{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Credits: Forked from [deep-learning-keras-tensorflow](https://github.com/leriomaggio/deep-learning-keras-tensorflow) by Valerio Maggio"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpresent": {
"id": "24ca50a0-b9ad-425d-a28f-6bd3ca3ac378"
},
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Introduction to Deep Learning"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpresent": {
"id": "3896ecb2-47fa-4dbc-a2ff-9c76e9dfe93e"
},
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Deep learning allows computational models that are composed of multiple processing **layers** to learn representations of data with multiple levels of abstraction."
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpresent": {
"id": "8c3060aa-fee9-438c-bc60-4685c0eb4750"
},
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"These methods have dramatically improved the state-of-the-art in speech recognition, visual object recognition, object detection and many other domains such as drug discovery and genomics. "
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpresent": {
"id": "6287766f-972f-4b4d-bee7-5418f0af74de"
},
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"**Deep learning** is one of the leading tools in data analysis these days and one of the most common frameworks for deep learning is **Keras**. "
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpresent": {
"id": "2f1c6299-954a-461a-b5c1-a86a1d12ad15"
},
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"The Tutorial will provide an introduction to deep learning using `keras` with practical code examples."
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpresent": {
"id": "5e13607b-3ec5-4a95-a2d8-f898f20748da"
},
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Artificial Neural Networks (ANN)"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpresent": {
"id": "4fa2e86a-be32-4e78-96d9-f511a07e3908"
},
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"In machine learning and cognitive science, an artificial neural network (ANN) is a network inspired by biological neural networks which are used to estimate or approximate functions that can depend on a large number of inputs that are generally unknown"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpresent": {
"id": "df0121bc-10f1-4ace-840e-6fc89c6fdc7f"
},
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"An ANN is built from nodes (neurons) stacked in layers between the feature vector and the target vector. "
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpresent": {
"id": "c25d7194-10bd-4196-9d4c-592bf6e188f9"
},
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"A node in a neural network is built from Weights and Activation function"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpresent": {
"id": "15260f90-13d1-4fcc-afc6-379c507cb950"
},
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"An early version of ANN built from one node was called the **Perceptron**"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpresent": {
"id": "92d4603e-7e39-4156-818c-785df6189fe8"
},
"slideshow": {
"slide_type": "-"
}
},
"source": [
"![](\"imgs/Perceptron.png\")
"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true,
"nbpresent": {
"id": "356d5ec7-3392-4daa-9671-4cc7111c5c91"
},
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"The Perceptron is an algorithm for supervised learning of binary classifiers. functions that can decide whether an input (represented by a vector of numbers) belongs to one class or another.\n",
"\n",
"Much like logistic regression, the weights in a neural net are being multiplied by the input vertor summed up and feeded into the activation function's input."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"A Perceptron Network can be designed to have *multiple layers*, leading to the **Multi-Layer Perceptron** (aka `MLP`)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![](\"imgs/MLP.png\")
"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true,
"nbpresent": {
"id": "5678486b-caf4-440b-be62-2f1286982c71"
},
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"The weights of each neuron are learned by **gradient descent**, where each neuron's error is derived with respect to it's weight."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Optimization is done for each layer with respect to the previous layer in a technique known as **BackPropagation**."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![](\"imgs/backprop.png\")
"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Building Neural Nets from scratch \n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Idea:\n",
"\n",
"We will build the neural networks from first principles. \n",
"We will create a very simple model and understand how it works. We will also be implementing backpropagation algorithm. \n",
"\n",
"**Please note that this code is not optimized and not to be used in production**. \n",
"\n",
"This is for instructive purpose - for us to understand how ANN works. \n",
"\n",
"Libraries like `theano` have highly optimized code."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"(*The following code is inspired from [these](https://github.com/dennybritz/nn-from-scratch) terrific notebooks*)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"# Import the required packages\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib\n",
"import matplotlib.pyplot as plt\n",
"import scipy"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"# Display plots inline \n",
"%matplotlib inline\n",
"# Define plot's default figure size\n",
"matplotlib.rcParams['figure.figsize'] = (10.0, 8.0)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"import random\n",
"random.seed(123)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"#read the datasets\n",
"train = pd.read_csv(\"data/intro_to_ann.csv\")"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"X, y = np.array(train.ix[:,0:2]), np.array(train.ix[:,2])"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
"(500, 2)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X.shape"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
"(500,)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y.shape"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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WfIUMY4z9BydbjJUhhYWFSExMRM2aNaGnpydXmzZt2mCQtzcGDBosKQu7dAmDv/NCYmJi\niT6dyRhjrPj46AfGygh/f39YWlrCxcUFVlZW6OLujmfPnn20TXp6Om7cuAHP/tLLdo7ffIOa6url\n+oDRwsJCHDlyBBMmTMDs2bNx//59ZYfEGGMKxckWYwoUGhqKqVOn4o/dexAdn4CEpMewa9QYrq6u\nKCws/GC7ihUrgoiQn58vVU5EePPmTbndwC8SidCxY0f8Mn8+9I2MkZGVDUdHR2zZskXZoTHGmMJw\nssWYAi1fsQK/+Pqipb09gLd3Hc6eNw8qlSohNDT0g+2qV6+Otu3aYf26dVLlgQGHUblSpVLZJK8I\nq1atglrVqjh/KQyTfvwRi5cuxdkLFzFlyhQ8f/5c2eExxphCcLLFmALFxsTAoZWjVJkgCGjp4IDY\n2NiPtl2zejW2bNqI/n16Y/26dfAZPgzjx4zB9u3bIQhFbhFQisTERAwbNgxmZmZo0KABFi5ciNzc\nXMn7+/fvx8TJ0heJ16lbF53d3XH48GFlhMwYYwrHyRZjClTPygqXw/+WKb96+TLq1av30baWlpaI\njIxEp44dER8bg4b16+Pu3btwcHBQVLifJSkpCa1bt4a+oRGOhZzEhs1bcPHSJXj07o13D77k5eWh\natWqMm3V1NSQl5dX2iEzxlip4KcR2RctNTUV4eHhUFdXR6tWrVChgvz/vkhNTYWvr69kxqV79+6Y\nNWsWtLW15e4jNDQU3t7e8N+3Hy3t7SESibB08WIcO3oEN27cKFNnen2uiRMnQqiogkVLlkjK8vPz\n0bxxI2z280ObNm0wbdo0vHr9Gus2bJTUefXqFRpa1UNwcDDs/1luZYyx8oCPfmBfNSLCwoULsWzZ\nMjRr3hwvXrxA7ps32LdvHxo3blxk+5ycHDg4OKCFvT3Gfj8egiBg/bq1CLt4EZcvX0b16tXljmXX\nrl2YMWMGKlSogPT0dDh+8w02+/nB6Au7R69Zs2ZYuXYdWtrbIzc3F3t3++NkSAji4+LQyM4O27dv\nx6tXr/BN69awqV8fAwcNRnLyC6xYugzqmhrITE9HeHg4NDU1lf1RGGNMLpxssa/a/v37MXvOHBwL\nOQkjIyMQEfbt3YOfpk5FXFwc1NTUPtrez88PAYGBOBh4RGp/VJ+ePeDm6ooxY8YUK56CggIkJiZC\nXV1d7nO2yhuXDh0wbORIdHJ1Q1c3N6iqqmLAoIFIS0vD2lWr4OHhgWXLlv2TfP4EKxtrqKurY8DA\nQejk5oahgwfBrmFDTJ8+HdevX0dycjKaN2/+xX5fjLHyj5Mt9lVr164dRo4Zgx49e0mVd3VzxfBh\nw+Dp6fnR9gMGDkQbZ2cMGuItVb7rj504dfIkdvv7l3jM5Z2/vz9+XbIEvXr3wZXwv7H/cIBk2TYt\nLQ3N7Gxx7NgxbN++HfpGxpj0449S7Y8HBWHFsqXIzspCVnY2zMzMcP3aNQwfPhxLliwpsw8FMMa+\nXnyoKfuqPX78GNbWNjLlVjY2ePLkSZHttbW08DjpsWy/SY+hraVVIjF+afr374/27dphzcoV8Bk9\nRmp/nIaGBjz7eyEgIAAaGhp48Z5jHp4+fYKY6BgMHOKN2/eiEBQcgjsxsTh//i9s2LChND8KY4yV\nKE622BepRYsWOBkSIlVWWFiIUydPonnz5kW29/b2xuZNG5GYkCApe5CYiE0b1sPb2/sjLb9egiBg\nxYoVsLa2fu+BrYWFhahQoQIGDhwI/z//QGxMjOS9ly9fYvHChTAwNMDosWMls1ja2tpYuGQJJ1uM\nsXKNL1djX6SpU6fCxcUFWlqa6N3XEy9evMC82T/DyNAQTk5ORbZv3Lgx5s6di1YtmqO9iwsEQcCp\n0FD4+vqiWbNmpfAJyq/+/fvjt7Vr0NHVVfK05f3YWOzYthU+Pj7Izs7GkiVL8O03jujk5gY1NTUE\nHTkCR0dHqFWrJrNcaC3nbCRjjJVVvGeLfbHCw8Mxa9YsnDt3DjVr1sTAgQPh6+tbrCcJU1JScPz4\ncQCAm5sbb9aWQ25uLrp264b0tHR4DRyIK5fDcejAAXTo2BHGpqYICgxE+/btsWjRIgQFBSE3Nxed\nO3fGmzdv4OLigqi4eKiqqkr62+2/C7t27sSpj5y4zxhjysAb5Bn7BxHx5upSVlBQgMDAQBw+fBgB\nAQE4fjJUcmVRTk4O3F1dMXDAdxg9erRUO09PT+SIRFi8dBnMzM0RdPQIJo4bhz179sDZ2VkJn0Q5\ncnNzERwcjNTUVDg5OaFOnTrKDokx9h68QZ6xf3CiVfpUVFTg4eEBZ2dnuLq5SRItAKhatSpmzJyJ\nnX/8IdNu586daNigAdo6tUZNtSpYs2IF/vzzz68q0QoPD4eFhQVWrlqN0NOn4ejoCB8fH4jFYmWH\nxhj7RLxnizGmMOnp6dAzMJAp19PXR3pamky5qqoqFi1ahEWLFkEsFhfrxP8vgUgkQs+ePfHbxk3o\n7O4OAMjKykJXNzds2LABY8eOVXKEjLFP8XX9ScYYK1Xt2rVDUGAgRCKRVPm+PXvQtm3bj7ZVdqIl\nFosRERGBK1euID8/v1TGDAoKQoOGDSWJFgBUr14dc+bNw7Zt20olBsZYyeOZLcbKuJs3b+LWrVuw\nsLCAk5OT0pOQ4mjSpAmcnZ3h7uqKGTNnQk9fH/v27MHe3f4ICwtTdngfFB4ejsGDB6NQLIaamhpS\nX73C2rVr0atXr6Ibf4aXL1+ilpmZTLmZuTlevnyp0LEZY4rDyRZjZVRWVhZ69+mD6KgofOPkhNu3\nbqFihQo4evQoTE1NlR2e3LZv346NGzdi/ry5yEhPR7t27RAWFoZatWopO7T3SklJQbdu3bB2wwZ0\n694DgiDgcng4+vbqidq1a6NRo0YKG7t169ZYsGAB3rx5gypVqkjKAw4fxjfffKOwcRljisVPIzKm\nYIWFhcjMzETNmjWLNSs1atQoZGZnY9OWrVBRUQERYenixTgdehLnz59XYMRft2XLliHy7l1s2rJV\nqnzp4sV4/OghNm3apNDxBwwYgKfPnmPOL7/A2MQEhw4cwLJfF+Ps2bNo0KCBQsdmjBUPP43ImJKJ\nxWIsWLAARkZGqFWrFmrVqoXVq1dDnn9Q5OXlwd/fHwt/XQIVlbcT0IIgYNKUKYiLi8P9+/eLFUtO\nTg7Onj2LsLCw957uzv7vwYMHsLWTnb2ya9QIiQ8eKHz8HTt2wLVTR4weMRyt7Vvi6uVwnD59mhMt\nxsoxTrYYw9ulo6ioKOTm5pZYnz/99BNOBIcg9Ow5JL9Ow6EjR7Ft+3asXLmyyLY5OTkgIplDVFVU\nVGBsbILk5GS549ixYwdq1aqFmTNnYdTo0ahduzYuXrwoU+/Fixfw8fGBrq4utLW14e3tjceP/38/\n5N27dxEUFISEf11hRETIyMhAQUGB3PGUdXZ2drhw/pxM+flz52Bna6vw8VVUVDB16lTcu3cPz58/\nx/59+2BbCuMyxhSIiMrM6204jJWe1NRU6t2nD2loaFCdunVJV1eXVqxY8dn9pqenk4aGBiUkPSZR\nQaHkdTPyDunr61NeXt5H24vFYqpfvz4dCw6Rah+TkEiampqUkZEhVxxhYWFkZGRE12/dlvRx+MhR\n0tHRoeTkZEm9rKwssra2pnHjJ1BMQiLFPXxEU6ZNJwsLC4qLi6P2Li5kYmJCrm5upKurS/369aM/\n//yTrK2tqVq1aqSurk4TJkygnJycz/jW3q+wsJAuXLhAR44ckYpZXunp6RQTE1NkbGKxmC5evEhT\np04lXV1dmvPLL5SSlk7pOSLatGUL6erqUmJi4id+CsbYl+ifvKXo/EaeSqX14mSLlbb2Li7kM3o0\npaSlk6igkG7dvUfWNja0ffv2z+r3xo0bZGtnJ5UovXsZGhrS48ePi+zj0KFDZGhoSDv9/enRs+cU\ndCKYGjRsSAsXLpQ7joEDB9LSFStlYvhu4EBavny5pN6GDRvIvWtXmXqe/fuTnV0jGjt+PGW+ySVR\nQSGlZmaRQ6tWpKenR8Ghpygnv4DuP3hIPT08qHefPp/0fX1IREQE1alTh2zt7Khjp06krq5Os2fP\nJrFYXGRbkUhEo0ePJnV1dbKsXZu0tLRo9uzZVFhYKFO3oKCAvLy8qHadOjRtxk/kNXAgaWhokKqq\nKlWtWpW+/fZbunbtWol+NsZY+cfJFmNFiIiIIFNTU8rKzZNKMEJOnaaGDRt+Vt8vXrwgDQ0NSn6d\nJtV3/KMk0tDQkJplEYvFFBUVRffu3ZNJIkJCQsjZ2Zm0tbWpadOmtGPHDrkSjXecnZ1lZsdEBYXk\nu/hX+uGHHyT1hgwZQus3bZKpt3LtWqpRsya9zsqWKm/StCkdOBwgVZaWnUP6+vp069Yt+umnn8jQ\n0JAqV65M7V1c6NKlS8X+Dt+8eUMmJia0/Y8/KCe/gEQFhfTgyVNqaGtLf/75Z5Hthw0bRl27d6dH\nz56TqKCQouMTyN7egby8vKhHz57U3sWFFi5cSK9fv6Zt27aRQytHqc95L/Y+aWpqUmRkZLFjZ4x9\nHeRNtnjPFvtq3b9/H02bNUPFihWlylvY2yM2Nvaz+tbT00OXLl0w8ftxyMnJAfD2NPXvR4/CkCFD\noKamBgAICwtDw4YN4erqCrfOnWFjYyP1pGHHjh1x9uxZvHz5EtevX8fgwYOLdf1QkyZN3nuB8+nQ\nk2jatKlUvAnxCTL17kbegbGxsdQxBAAQde8enNu1kypTVVVFK0dHDBs+HJF37yL41Gk8TXmJfl5e\n6N69O65duyZ33MDbAz7r1rNCv/5eks+sr6+PefMXYOPGjR9tm5ycjIMHD2Lztu3Q1dUFAJiZmaGe\ntRXC/v4bXbp2xbjxE3D7zh20atUKO3bswA8/Tpb6nBaWlujbr5/kInLGGPtUfM4W+2pZW1vj2tWr\nKCgokDzxBwDhYWGwsbH57P43btyI4cOHo665GaysrBEVdQ8eHh749ddfAQBPnjxBjx49sG7jRnTt\n1h0AEHz8OHr37o2rV6/C3Nz8s2MYP3487O3tYWFpgYGDhyAnJwfLfv0Vz54+Re/evSX1hg4ditat\nW6Nvv36wtbMDAMTGxOBIwGHk5ubi6dOnMDIyktQ3MDRE5O3bcGjVSlImFotx+9ZtZGdn4cxfF1Cp\nUiUAwIBBg5GdnQPfhQtx+NAhuWN/+vQp6lnVkymvZ2WFJ0+efLRtYmIi6tSpC3V1dUnZvbt3ERoS\ngoi79yTlrp07Y/TIEQgJDoZ6TXWZfmrWVEd2drbcMTPG2HvJM/1VWi/wMiIrZa5ubjRk6FB69vIV\niQoK6erNCKpTty798ccfJTZGUlIS/fXXX/Ts2TOp8jlz5tCosWNllu4m/DCJpk+fXmLj37p1i1zd\n3EhFRYWqVKlCbdu1o9WrV1NSUpJUvd27d5OWlha1d3Ghjp06kYaGBm3dupVmzZpFzZu3oEuXr1B2\nXj4Fh54iXV1dsmvUSPIAQIboDU2dPoOqV69Offv1k/lM0fEJZGxsXKy4w8LCqHadOjLLvMtWrqK+\nnp4fbftuGff5q1RJu4W/LiGf0WNkYjt38RJpamnJxJ2amUUWlpYUHh5e7O+cMfZ1gJzLiDyzxb5q\ne/fswbhx42BlaQENDQ3k5+dj1qxZGDBggExdIsLFixfx4MED2NnZyX2SuImJCUxMTGTK4xMS8O17\n7gds2rwZ1q5ciYhbt1CjRg0MHDAA7u7uxVo+fGfnzp1Yvnw5YmJiYGxsjNdpaahQoQIuXrqEuXPn\nYsyYMZg/fz4EQUC/fv3g7u6O06dPo7CwEPv37UPNmjVBRNDR0cGAfp548OABGjRogBUrViA6OhpN\nbRvCytoaMTEx0NbSwuxf5iPg4AGZOOJiY2FoaFis2B0cHFC7dm0MGTgA8+YvgKGREQ7u34fFvgtw\n8uTJj7bV09NDr169MHLYUKzbsBG6urrIyclG2uvXMnVzsrNhaWmJyNu3MXTQIAwcPBhp6WlYtWw5\nnFq3RsuWLYsVN2OMyZAnIyutF3hmi/1HYWFhsTaEf0hBQQEFBgbS1KlTaenSpTKzTGlpaRQfH//B\nIxkeP35MTZs2JZv69cmzf38yNTUlt86dKTMz85NjWrhwIQ0ZOlRmpmXI0KFUv0ED2nfoEG3w8yNr\nGxupzex6PJPxAAAgAElEQVTyWrt2LdWzsqITJ0Mp7sFDUldXp1PnzkvGSXr+gmzq16eDBw/K3ed/\nfxavX7+mSZMmkXPbtiQqKKT0HBGZ1qpFW3fskGxqf/wimZo0bUqbN28u9mfIzs6myZMnk46ODlWs\nWJHat29Pf//9t1xtRSIRjRo1imrUqEFGRkakqqpKampqdCc6RvIdZL7JJZeOHWnJ8hX07OUrmjd/\nAbW0tycNDQ3atm3be59cZIyxd8BPI7LyLCQkhOzt7UkQBNLR0aHp06fTmzdvPqmvjIwMcnR0pBYt\nWtKceb/QYG9v0tLSomPHjsndh7OzM82aPUeSQGS+yaX+331HPj4+nxQT0dulLgMDA/pt40bKEL2h\nzDe5tGnLVqpRowbFP0qSJATPXr4iAwMDunv3rtx95+bmkr6+vuR8rVVr11E/Ly+ZxO73XbvI1c1N\n0k4kElF6enqxPoe3tzf9tnGjpM93S7E29evTt85tSUNDg6ZMmfLZSfOntA8KCiI9PT1atnIlJT5+\nQj9Om0Y1atSgMeO+p3kLFlDtOnWok6srpeeIJPFn5+VTlSpVKCsr67PiZYx9+eRNtkpkGVEQhK0A\n3AG8ICK7D9RZA8ANQDaAIUQUURJjsy/P6dOnMWjQICxbtQoqKipITEjA6dBQDB48GHv27CmyfVJS\nEtavX4/bkZEwNzNDTk4OzCwssHXH75KluCFDh6FPzx54+PAhqlat+tH+4uLiEB0djSMngiXtVVRU\nsGjJUthaW2H16tVQVVUt9ufU09PDyZMnMW7cOMyYOhWCIKBy5cpYsmKF1GZ0DQ0N9OrTB0ePHkX9\n+vXl6vvhw4dQq1oV9f+54uVlSgpq1TKTqVerlhlepqTgxYsXmDhxIo4cOYLCwkJUr14dtnZ2+HXx\n4iKX0QwNDREb8/+nNxva2uLW3XsYN2oUnj19gqioKBgYGMgV98d8yjLqnDlzsMFvMzq7uwMA5vsu\nRLcePdGpXVt4eXnh+bNnCAoOQeXKlSVtgo8fh42NDapVq/bZMTPGGFBy1/VsB9DpQ28KguAGoDYR\n1QXgA+Djz22zr5qvry+GDBuGHydOxKb1G3Dj+nXcuH4dISEhiIqK+mjbiIgING/eHFk5IngPHw4d\nPX0cOHgQLe0dpP6ydmjVCnaNGhW59wd4e5WPiYmp5Om6d/T09CAIgszTakSE/fv3o1v37nBxccGv\nv/6K9PT09/Zta2uL8+fPIz4+Hvfv30ftOnVQy7SWTL03IpFUQlAUHR0dvE5NRUZGBgCglaMjjgUd\nlbkX8WhgIFq1aoUOHTpA39AI8Y+S8CojE6vWrcPNmzfh5uaGkJCQj441dOhQ/Lnzd1z/19EOMdHR\nOH4sCAsXLiyRROvp06dISkp6NwMul4KCAty8eROunTtLlbdo0QIOrRzRp08fzJw5E726dUXw8eN4\n/Pgx/tz5O8b4jISvr+9nx8wYYxLyTH/J8wJgBuD2B97bCMDzX7+PAqD/nnqKmedj5Ur16tVJW1ub\njoeclCztPElOobr16tGYMWM+2rZt27ZSS1qigkI689cFMjA0pAzRG6nyHj17kr+/f5HxZGRkkKam\nJsUkJEq1Dw49RdbW1jLLWz4+PtSocWPatnMnHT5ylPp4elKDBg0oNTW1yLFWrFhBHTp2lJzWLioo\npOi4eNLS0qKHDx8W2f7fvLy8aPjIkZT5Jpdy8guobbt21KVrVwq/dp1iEx/Q3F/mk6GhIW3atIla\nOTpKlkjfvRYsWkwdOnYkOzu7IpfwDh06RDo6OuTU5ltq2649aWlp0e+//16seMPDw8mjd2+ytrYm\nVzc3Cg4Optu3b5OjoyNpa2uTnp4eNWnSRO4DUsViMWlra9PdmFipz5Wdl0/mFhYUERFBYrGYdu3a\nRQ4ODmRoaEiubm50/vz5YsXNGPt6obT3bBWRbB0F4Piv358C0PQ99RT4lbDywtDQkNp8+y2N8PGh\nzl260MyfZ1Pi4ye0e/9+at6ixQfbZWZmkpqamtT+m3evuvXq0V9hf8uc5P7ixQu5YvL19aUGDRvS\n8ZCT9CQ5hfz37SNjY2Pav3+/VL0bN26QiYmJzMnxXgMG0Lx584oc582bN9SxUydq3KQJ+S7+lSZP\nmUp6enq0du1aueL8t9evX1PHTp3IxMSEuvfoQcbGxlSnbl0yt7AgPT09GjhwIN2/f5/mzp1L0376\nSeY7u/B3ODVp2vTtSfhy3EmYk5NDx48fp6NHjxb7wYHg4GDS09Oj1evW0Y3bkbTt99+pVq1apKGh\nQRv8/CjzTS5l5+WT/759pKOjQwkJCXL1O336dOri7i45GT4nv4AWLFpMLVu2LJEHLxhjXzd5k63S\nOvrhfZst3rseMHfuXMmvnZ2d4ezsrJiIWJll+M+BmS4dOsKlY0ecOnkSji1bYNWatRCJRB9sV6HC\n21Xx/Px8qSU3IkJ2djbWrVmNocOG48GDRCxZvBhTp06Fnp6eXDHNmDEDhoaG+GnaVMnRD5s3b4ab\nm5tUvePHj8OjT1/UqFFDqnyI91DM+mkGZs+e/dFxVFVVcfzYMZw4cQInT55EjRo1cO7cuU86ZFVD\nQwMhwcGIjIxETEwMfpk3D3Z2slsqzc3NsXfffpny27ciYGRsjPuxsZIT7z9GTU1N5vuQBxFh6tSp\n2Lh5C9y6dAEA2NSvD7tGjdHWqTX6eX0nOXS2Zy8PXL18BRs2bMCSJUuK7Hvu3Lnw9vaGlaUFWjs5\nISoqCqqVKyMgIOCT9oAxxr5u586dw7lz54rfUJ6MTJ4XireMGA1eRmTvkZ2dTRoaGnTlxk2Zu/wa\n2trSyJEjP9revWtX+sV3oVTbA4cDyMLCgqZMmUKtnZyol4cHnThxQiHxL1u2jEb4+MjMEh0KPEKt\nnZzK5FECWVlZZGxsTBu3bJEsJV69GUHGJibUu2/fEr9c+r9SUlJIXV2dsvPyZb43K2truhh+Waps\n78GD1LVbt2KNERMTQ3v27KGLFy/yjBZjrMRAzpktgYqx4fRjBEEwB3CUiGzf815nAGOJqIsgCA4A\nVhGRw3vqUUnFw8qn0NBQzJ33C07/635AAMjMzISBjjaio6JQt27dD7ZPSEhA27Zt0bxFC7Rxbovb\ntyJwJCAAhw8fRuvWrRUdPh4+fIimTZvi0uUrMLewAADk5eWhY7u2uHrlCqpVq4bvvvsOv/76K2rW\nrKnweOQVGRkJT09PvEpNhYaGBp4/ewYdHR3UqFEDgYGBOHXqFI6fOAG1KlXg5eUFNze3EpsZys7O\nhoGBAeIePpK6XqewsBBmxkY4+9cF1K33/2t7Zs2YAYgLsWzZshIZnzHGPpUgCCCiIv8wLJGnEQVB\n8AcQBqCeIAiPBEHwFgTBRxCEkQBARMcBJAqCEAdgE4AxJTEu+/KoqKggPy9PpjwvLw+VK1VCnTp1\nPtre0tISkZGRaN+uHaLuRKLOP78vjUQLeHvZ8fz58+HUygFTJ0/GIt8FsKtvAyLCy/QM3LoXhWyR\nCN26dSvyybrnz5/jxo0byMrKKnYcd+7cQS8PD6irq8PU1BQzZsyQXIj9Pra2trh79y6OHzuGgQMG\noG/fvrC3t0efPn3Qp08f+O/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C8HYWrGwQBIHKUjxMsV6+fIlNmzbh2vXrMDYywsiRI2Fn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\nDX9u7LtHVykAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#Let's plot the dataset and see how it is\n",
"plt.scatter(X[:,0], X[:,1], s=40, c=y, cmap=plt.cm.BuGn)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Start Building our ANN building blocks\n",
"\n",
"Note: This process will eventually result in our own Neural Networks class"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### A look at the details"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![](\"imgs/mlp_details.png\")
"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Function to generate a random number, given two numbers\n",
"\n",
"**Where will it be used?**: When we initialize the neural networks, the weights have to be randomly assigned."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"# calculate a random number where: a <= rand < b\n",
"def rand(a, b):\n",
" return (b-a)*random.random() + a"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"# Make a matrix \n",
"def makeMatrix(I, J, fill=0.0):\n",
" return np.zeros([I,J])"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Define our activation function. Let's use sigmoid function"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# our sigmoid function\n",
"def sigmoid(x):\n",
" #return math.tanh(x)\n",
" return 1/(1+np.exp(-x))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Derivative of our activation function. \n",
"\n",
"Note: We need this when we run the backpropagation algorithm\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# derivative of our sigmoid function, in terms of the output (i.e. y)\n",
"def dsigmoid(y):\n",
" return y - y**2"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Our neural networks class\n",
"\n",
"When we first create a neural networks architecture, we need to know the number of inputs, number of hidden layers and number of outputs.\n",
"\n",
"The weights have to be randomly initialized."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"```python\n",
"class ANN:\n",
" def __init__(self, ni, nh, no):\n",
" # number of input, hidden, and output nodes\n",
" self.ni = ni + 1 # +1 for bias node\n",
" self.nh = nh\n",
" self.no = no\n",
"\n",
" # activations for nodes\n",
" self.ai = [1.0]*self.ni\n",
" self.ah = [1.0]*self.nh\n",
" self.ao = [1.0]*self.no\n",
" \n",
" # create weights\n",
" self.wi = makeMatrix(self.ni, self.nh)\n",
" self.wo = makeMatrix(self.nh, self.no)\n",
" \n",
" # set them to random vaules\n",
" self.wi = rand(-0.2, 0.2, size=self.wi.shape)\n",
" self.wo = rand(-2.0, 2.0, size=self.wo.shape)\n",
"\n",
" # last change in weights for momentum \n",
" self.ci = makeMatrix(self.ni, self.nh)\n",
" self.co = makeMatrix(self.nh, self.no)\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Activation Function"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```python\n",
"def activate(self, inputs):\n",
" \n",
" if len(inputs) != self.ni-1:\n",
" print(inputs)\n",
" raise ValueError('wrong number of inputs')\n",
"\n",
" # input activations\n",
" for i in range(self.ni-1):\n",
" self.ai[i] = inputs[i]\n",
"\n",
" # hidden activations\n",
" for j in range(self.nh):\n",
" sum_h = 0.0\n",
" for i in range(self.ni):\n",
" sum_h += self.ai[i] * self.wi[i][j]\n",
" self.ah[j] = sigmoid(sum_h)\n",
"\n",
" # output activations\n",
" for k in range(self.no):\n",
" sum_o = 0.0\n",
" for j in range(self.nh):\n",
" sum_o += self.ah[j] * self.wo[j][k]\n",
" self.ao[k] = sigmoid(sum_o)\n",
"\n",
" return self.ao[:]\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### BackPropagation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```python\n",
"def backPropagate(self, targets, N, M):\n",
" \n",
" if len(targets) != self.no:\n",
" print(targets)\n",
" raise ValueError('wrong number of target values')\n",
"\n",
" # calculate error terms for output\n",
" output_deltas = np.zeros(self.no)\n",
" for k in range(self.no):\n",
" error = targets[k]-self.ao[k]\n",
" output_deltas[k] = dsigmoid(self.ao[k]) * error\n",
"\n",
" # calculate error terms for hidden\n",
" hidden_deltas = np.zeros(self.nh)\n",
" for j in range(self.nh):\n",
" error = 0.0\n",
" for k in range(self.no):\n",
" error += output_deltas[k]*self.wo[j][k]\n",
" hidden_deltas[j] = dsigmoid(self.ah[j]) * error\n",
"\n",
" # update output weights\n",
" for j in range(self.nh):\n",
" for k in range(self.no):\n",
" change = output_deltas[k] * self.ah[j]\n",
" self.wo[j][k] += N*change + \n",
" M*self.co[j][k]\n",
" self.co[j][k] = change\n",
"\n",
" # update input weights\n",
" for i in range(self.ni):\n",
" for j in range(self.nh):\n",
" change = hidden_deltas[j]*self.ai[i]\n",
" self.wi[i][j] += N*change + \n",
" M*self.ci[i][j]\n",
" self.ci[i][j] = change\n",
"\n",
" # calculate error\n",
" error = 0.0\n",
" for k in range(len(targets)):\n",
" error += 0.5*(targets[k]-self.ao[k])**2\n",
" return error\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"# Putting all together\n",
"\n",
"class ANN:\n",
" def __init__(self, ni, nh, no):\n",
" # number of input, hidden, and output nodes\n",
" self.ni = ni + 1 # +1 for bias node\n",
" self.nh = nh\n",
" self.no = no\n",
"\n",
" # activations for nodes\n",
" self.ai = [1.0]*self.ni\n",
" self.ah = [1.0]*self.nh\n",
" self.ao = [1.0]*self.no\n",
" \n",
" # create weights\n",
" self.wi = makeMatrix(self.ni, self.nh)\n",
" self.wo = makeMatrix(self.nh, self.no)\n",
" \n",
" # set them to random vaules\n",
" for i in range(self.ni):\n",
" for j in range(self.nh):\n",
" self.wi[i][j] = rand(-0.2, 0.2)\n",
" for j in range(self.nh):\n",
" for k in range(self.no):\n",
" self.wo[j][k] = rand(-2.0, 2.0)\n",
"\n",
" # last change in weights for momentum \n",
" self.ci = makeMatrix(self.ni, self.nh)\n",
" self.co = makeMatrix(self.nh, self.no)\n",
" \n",
"\n",
" def backPropagate(self, targets, N, M):\n",
" \n",
" if len(targets) != self.no:\n",
" print(targets)\n",
" raise ValueError('wrong number of target values')\n",
"\n",
" # calculate error terms for output\n",
" output_deltas = np.zeros(self.no)\n",
" for k in range(self.no):\n",
" error = targets[k]-self.ao[k]\n",
" output_deltas[k] = dsigmoid(self.ao[k]) * error\n",
"\n",
" # calculate error terms for hidden\n",
" hidden_deltas = np.zeros(self.nh)\n",
" for j in range(self.nh):\n",
" error = 0.0\n",
" for k in range(self.no):\n",
" error += output_deltas[k]*self.wo[j][k]\n",
" hidden_deltas[j] = dsigmoid(self.ah[j]) * error\n",
"\n",
" # update output weights\n",
" for j in range(self.nh):\n",
" for k in range(self.no):\n",
" change = output_deltas[k] * self.ah[j]\n",
" self.wo[j][k] += N*change + M*self.co[j][k]\n",
" self.co[j][k] = change\n",
"\n",
" # update input weights\n",
" for i in range(self.ni):\n",
" for j in range(self.nh):\n",
" change = hidden_deltas[j]*self.ai[i]\n",
" self.wi[i][j] += N*change + M*self.ci[i][j]\n",
" self.ci[i][j] = change\n",
"\n",
" # calculate error\n",
" error = 0.0\n",
" for k in range(len(targets)):\n",
" error += 0.5*(targets[k]-self.ao[k])**2\n",
" return error\n",
"\n",
"\n",
" def test(self, patterns):\n",
" self.predict = np.empty([len(patterns), self.no])\n",
" for i, p in enumerate(patterns):\n",
" self.predict[i] = self.activate(p)\n",
" #self.predict[i] = self.activate(p[0])\n",
" \n",
" def activate(self, inputs):\n",
" \n",
" if len(inputs) != self.ni-1:\n",
" print(inputs)\n",
" raise ValueError('wrong number of inputs')\n",
"\n",
" # input activations\n",
" for i in range(self.ni-1):\n",
" self.ai[i] = inputs[i]\n",
"\n",
" # hidden activations\n",
" for j in range(self.nh):\n",
" sum_h = 0.0\n",
" for i in range(self.ni):\n",
" sum_h += self.ai[i] * self.wi[i][j]\n",
" self.ah[j] = sigmoid(sum_h)\n",
"\n",
" # output activations\n",
" for k in range(self.no):\n",
" sum_o = 0.0\n",
" for j in range(self.nh):\n",
" sum_o += self.ah[j] * self.wo[j][k]\n",
" self.ao[k] = sigmoid(sum_o)\n",
"\n",
" return self.ao[:]\n",
" \n",
"\n",
" def train(self, patterns, iterations=1000, N=0.5, M=0.1):\n",
" # N: learning rate\n",
" # M: momentum factor\n",
" patterns = list(patterns)\n",
" for i in range(iterations):\n",
" error = 0.0\n",
" for p in patterns:\n",
" inputs = p[0]\n",
" targets = p[1]\n",
" self.activate(inputs)\n",
" error += self.backPropagate([targets], N, M)\n",
" if i % 5 == 0:\n",
" print('error in interation %d : %-.5f' % (i,error))\n",
" print('Final training error: %-.5f' % error)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Running the model on our dataset"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"error in interation 0 : 53.62995\n",
"Final training error: 53.62995\n",
"Final training error: 47.35136\n",
"1 loop, best of 1: 97.6 ms per loop\n"
]
}
],
"source": [
"# create a network with two inputs, one hidden, and one output nodes\n",
"ann = ANN(2, 1, 1)\n",
"\n",
"%timeit -n 1 -r 1 ann.train(zip(X,y), iterations=2)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Predicting on training dataset and measuring in-sample accuracy"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1 loop, best of 1: 22.6 ms per loop\n"
]
}
],
"source": [
"%timeit -n 1 -r 1 ann.test(X)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
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