No newline at end of file
+}
diff --git a/mec-5.4.4-json-data-wrangling-mini-project/Mini_Project_Wrangling_Json_Exercise.ipynb b/mec-5.4.4-json-data-wrangling-mini-project/Mini_Project_Wrangling_Json_Exercise.ipynb
index a8bfea9e2..b10950b5c 100755
--- a/mec-5.4.4-json-data-wrangling-mini-project/Mini_Project_Wrangling_Json_Exercise.ipynb
+++ b/mec-5.4.4-json-data-wrangling-mini-project/Mini_Project_Wrangling_Json_Exercise.ipynb
@@ -1,6 +1,7 @@
{
"cells": [
{
+ "attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
@@ -27,6 +28,7 @@
]
},
{
+ "attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
@@ -42,10 +44,11 @@
"outputs": [],
"source": [
"import json\n",
- "from pandas.io.json import json_normalize"
+ "from pandas import json_normalize"
]
},
{
+ "attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
@@ -232,6 +235,7 @@
]
},
{
+ "attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
@@ -574,6 +578,7 @@
]
},
{
+ "attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [