{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# **Linear Regression**\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Table of contents:\n", "\n", "1. [What is Linear Regression?](#What-is-Linear-Regression)\n", "1. [Single Linear Regression](#Single-Linear-Regression)\n", "1. [Multiple Linear Regression](#Multiple-Linear-Regression)\n", "1. [Logistic Regression](#Logistic-Regression)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What is Linear Regression?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](https://upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Linear_regression.svg/1200px-Linear_regression.svg.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- It is a Machine Learning Model.\n", "- It is used to \"fit a straight line\" to the data.\n", "- Finds a linear relationship between input data and output data.\n", "\n", "*What is linear?*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Linear means that it is an algebraic function which finds a relationship that looks like so:\n", "$$ y = f(x) $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Where f is a polynomial function of **degree 1.**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thus, the final function will look like so: $$y = w*x + b$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](https://acadgild.com/blog/wp-content/uploads/2018/07/Linear-Regression.jpg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Where w and b are 2 *parameters* that the model will find out." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "y is known an the **dependent variable**, as it depends on x.\n", "\n", "x is known as the **independent variable**, since it is our input and is independent of any constraints." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, how is this going to be calculated? This is where the math kicks in." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Parameter Calculation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A simple way to think about this problem:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Suppose you are given as sample data house area in square feet, and corresponding values of house prices. Now, your x value is the house area, and the y value is the value of house prices.\n", "- Here, we are considering that given the area, we want to predict the price of the house. Thus, the price is *dependent* on the area." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, now we want the values of w and b that allow us to perform this task. But a simple question arises - *how do we judge the performance of our model?*\n", "\n", "The answer lies in what we saw in the previous lecture - a **performance metric.**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](http://onlinestatbook.com/2/regression/graphics/reg_error.gif)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a regression task, as the name of the model implies. So we will use a regression metric.\n", "\n", "We generally resort to use of the mean squared error.\n", "\n", "$$J = \\frac{1}{2n}*\\sum_{i=0}^{n-1} (\\hat{y}_{i} - y_{i})^2$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To get the best values of the parameters, we will look at **gradient descent** and **backpropogation** using this toy example, so we can gain clarity and understand these concepts that are so widely used in Deep Learning." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mathematical way of finding the right value for a parameter is by using partial differentiation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**What is differentiation? What does it represent?**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's start at what is the rate of change of a function with respect to a variable.\n", "\n", "So, given a graph, we want to find out the rate of change of $f(x)$ from some $x_{1}$ to some $x_{2}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](http://xaktly.com/Images/Mathematics/Slope/SlopeDefinition.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What does this represent?\n", "\n", "This represents the average amount of change of y per unit of x.\n", "\n", "When we bring $x_{2}$ closer and closer to $x_{1}$, we eventually end up with:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](https://www.themathpage.com/aCalc/calc_IMG/007b.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](https://dj1hlxw0wr920.cloudfront.net/userfiles/wyzfiles/8e482816-953a-4e39-b715-f8ef0f6ae356.gif)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mathematical notation for the same is:\n", "$$\\frac{dy}{dx} = \\lim_{h \\to 0} \\frac{f(x+h) - f(x)}{h}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, what are we doing when we are computing the derivative? We are finding out the rate of change of $y$ wrt $x$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we also know one more fact:\n", "\n", "When we want to find the value of $x$ at which $f(x)$ is minimum, we do $\\frac{dy}{dx}=0$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, we want to find the value of w and b at which we get the minimum value of our performance metric(since it is an error, we want to minimize it). So we naturally resort to our best friend, $\\frac{dy}{dx} = 0$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ \\frac{\\partial{J(w,b)}}{\\partial{w}} = 0$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since this is a function that depends on 2 parameters, we use the partial derivative." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](https://cdn-images-1.medium.com/max/1600/1*jNyE54fTVOH1203IwYeNEg.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, we update the weights with the gradient value. \n", "\n", "The idea is that the derivative tells us what is the contribution of the parameter that we are differentiating with respect to, to the error value." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\frac{\\partial{J}}{\\partial{w}} = (\\hat{y}-y)*x$$\n", "\n", "$$\\frac{\\partial{J}}{\\partial{b}} = (\\hat{y}-y)$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the following update rule:\n", "$$ w = w - \\alpha * \\frac{\\partial{J}}{\\partial{w}}$$\n", "\n", "$$ b = b - \\alpha * \\frac{\\partial{J}}{\\partial{b}}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\alpha$ is known as the *learning rate*." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We perform this for all the samples we have, multiplr times over, until the gradient(value of the derivative) becomes small enough to terminate." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Enough theory now. Let's code!**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Single Linear Regression" ] }, { "cell_type": "code", "execution_count": 140, "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 222, "metadata": {}, "outputs": [], "source": [ "X = np.linspace(1,100,num=100)*5+np.random.randn(100)*30" ] }, { "cell_type": "code", "execution_count": 223, "metadata": {}, "outputs": [], "source": [ "Y = np.linspace(1,50,num=100)" ] }, { "cell_type": "code", "execution_count": 224, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 225, "metadata": {}, "outputs": [], "source": [ "def plot_graph(X,Y,marker = 'bo',ylabel = 'House Price in lakhs', xlabel = 'Area in Square Feet'):\n", " plt.figure(figsize=(8,5))\n", " plt.ylabel(ylabel)\n", " plt.xlabel(xlabel)\n", " if marker is not None:\n", " plt.plot(X,Y,marker, markersize=1)\n", " else:\n", " plt.plot(X,Y)" ] }, { "cell_type": "code", "execution_count": 226, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_graph(X,Y)" ] }, { "cell_type": "code", "execution_count": 227, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 227, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "W,b = np.random.randn(2)\n", "alpha = 0.000001\n", "plt.figure(figsize=(8,5))\n", "plt.ylabel('House Price in lakhs')\n", "plt.xlabel('Area in Square Feet')\n", "plt.plot(X,W*X+b)\n", "plt.plot(X,Y,'bo',markersize=2)" ] }, { "cell_type": "code", "execution_count": 228, "metadata": {}, "outputs": [], "source": [ "W_list = [W]\n", "b_list = [b]\n", "J_list = []" ] }, { "cell_type": "code", "execution_count": 229, "metadata": {}, "outputs": [], "source": [ "for xi, yi in zip(X,Y):\n", " yhat = W * xi + b\n", " J = 1/2*(yhat - yi)**2\n", " W -= alpha*(yhat-yi)*xi\n", " b -= alpha*(yhat-yi)\n", " W_list.append(W)\n", " b_list.append(b)\n", " J_list.append(J)" ] }, { "cell_type": "code", "execution_count": 230, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.09977198114664937" ] }, "execution_count": 230, "metadata": {}, "output_type": "execute_result" } ], "source": [ "W" ] }, { "cell_type": "code", "execution_count": 231, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.846931335583396" ] }, "execution_count": 231, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b" ] }, { "cell_type": "code", "execution_count": 232, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 232, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.ylabel('House Price in lakhs')\n", "plt.xlabel('Area in Square Feet')\n", "plt.plot(X,Y,'bo', markersize=3)\n", "plt.plot(X, W*X+b)" ] }, { "cell_type": "code", "execution_count": 233, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_graph(np.arange(len(W_list)),W_list, xlabel = 'Iteration', ylabel = 'W', marker = None)\n", "plot_graph(np.arange(len(b_list)),b_list, xlabel = 'Iteration', ylabel = 'b', marker = None)\n", "plot_graph(np.arange(len(J_list)),J_list, xlabel = 'Iteration', ylabel = 'J per sample', marker = None)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This will be really slow! Going through each sample one by one and updating the gradients accordingly and updating is a slow process. So, to solve this and to make operatrions faster, we will calculate the gradients for a batch of samples together and update the weights and biases by the mean value of the gradients." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, to do this, we should use vector opeartions that can help speed up this process." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$X = [ \\left( \\begin{array} {ccc} x_{0} & x_{1} \\end{array} \\right) ]$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$W = [ \\left( \\begin{array} {ccc} w_{0} \\\\ w_{1} \\end{array} \\right) ]$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$X*W = w_{0}*x_{0} + w_{1}*x_{1}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$x_{0} = 1$, hence we get back our original equation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, this can be applied to matrices. Note the shape of X is $1 * 2$, and the shape of W is $2 * 1$. Thus, is we add multiple rows to our x, we get an X of shape $n * 2$ where n is the number of examples." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The resulting $X*W$ gives us an $n * 1$ matrix where each row is our prediction." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thus, we can now calculate the loss (J) and the gradients easily, and speed this up." ] }, { "cell_type": "code", "execution_count": 234, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(100,)\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X_arr = np.vstack((X,np.ones(X.shape))).transpose()\n", "print(X.shape)\n", "#raise ValueError\n", "W = np.random.randn(2).reshape(2,1)\n", "alpha = 0.000001\n", "plt.figure(figsize=(8,5))\n", "plt.ylabel('House Price in lakhs')\n", "plt.xlabel('Area in Square Feet')\n", "plt.plot(X,np.matmul(X_arr,W))\n", "plt.plot(X,Y,'bo',markersize=2)\n", "\n", "W_list = [W[0,0]]\n", "b_list = [W[1,0]]\n", "J_list = []" ] }, { "cell_type": "code", "execution_count": 248, "metadata": {}, "outputs": [], "source": [ "batch_size = 10\n", "num_epochs = 5\n", "for epoch in range(num_epochs):\n", " for idx in range(len(X)//batch_size):\n", " X_temp = X_arr[idx*10:(idx+1)*10,:]\n", " Y_temp = Y[idx*10:(idx+1)*10].reshape(10,1)\n", " yhat = np.matmul(X_temp,W)\n", " J = 1/(2*batch_size)*(yhat - Y_temp)**2\n", " W -= np.mean((alpha*(yhat-Y_temp)*X_temp), axis=0).reshape(2,1)\n", " W_list.append(W[0,0])\n", " b_list.append(W[1,0])\n", " J_list.append(J.mean())" ] }, { "cell_type": "code", "execution_count": 249, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0.09788443],\n", " [-0.48958871]])" ] }, "execution_count": 249, "metadata": {}, "output_type": "execute_result" } ], "source": [ "W" ] }, { "cell_type": "code", "execution_count": 250, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 250, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.ylabel('House Price in lakhs')\n", "plt.xlabel('Area in Square Feet')\n", "plt.plot(X,Y,'bo', markersize=3)\n", "plt.plot(X, np.matmul(X_arr,W))" ] }, { "cell_type": "code", "execution_count": 251, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_graph(np.arange(len(W_list)),W_list, xlabel = 'Iteration', ylabel = 'W', marker = None)\n", "plot_graph(np.arange(len(b_list)),b_list, xlabel = 'Iteration', ylabel = 'b', marker = None)\n", "plot_graph(np.arange(len(J_list)),J_list, xlabel = 'Iteration', ylabel = 'J per batch', marker = None)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This was single linear regression, as it modelled the relationship between 1 independent and 1 independent variable. Now, let us look at multiple linear regression, to model the relationship between 2 or more independent variable and 1 dependent variable. Remeber, now we cannot visualise the entire input space." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multiple Linear Regression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$y = w_{0} + w_{1}*x_{1} + w_{2}*x_{2} +\\space...\\space+ w_{n}*x_{n}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, the input is an n-dimensional vector." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An n-dimenional vector means an array that has n elements." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, the first way to perform our linear regression calculation without using vectors/arrays looks like a really bad idea. Why?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because defining n constants manually is a pain." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hence, we use our second approach, that is to use an input array of size $m * n$, where m is the number of training samples and n is the dimensionality of the input vector.\n", "\n", "Now, we have a weight vector of dimensionality $n * 1$. Thus, we have the output dimensions as $m*1$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\frac{\\partial{J}}{\\partial{w_{j}}} = \\sum_{i = 1}^{n}\\frac{(\\hat{y}_{i}-y_{i})*x^{j}_{i}}{n}$$\n", "\n", "We use the following update rule:\n", "$$ w_{i} = w_{i} - \\alpha * \\frac{\\partial{J}}{\\partial{w_{i}}}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, try to modify the earlier code and arrive at the code for multiple linear regression." ] }, { "cell_type": "code", "execution_count": 305, "metadata": {}, "outputs": [], "source": [ "from sklearn.datasets import load_diabetes, make_regression" ] }, { "cell_type": "code", "execution_count": 275, "metadata": {}, "outputs": [], "source": [ "data = load_diabetes()" ] }, { "cell_type": "code", "execution_count": 277, "metadata": {}, "outputs": [], "source": [ "X, Y = data['data'], data['target']" ] }, { "cell_type": "code", "execution_count": 306, "metadata": {}, "outputs": [], "source": [ "X,Y = make_regression(500,4)" ] }, { "cell_type": "code", "execution_count": 307, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(500, 4)" ] }, "execution_count": 307, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X.shape" ] }, { "cell_type": "code", "execution_count": 308, "metadata": {}, "outputs": [], "source": [ "W = np.random.rand(X.shape[1]+1,1)" ] }, { "cell_type": "code", "execution_count": 309, "metadata": {}, "outputs": [], "source": [ "X_arr = np.hstack((X,np.ones((X.shape[0],1))))" ] }, { "cell_type": "code", "execution_count": 310, "metadata": {}, "outputs": [], "source": [ "W1_list = [W[0,0]]\n", "W2_list = [W[1,0]]\n", "W3_list = [W[2,0]]\n", "W4_list = [W[3,0]]\n", "W5_list = [W[4,0]]\n", "J_list = []" ] }, { "cell_type": "code", "execution_count": 311, "metadata": {}, "outputs": [], "source": [ "alpha = 0.1\n", "batch_size = 10\n", "num_epochs = 5\n", "for epoch in range(num_epochs):\n", " for idx in range(len(X)//batch_size):\n", " X_temp = X_arr[idx*batch_size:(idx+1)*batch_size,:]\n", " Y_temp = Y[idx*batch_size:(idx+1)*batch_size].reshape(batch_size,1)\n", " yhat = np.matmul(X_temp,W)\n", " J = 1/(2*batch_size)*(yhat - Y_temp)**2\n", " W -= np.mean((alpha*(yhat-Y_temp)*X_temp), axis=0).reshape(W.shape[0],1)\n", " W1_list.append(W[0,0])\n", " W2_list.append(W[1,0])\n", " W3_list.append(W[2,0])\n", " W4_list.append(W[3,0])\n", " W5_list.append(W[4,0])\n", " J_list.append(J.mean())" ] }, { "cell_type": "code", "execution_count": 312, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAf4AAAFACAYAAABdrx4gAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAIABJREFUeJzt3XuUpHV95/H3t6q6ey4MzAwzCM6ggzqrURMRJ4hiXBSjYC64Hj2B5ChRNpMLJhqziZj8QTaXjVk3MZqNJiSgmPXGGg2cPSjhELxhuAyICCIyKpdxEAYGhhGYme6u7/5RT3VXX6eqpqurnun365w+Vc+vnq7+8Vjjp37XJzITSZK0NFT6XQFJkrR4DH5JkpYQg1+SpCXE4JckaQkx+CVJWkIMfkmSlhCDX5KkJcTglyRpCTH4JUlaQmr9rkAvrFu3Ljdt2tTvakiStGhuvvnmhzNz/cHOOyyDf9OmTWzbtq3f1ZAkadFExL3tnGdXvyRJS4jBL0nSEmLwS5K0hBj8kiQtIQa/JElLiMEvSdISYvBLkrSEGPySJC0hBr8kSUtIz4I/Ii6JiIci4vaWsvdHxHci4raI+HxErG557b0RsT0i7oqI17WUn1GUbY+IC3pV3079x/ceYf/YeL+rIUlSR3rZ4v8YcMa0squBF2bmTwHfBd4LEBHPB84GXlD8zocjohoRVeDvgDOB5wPnFOf21UOP7+Ocf7yeL97+o35XRZKkjvQs+DPzK8DuaWX/lpljxeH1wMbi+VnApzNzf2b+ANgOnFz8bM/M72fmAeDTxbl9tW+0Xjza4pcklUs/x/jfDnyheL4BuL/ltR1F2VzlM0TE1ojYFhHbdu3a1YPqTqpnFo89/TOSJC24vgR/RPwRMAZ8olk0y2k5T/nMwsyLMnNLZm5Zv/6gdyU8JJPBb/JLkspl0W/LGxHnAj8PnJ45kZw7gONbTtsI7Cyez1XeN82Wvi1+SVLZLGqLPyLOAN4D/GJmPtny0hXA2RExEhEnAJuBG4GbgM0RcUJEDNOYAHjFYtZ5Ns3vK2mLX5JUMj1r8UfEp4DTgHURsQO4kMYs/hHg6ogAuD4zfyMz74iIy4Bv0xgCOD8zx4v3eQdwFVAFLsnMO3pV53ZNtPht8kuSSqZnwZ+Z58xSfPE85/858OezlF8JXLmAVTtkzbH9cXNfklQy7tzXhbpd/ZKkkjL4u5ATk/sMfklSuRj8XXAdvySprAz+LtjilySVlcHfhckx/j5XRJKkDhn8XXA5nySprAz+LqRj/JKkkjL4u1B3jF+SVFIGfxdcxy9JKiuDvwsu55MklZXB34VmQ3/cFr8kqWQM/i5MtvgNfklSuRj8XWh28Zv7kqSyMfi7MNHid5BfklQyBn8XXMcvSSorg78L9XrxaF+/JKlkDP4uuI5fklRWBn8XJnfu6289JEnqlMHfhXQ5nySppAz+LtjilySVlcHfBcf4JUllZfB3oRn84zb5JUklY/B3Ie3qlySVlMHfBbv6JUllZfB3YXJyn8EvSSoXg78LdbfslSSVlMHfBdfxS5LKyuDvgrfllSSVlcHfhbotfklSSRn8XXBynySprAz+LqST+yRJJWXwd6Fedx2/JKmcehb8EXFJRDwUEbe3lK2NiKsj4u7icU1RHhHxoYjYHhG3RcRJLb9zbnH+3RFxbq/q24lmS98teyVJZdPLFv/HgDOmlV0AXJOZm4FrimOAM4HNxc9W4CPQ+KIAXAi8FDgZuLD5ZaGfXMcvSSqrngV/Zn4F2D2t+Czg0uL5pcAbWso/ng3XA6sj4jjgdcDVmbk7Mx8Frmbml4lFl07ukySV1GKP8T8tMx8AKB6PKco3APe3nLejKJurfIaI2BoR2yJi265duxa84q0m9+rv6Z+RJGnBDcrkvpilLOcpn1mYeVFmbsnMLevXr1/Qyk3ncj5JUlktdvA/WHThUzw+VJTvAI5vOW8jsHOe8r5K3MBHklROix38VwDNmfnnApe3lL+1mN1/CrCnGAq4CnhtRKwpJvW9tijrq8kx/v7WQ5KkTtV69cYR8SngNGBdROygMTv/fcBlEXEecB/w5uL0K4HXA9uBJ4G3AWTm7oj4U+Cm4rw/yczpEwYXnev4JUll1bPgz8xz5njp9FnOTeD8Od7nEuCSBazaIavb4pckldSgTO4rFW/SI0kqK4O/C+7VL0kqK4O/CxNd/Sa/JKlkDP4u2NUvSSorg78LTu6TJJWVwd+FTJfzSZLKyeDvgl39kqSyMvi7YFe/JKmsDP4u2OKXJJWVwd+FZt6b+5KksjH4u2CLX5JUVgZ/Fwx+SVJZGfxdmNy5r7/1kCSpUwZ/F9IWvySppAz+LjRb+ga/JKlsDP4u1L07nySppAz+LtQnlvOZ/JKkcjH4u5C2+CVJJWXwd8HlfJKksjL4uzC5nM/glySVi8HfhfrEbXn7XBFJkjpk8HchJ+7OZ/JLksrF4O+Cy/kkSWVl8B/EeD259Ov3cOv9j02UOblPklRWBv9BBHDhFXfwpbsemiir29UvSSopg/8gKpWgEjA2PhnyruOXJJWVwd+GWrXCaMut+GzxS5LKyuBvw1AlprT4W5fzuW2vJKlMDP421KoVxsZntvjBtfySpHIx+NswVA1G6zPH+MHufklSuRj8bahVprb4W7PeCX6SpDIx+NtQq84+xj/9uSRJg64vwR8RvxsRd0TE7RHxqYhYFhEnRMQNEXF3RHwmIoaLc0eK4+3F65sWu75D1cqUrv7WsDf3JUllsujBHxEbgN8BtmTmC4EqcDbwl8AHMnMz8ChwXvEr5wGPZuZzgA8U5y2qWiXmnNxni1+SVCb96uqvAcsjogasAB4AXg18tnj9UuANxfOzimOK10+PiFjEujbW8c+ygQ8Y/JKkcln04M/MHwL/C7iPRuDvAW4GHsvMseK0HcCG4vkG4P7id8eK84+e/r4RsTUitkXEtl27di1onYeqwdgsG/gAtBRLkjTw+tHVv4ZGK/4E4OnASuDMWU5txutsrfsZzezMvCgzt2TmlvXr1y9UdYFmV7+T+yRJ5dePrv7XAD/IzF2ZOQp8Dng5sLro+gfYCOwsnu8AjgcoXj8K2L2YFW509TvGL0kqv34E/33AKRGxohirPx34NnAt8KbinHOBy4vnVxTHFK//ey7yPrmNrv65xvgXsyaSJB2afozx30Bjkt4twLeKOlwEvAd4d0RspzGGf3HxKxcDRxfl7wYuWOw6T9/AZ+pyPpNfklQetYOfsvAy80LgwmnF3wdOnuXcfcCbF6NecxmqxpRZ/a0T+mzxS5LKxJ372lCrVKbN6ndynySpnAz+Nkzfsjed3CdJKimDvw2NLXvnGuPvR40kSeqOwd8G1/FLkg4XBn8bZm7ZO/nauLP7JEklYvC3YeaWvUklms/7VClJkrpg8LehsY5/6qY9tUrj0rmOX5JUJgZ/Gxrr+Ke2+KtFk98WvySpTAz+NtRmbNnbmPAHTu6TJJXLQXfui4hTgT8GnlmcH0Bm5rN6W7XBUatUGK8nmUlENFr8VYNfklQ+7WzZezHwu8DNwHhvqzOYhoqQHx1PhmuN4G+2+M19SVKZtBP8ezLzCz2vyQCrVRsjImP1OsNUqCctY/wmvySpPOYM/og4qXh6bUS8H/gcsL/5embe0uO6DYxm6765lj8zqVWrgJP7JEnlMl+L/6+mHW9peZ7Aqxe+OoNpqNniL2b22+KXJJXVnMGfma9azIoMsloxxt+c2T91jN/glySVx0GX80XE/4iI1S3HayLiz3pbrcEyVGzW01zLX69PruNvWd4vSdLAa2cd/5mZ+VjzIDMfBV7fuyoNnokW/8QYv139kqRyaif4qxEx0jyIiOXAyDznH3ZaZ/VD0dXvOn5JUgm1s5zv/wDXRMRHaUzqezvw8Z7WasAMTZvV35jc19yrv2/VkiSpYwcN/sz8nxFxG/AaGrv2/WlmXtXzmg2QiRb/+MzJfbb4JUll0s6WvX+Zme8BvjhL2ZLQ7NYfLbr6p47x961akiR1rJ0x/p+dpezMha7IIGvO6rfFL0kqu/l27vtN4LeAZxVd/U2rgOt6XbFBMjmrv2jxM9nidx2/JKlM5uvq/yTwBeAvgAtayvdm5u6e1mrATNykZ5YNfOqu45cklch8O/ftAfYA5wBExDHAMuCIiDgiM+9bnCr2X625gc9YncwsxvgbZXb1S5LKpJ2d+34hIu4GfgB8GbiHRk/AkjG5ZW99Yvlezcl9kqQSamdy358BpwDfzcwTgNNZYmP8zZv0jI7nRAvfDXwkSWXUTvCPZuYjQCUiKpl5LXBij+s1UJqt+7F6faKF76x+SVIZtbNz32MRcQTwVeATEfEQMNbbag2W2Vr8k2P8fauWJEkda6fFfxbwFPAuGpv4fA/4hV5WatC03qRn+hi/y/kkSWXSzpa9T0TEscDJwG7gqqLrf8lozupvdPUXLX7H+CVJJdTOrP7/CtwIvBF4E3B9RLy91xUbJMOzTe5zHb8kqYTa6er/feDFmfmrmXku8BLgkPbpj4jVEfHZiPhORNwZES+LiLURcXVE3F08rinOjYj4UERsj4jbIuKkQ/nb3Wjdua85pl91cp8kqYTaCf4dwN6W473A/Yf4dz8IfDEznwe8CLiTxu6A12TmZuAaJncLPBPYXPxsBT5yiH+7Y5Pr+HNiTH9yjH+xayNJUvfm26v/3cXTHwI3RMTlNLapP4tG139XIuJI4JXArwJk5gHgQEScBZxWnHYp8CUaPQtnAR/PRuJeX/QWHJeZD3Rbh041b9IzOqXF7859kqTyma/Fv6r4+R7wrzRCH+By4FBC91nALuCjEfGNiPiniFgJPK0Z5sXjMcX5G5jaw7CjKJsiIrZGxLaI2LZr165DqN5MlUpQicas/hlj/Oa+JKlE5tur/7/38G+eBPx2Zt4QER9k6k2ApotZymbEbWZeBFwEsGXLlgWP41q1wmjrrH7H+CVJJdTOGP9C2wHsyMwbiuPP0vgi8GBEHAdQPD7Ucv7xLb+/Edi5SHWdMFSJKev4h1zOJ0kqoUUP/sz8EXB/RDy3KDod+DZwBXBuUXYujSEFivK3FrP7TwH2LOb4flOtWilm9U/buc++fklSicy7gU9EVIHfycwPLPDf/W0a2/8OA98H3kbjS8hlEXEecB/w5uLcK4HXA9uBJ4tzF91QNRit5yx79fejNpIkdWfe4M/M8WK2/YIGf2beCmyZ5aXTZzk3gfMX8u93o1YpWvx1x/glSeXVzk16rouI/w18BniiWZiZt/SsVgOoVp06xt9c22/uS5LKpJ3gf3nx+CctZQm8euGrM7iGqpWiq98WvySpvNq5Sc+rFqMig65WiSmT+xzjlySVUTs36XlaRFwcEV8ojp9fTMBbUmrVSnGTnsaxO/dJksqoneV8HwOuAp5eHH8XeFevKjSohqrBWL0+y179Br8kqTzaCf51mXkZUAfIzDFgvKe1GkC1YgOfmXfn62OlJEnqUDvB/0REHE2xTW5zE52e1moANbr6ZxvjN/klSeXRzqz+d9PYPe/ZEXEdsB54U09rNYCGqsG+0cngr1SCCHfukySVSzuz+m+JiP8MPJfGDXPuyszRntdswDQ28BmbWLdfiaASYVe/JKlUDhr8EbEM+C3gFTS6+78aEX+fmft6XblBMlSNYlZ/0eKPxo9d/ZKkMmmnq//jwF7gb4vjc4B/ZnIv/SWhVqkwVq9PtPArEYQtfklSybQT/M/NzBe1HF8bEd/sVYUGVXPL3mYLP4oWv8v5JEll0s6s/m8UM/kBiIiXAtf1rkqDqbFl7+Q6/skxfoNfklQe7bT4Xwq8NSLuK46fAdwZEd+icfO8n+pZ7QbI9HX8Tu6TJJVRO8F/Rs9rUQITW/bWJyf3hZP7JEkl085yvnsXoyKDbmLL3uI4iha/uS9JKpN2xvhFcx2/y/kkSeVm8LepsY6/PtHCDyf3SZJKaM6u/ojYC8yVavuB7wF/lJnX9KJig6ZWDcbq01r8lWC83ueKSZLUgTmDPzNXzfVaRFSBFwKfKB4Pe7VKhfF6Ml5vruMP1/FLkkqnq67+zBzPzG8yuZvfYW+o2rgb34GxRhO/McZvV78kqVwOaYw/M/9hoSoy6GrVxqU6MN4MftfxS5LKx8l9bapVprf4w3X8kqTSMfjbNNRs8RfBH0VXv7kvSSoTg79NteYY/5Suflv8kqRyMfjb1Gzx7x8tgr+CY/ySpNIx+Ns0Umtcqn2j44Bj/JKkcjL42zQR/GPN4G+O8Rv8kqTyMPjbNFwE/1MHmpP7iuV87twnSSoRg79NI7Uq0Nrib3T1j9vilySViMHfpmaLf9+Bya7+asWufklSufQt+COiGhHfiIj/VxyfEBE3RMTdEfGZiBguykeK4+3F65v6Ud/mGP9TLZP7nNUvSSqbfrb43wnc2XL8l8AHMnMz8ChwXlF+HvBoZj4H+EBx3qIbnjarv7GBj7P6JUnl0pfgj4iNwM8B/1QcB/Bq4LPFKZcCbyien1UcU7x+enH+omqO8T81ZTmfLX5JUrn0q8X/N8AfAM058UcDj2XmWHG8A9hQPN8A3A9QvL6nOH9RTbb4p+7c5xi/JKlMFj34I+LngYcy8+bW4llOzTZea33frRGxLSK27dq1awFqOtXMDXy8La8kqXz60eI/FfjFiLgH+DSNLv6/AVZHRK04ZyOws3i+AzgeoHj9KGD39DfNzIsyc0tmblm/fv2CV3p68LuOX5JURose/Jn53szcmJmbgLOBf8/MXwGuBd5UnHYucHnx/IrimOL1f88+9K8Pz5jVj1v2SpJKZ5DW8b8HeHdEbKcxhn9xUX4xcHRR/m7ggn5Ubrja3Llv6nI+c1+SVCa1g5/SO5n5JeBLxfPvAyfPcs4+4M2LWrFZRATDtQr7xlom91VgdNzklySVxyC1+AfeSK3CgSL4o7gtr1v2SpLKxODvQHOCH7hznySpnAz+DjQ38YHmcj7X8UuSysXg78DwrC1+g1+SVB4Gfwdau/ojGhP+XMcvSSoTg78DM1v8ruOXJJWLwd+B2Sb3mfuSpDIx+DswY3JfxRa/JKlcDP4ODE8Z42/eltfglySVh8HfgWZXf6W4X6Bd/ZKksjH4OzA8EfxRPOLOfZKkUjH4OzAyI/jt6pcklYvB34Fmiz9auvpdxy9JKhODvwPNWf2tXf1u2StJKhODvwPDs0zu8yY9kqQyMfg7MGOM33X8kqSSMfg7MH2MP2zxS5JKxuDvwMQYf8UxfklSORn8HXA5nySp7Az+Dji5T5JUdgZ/B0YmxvijeHRynySpXAz+Dsy2V3/dJr8kqUQM/g40J/cFk5P7zH1JUpkY/B2YMcZfcXKfJKlcDP4OTB/j97a8kqSyMfg7MNHiL65axcl9kqSSMfg7MPMmPXb1S5LKxeDvwPC0DXzcsleSVDYGfwdGpu3V35zk57a9kqSyMPg7MH3L3mYPwL7Ret/qJElSJwz+Dkxfzrd2xTAAjz55oF9VkiSpIwZ/B6ZP7ltdBP/uJwx+SVI5LHrwR8TxEXFtRNwZEXdExDuL8rURcXVE3F08rinKIyI+FBHbI+K2iDhpsevcNFSdnNQHsHalLX5JUrn0o8U/BvxeZv4EcApwfkQ8H7gAuCYzNwPXFMcAZwKbi5+twEcWv8oNEcFIrTLZ1b9yCIBHnxydce67L7uVa7/z0GJWT5Kkg1r04M/MBzLzluL5XuBOYANwFnBpcdqlwBuK52cBH8+G64HVEXHcIld7wnCtMtHVv6Y5xj+tq3/f6Difu+WHfPm7uxa9fpIkzaevY/wRsQl4MXAD8LTMfAAaXw6AY4rTNgD3t/zajqKsL0Zq1YkW/1HLh4iYOcbfPN67b2yxqydJ0rz6FvwRcQTwL8C7MvPx+U6dpWzGwvmI2BoR2yJi265dvWtpj9QqE2P8tWqFI5cNzRjjnwz+mUMAkiT1U1+CPyKGaIT+JzLzc0Xxg80u/OKxOUC+Azi+5dc3Ajunv2dmXpSZWzJzy/r163tW99YxfmhM8Jve4n/4x/sBW/ySpMHTj1n9AVwM3JmZf93y0hXAucXzc4HLW8rfWszuPwXY0xwS6IfWMX6ANSuGeGza5L7mF4HHbfFLkgZMrQ9/81TgLcC3IuLWouwPgfcBl0XEecB9wJuL164EXg9sB54E3ra41Z1qZFrwr105zM7H9k0555EfO8YvSRpMix78mfk1Zh+3Bzh9lvMTOL+nlerAypEa1Upri3+YO3Y2pijc/eBennPMETziGL8kaUD1o8Vfahf+wgumHK8pxvhvue9R3vjhr/OZrafwSMsYf2ZOTAaUJKnfDP4OPffYVVOO16wYZv9Ynf/43iMA3PXg3okx/rF6sm+0zvLh6qLXU5Kk2bhX/yFq7t73tbsfBuDeR57k4ZZZ/k7wkyQNEoP/EDV377v53kcBuPeRJ9j9xH6Gq41L6zi/JGmQGPyHqHmjngPjdaDR4n/kxwc4fu1yAB53Zr8kaYAY/IeoeWtegGOPXMY9jzzBkwfGOWHdSsAlfZKkwWLwH6Jmix/gjBcey+h4YzfhTUc3g9+ufknS4DD4D1HzRj3Lhiqc9tzJrYI3FS3+x5+yxS9JGhwu5ztE1UqwevkQz1i7gmetO2Ki3Ba/JGkQGfwL4BWb1/MTx63i6auXUasEY/Vk45rlVCvhGL8kaaAY/Avgb8958cTzjWuWc88jT7Ju1QhHjNRs8UuSBopj/AvsmUevZLhWYeVwlSOX12zxS5IGii3+BfaK56yjXuzPv2pkyJ37JEkDxeBfYL/2ymfxa698FgCrltXcwEeSNFDs6u+hVcuG7OqXJA0Ug7+Hjlzm5D5J0mAx+Hto1TIn90mSBovB30NHLh9i775RMrPfVZEkCTD4e2rVshr1hCcOjPe7KpIkAQZ/T61aNgS4ba8kaXAY/D207ogRAHY+tq/PNZEkqcHg76EXbTwKgG/c92ifayJJUoPB30PHHLmMDauX8437Hut3VSRJAgz+nnvJM9dw8722+CVJg8Hg77GTnrGaHz2+j52PPdXvqkiSZPD32kueuRaAWxznlyQNAIO/x5533CqWDVX46HX38Oa//zqX3/rDfldJkrSEeXe+HhuqVnjJM9dw3fZHWLNiiHd++lbu+tFeTj5hLS8+fg1HrRjqdxUlSUtIHI7byW7ZsiW3bdvW72pMeGDPU+x+4gDPOeYIfv//3sYV39wJwM9sXsc/n/fSPtdOknQ4iIibM3PLwc6zq38RHHfUcl7w9KMYqVX54Nkn8tU/eBVvP/UEvnr3w9z7yBP9rp4kaQkx+BdZRHD82hVsfeWzqFaCT990P3ueGuWme3bz0F53+JMk9ZZj/H1y7FHLePXzjuFTN97HZ2/ewa69+wF49fOO4f1v+imOLrb7lSRpIZWmxR8RZ0TEXRGxPSIu6Hd9FsIvv/QZPPbkKGtXDPPhXzmJd71mM1+7+2F+7kNfY/tDe2ecv+fJUX68f6wPNZUkHS5KMbkvIqrAd4GfBXYANwHnZOa3Zzt/0Cb3zWfbPbt54YajWDZUBeD2H+7hVz96E7VK8A9veQkRsPuJA9zwg9187Lp7WLWsxt+cfSIvf/Y6Hv7xfj55w30cd9Qy3njSRqqV6PN/jSSpX9qd3FeW4H8Z8MeZ+bri+L0AmfkXs51fpuCfzXd+9Di/9A/Xs+epydv5RsDP/eRxfPuBx/n+ric4ZtUIe/eN8dToOADPPHoFy4eq7B+rc9TyITYdvYKnHbmM7/xoLxHwoo2rWT5cZbyejI7XGalVOWJZjb37Rtk/WmdkqMJIrcpwrcJIy08lDs8vE3GY/ndJKo8XbTyKY45ctmDv127wl2WMfwNwf8vxDmDKOriI2ApsBXjGM56xeDXrgecdeySXn38qN96zm7UrhlmzcpgNq5dz7FHLeGL/GB//j3v5wcM/plat8PZTT+C7D+7lUzfex4rhKkPVCo89OcqNP9jNg3v3s/mYI6hn8uXv7qIE3/Ekacm46C0v4bUvOHbR/25Zgn+25tmUGMvMi4CLoNHiX4xK9dKmdSvZtG7ljPKVIzV+87RnTyl7zjFH8PqfPG7GufV6Uim6//eNjlPPpFoJapUK+0bHeWL/GEcsq7GsVuXAeJ39Y3X2j42zf7TOgfE6+0bH/bIgST1y/NoVffm7ZQn+HcDxLccbgZ19qktpVFrG/JtzCJpWjtRYOTL5P/+ySrU4x50EJelwVpZZ/TcBmyPihIgYBs4GruhznSRJKp1StPgzcywi3gFcBVSBSzLzjj5XS5Kk0ilF8ANk5pXAlf2uhyRJZVaWrn5JkrQADH5JkpYQg1+SpCXE4JckaQkx+CVJWkIMfkmSlhCDX5KkJaQUd+frVETsAu5d4LddBzy8wO+51HgNF4bX8dB5DReG1/HQLeQ1fGZmrj/YSYdl8PdCRGxr53aHmpvXcGF4HQ+d13BheB0PXT+uoV39kiQtIQa/JElLiMHfvov6XYHDgNdwYXgdD53XcGF4HQ/dol9Dx/glSVpCbPFLkrSEGPySJC0hBv9BRMQZEXFXRGyPiAv6XZ8yiYh7IuJbEXFrRGwrytZGxNURcXfxuKbf9RwkEXFJRDwUEbe3lM16zaLhQ8Vn87aIOKl/NR8sc1zHP46IHxafx1sj4vUtr723uI53RcTr+lPrwRIRx0fEtRFxZ0TcERHvLMr9PLZpnmvY18+iwT+PiKgCfwecCTwfOCcint/fWpXOqzLzxJZ1qhcA12TmZuCa4liTPgacMa1srmt2JrC5+NkKfGSR6lgGH2PmdQT4QPF5PDEzrwQo/k2fDbyg+J0PF//2l7ox4Pcy8yeAU4Dzi2vl57F9c11D6ONn0eCf38nA9sz8fmYeAD4NnNXnOpXdWcClxfNLgTf0sS4DJzO/AuyeVjzXNTsL+Hg2XA+sjojjFqemg22O6ziXs4BPZ+b+zPwBsJ3Gv/0lLTMfyMxbiud7gTuBDfh5bNs813Aui/JZNPjntwG4v+V4B/P/j6apEvi3iLg5IrYWZU/LzAeg8Y8COKZvtSuPua6Zn8/OvaPohr6kZZjJ63gQEbEJeDFwA34euzLtGkIfP4sG//xiljLXP7bv1Mw8iUYX4PkR8co6T7lxAAADm0lEQVR+V+gw4+ezMx8Bng2cCDwA/FVR7nWcR0QcAfwL8K7MfHy+U2cp8zoy6zXs62fR4J/fDuD4luONwM4+1aV0MnNn8fgQ8HkaXVYPNrv/iseH+lfD0pjrmvn57EBmPpiZ45lZB/6RyS5Ur+McImKIRmB9IjM/VxT7eezAbNew359Fg39+NwGbI+KEiBimMeniij7XqRQiYmVErGo+B14L3E7j+p1bnHYucHl/algqc12zK4C3FrOpTwH2NLtgNdO08eb/QuPzCI3reHZEjETECTQmp9242PUbNBERwMXAnZn51y0v+Xls01zXsN+fxdpCv+HhJDPHIuIdwFVAFbgkM+/oc7XK4mnA5xufe2rAJzPzixFxE3BZRJwH3Ae8uY91HDgR8SngNGBdROwALgTex+zX7Erg9TQmAD0JvG3RKzyg5riOp0XEiTS6Tu8Bfh0gM++IiMuAb9OYhX1+Zo73o94D5lTgLcC3IuLWouwP8fPYibmu4Tn9/Cy6Za8kSUuIXf2SJC0hBr8kSUuIwS9J0hJi8EuStIQY/JIkLSEGv7TERcSPi8dNEfHLC/zefzjt+OsL+f6SOmfwS2raBHQU/G3cOWxK8Gfmyzusk6QFZvBLanof8DPF/cF/NyKqEfH+iLipuJnIrwNExGnFPcY/CXyrKPvX4mZMdzRvyBQR7wOWF+/3iaKs2bsQxXvfHhHfiohfannvL0XEZyPiOxHxiWL3M0kLxJ37JDVdAPy3zPx5gCLA92TmT0fECHBdRPxbce7JwAuLW4cCvD0zd0fEcuCmiPiXzLwgIt6RmSfO8rfeSOMGJS8C1hW/85XitRfTuB/5TuA6GruffW3h/3OlpckWv6S5vJbG3uu30riV6NE09g4HuLEl9AF+JyK+CVxP4yYjm5nfK4BPFTcqeRD4MvDTLe+9o7iBya00hiAkLRBb/JLmEsBvZ+ZVUwojTgOemHb8GuBlmflkRHwJWNbGe89lf8vzcfz/KWlB2eKX1LQXWNVyfBXwm8VtRYmI/1TcaXG6o4BHi9B/HnBKy2ujzd+f5ivALxXzCNYDr8Q74kmLwm/SkppuA8aKLvuPAR+k0c1+SzHBbhfwhll+74vAb0TEbcBdNLr7my4CbouIWzLzV1rKPw+8DPgmjTuU/UFm/qj44iCph7w7nyRJS4hd/ZIkLSEGvyRJS4jBL0nSEmLwS5K0hBj8kiQtIQa/JElLiMEvSdIS8v8B5GcOnVzxZzwAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_graph(np.arange(len(W1_list)),W1_list, xlabel = 'Iteration', ylabel = 'W1', marker = None)\n", "plot_graph(np.arange(len(W2_list)),W2_list, xlabel = 'Iteration', ylabel = 'W2', marker = None)\n", "plot_graph(np.arange(len(W1_list)),W3_list, xlabel = 'Iteration', ylabel = 'W3', marker = None)\n", "plot_graph(np.arange(len(W2_list)),W4_list, xlabel = 'Iteration', ylabel = 'W4', marker = None)\n", "plot_graph(np.arange(len(W1_list)),W5_list, xlabel = 'Iteration', ylabel = 'W5', marker = None)\n", "plot_graph(np.arange(len(J_list)),J_list, xlabel = 'Iteration', ylabel = 'J per batch', marker = None)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thus, we implement our multiple linear regression. This multiple linear regression is the base for neural networks, where we use backpropogation(via the use of chain rule) to propogate the gradients backward." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An artificial neural network can be viewed as a series of linear regression units. The hidden layer contains a number of such units, each of which generate an output. This layer's output is used as input to the next layer's output and so on." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](https://i.stack.imgur.com/qtSik.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The use of the chain rule of calculus enables gradient calculation for each weight in the matrix." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Logistic Regression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The same linear regression can be used to perform classification, by passing the output through a layer known as the sigmoid layer.\n", "\n", "Consider that you are classifying whether the input is good or bad. Now, for 'good' input, you say that your output should be higher that a certain threshold. This is the principle behind Logistic Regression." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use a function called sigmoid to map the outputs from the set of real numbers to \\[0,1], and then define a threshold(usually 0.5) for classification." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$y = sigmoid(w_{0} + w_{1}*x_{1} + w_{2}*x_{2} +\\space...\\space+ w_{n}*x_{n})$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$sigmoid(x) = \\frac{1}{1+e^{-x}}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](https://upload.wikimedia.org/wikipedia/commons/thumb/5/53/Sigmoid-function-2.svg/2000px-Sigmoid-function-2.svg.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The problem is we have labels as outputs. Hence, we have to use a different loss function known as the crossentropy function. The same math will be used to determine gradients, and then perform calculation of weights." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](https://image.slidesharecdn.com/cikm-16-rtb-full-170316083738/95/learning-prediction-and-optimisation-in-rtb-display-advertising-44-638.jpg?cb=1489653680)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 2 }