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‎.ipynb_checkpoints/NaiveBayes-checkpoint.ipynb

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‎.ipynb_checkpoints/conditionalprobabilityexercise-checkpoint.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {
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"deletable": true,
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"editable": true
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},
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"source": [
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"# Conditional Probability Activity & Exercise"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"deletable": true,
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"editable": true
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},
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"source": [
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"Below is some code to create some fake data on how much stuff people purchase given their age range.\n",
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"\n",
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"It generates 100,000 random \"people\" and randomly assigns them as being in their 20's, 30's, 40's, 50's, 60's, or 70's.\n",
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"\n",
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"It then assigns a lower probability for young people to buy stuff.\n",
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"\n",
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"In the end, we have two Python dictionaries:\n",
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"\n",
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"\"totals\" contains the total number of people in each age group.\n",
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"\"purchases\" contains the total number of things purchased by people in each age group.\n",
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"The grand total of purchases is in totalPurchases, and we know the total number of people is 100,000.\n",
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"\n",
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"Let's run it and have a look:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": false,
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"deletable": true,
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"editable": true
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},
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"outputs": [],
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"source": [
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"from numpy import random\n",
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"random.seed(0)\n",
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"\n",
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"totals = {20:0, 30:0, 40:0, 50:0, 60:0, 70:0}\n",
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"purchases = {20:0, 30:0, 40:0, 50:0, 60:0, 70:0}\n",
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"totalPurchases = 0\n",
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"for _ in range(100000):\n",
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" ageDecade = random.choice([20, 30, 40, 50, 60, 70])\n",
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" purchaseProbability = float(ageDecade) / 100.0\n",
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" totals[ageDecade] += 1\n",
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" if (random.random() < purchaseProbability):\n",
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" totalPurchases += 1\n",
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" purchases[ageDecade] += 1"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": false,
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"deletable": true,
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"editable": true
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"{20: 16576, 30: 16619, 40: 16632, 50: 16805, 60: 16664, 70: 16704}"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"totals"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": false,
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"deletable": true,
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"editable": true
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"{20: 3392, 30: 4974, 40: 6670, 50: 8319, 60: 9944, 70: 11713}"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"purchases"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"collapsed": false,
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"deletable": true,
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"editable": true
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"45012"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"totalPurchases"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"deletable": true,
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"editable": true
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},
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"source": [
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"Let's play with conditional probability.\n",
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"\n",
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"First let's compute P(E|F), where E is \"purchase\" and F is \"you're in your 30's\". The probability of someone in their 30's buying something is just the percentage of how many 30-year-olds bought something:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {
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"collapsed": false,
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"deletable": true,
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"editable": true
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"P(purchase | 30s): 0.29929598652145134\n"
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]
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}
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],
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"source": [
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"PEF = float(purchases[30]) / float(totals[30])\n",
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"print('P(purchase | 30s): ' + str(PEF))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"deletable": true,
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"editable": true
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},
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"source": [
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"P(F) is just the probability of being 30 in this data set:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {
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"collapsed": false,
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"deletable": true,
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"editable": true
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"P(30's): 0.16619\n"
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]
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}
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],
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"source": [
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"PF = float(totals[30]) / 100000.0\n",
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"print(\"P(30's): \" + str(PF))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"deletable": true,
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"editable": true
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},
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"source": [
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"And P(E) is the overall probability of buying something, regardless of your age:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {
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"collapsed": false,
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"deletable": true,
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"editable": true
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"P(Purchase):0.45012\n"
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]
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}
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],
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"source": [
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"PE = float(totalPurchases) / 100000.0\n",
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"print(\"P(Purchase):\" + str(PE))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"deletable": true,
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"editable": true
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},
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"source": [
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"If E and F were independent, then we would expect P(E | F) to be about the same as P(E). But they're not; PE is 0.45, and P(E|F) is 0.3. So, that tells us that E and F are dependent (which we know they are in this example.)\n",
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"\n",
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"What is P(E)P(F)?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {
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"collapsed": false,
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"deletable": true,
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"editable": true
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"P(30's)P(Purchase)0.07480544280000001\n"
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]
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}
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],
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"source": [
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"print(\"P(30's)P(Purchase)\" + str(PE * PF))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"deletable": true,
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"editable": true
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},
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"source": [
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"P(E,F) is different from P(E|F). P(E,F) would be the probability of both being in your 30's and buying something, out of the total population - not just the population of people in their 30's:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {
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"collapsed": false,
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"deletable": true,
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"editable": true
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"P(30's, Purchase)0.04974\n"
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]
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}
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],
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"source": [
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"print(\"P(30's, Purchase)\" + str(float(purchases[30]) / 100000.0))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"deletable": true,
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"editable": true
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},
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"source": [
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"P(E,F) = P(E)P(F), and they are pretty close in this example. But because E and F are actually dependent on each other, and the randomness of the data we're working with, it's not quite the same.\n",
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"\n",
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"We can also check that P(E|F) = P(E,F)/P(F) and sure enough, it is:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {
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"collapsed": false,
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"deletable": true,
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"editable": true
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0.29929598652145134\n"
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]
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}
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],
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"source": [
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"print((purchases[30] / 100000.0) / PF)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"deletable": true,
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"editable": true
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},
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"source": [
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"## Your Assignment"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"deletable": true,
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"editable": true
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},
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"source": [
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"Modify the code above such that the purchase probability does NOT vary with age, making E and F actually independent.\n",
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"\n",
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"Then, confirm that P(E|F) is about the same as P(E), showing that the conditional probability of purchase for a given age is not any different than the a-priori probability of purchase regardless of age.\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false,
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"deletable": true,
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"editable": true
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},
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"outputs": [],
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"source": [
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"PE = "
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.2"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}

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