hw2_2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bike Rides and the Poisson Model\n",
    "\n",
    "To help the urban planners, you are called to model the daily bike rides in NYC using [this dataset](https://gist.github.com/sachinsdate/c17931a3f000492c1c42cf78bf4ce9fe/archive/7a5131d3f02575668b3c7e8c146b6a285acd2cd7.zip).  The dataset contains date, day of the week, high and low temp, precipitation and bike ride couunts as columns. \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Maximum Likelihood I \n",
    " \n",
    "The obvious choice in distributions is the [Poisson distribution](https://en.wikipedia.org/wiki/Poisson_distribution) which depends only on one parameter, λ, which is the average number of occurrences per interval. We want to estimate this parameter using Maximum Likelihood Estimation.\n",
    "\n",
    "Implement a Gradient Descent algorithm from scratch that will estimate the Poisson distribution according to the Maximum Likelihood criterion. Plot the estimated mean vs iterations to showcase convergence towards the true mean. \n",
    "\n",
    "References: \n",
    "\n",
    "1. [This blog post](https://towardsdatascience.com/the-poisson-process-everything-you-need-to-know-322aa0ab9e9a). \n",
    "\n",
    "2. [This blog post](https://towardsdatascience.com/understanding-maximum-likelihood-estimation-fa495a03017a) and note the negative  log likelihood function.  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2680.042060172422\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Code here\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "learning_rate=0.1\n",
    "num_iters=3000\n",
    "data=pd.read_csv(\"nyc_bb_bicyclist_counts.csv\")\n",
    "n=data.shape[0]\n",
    "# print(data)\n",
    "bb_count=np.array(data['BB_COUNT'])\n",
    "# print(bb_count)\n",
    "lambda1=10000\n",
    "iter_l=[]\n",
    "\n",
    "for i in range(num_iters):\n",
    "    lambda1 = lambda1-learning_rate*(n-bb_count.sum()/lambda1)\n",
    "    iter_l.append(lambda1)\n",
    "    \n",
    "print(lambda1)\n",
    "plt.plot(iter_l)\n",
    "plt.title('iteration time-lambda')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Maximum Likelihood II\n",
    "\n",
    "A colleague of yours suggest that the parameter $\\lambda$ must be itself dependent on the weather and other factors since people bike when its not raining. Assume that you model $\\lambda$ as \n",
    "\n",
    "$$\\lambda_i = \\exp(\\mathbf w^T \\mathbf x_i)$$\n",
    "\n",
    "where $\\mathbf x_i$ is one of the example features and $\\mathbf w$ is a set of parameters. \n",
    "\n",
    "Train the model with SGD with this assumption and compare the MSE of the predictions with the `Maximum Likelihood I` approach. \n",
    "\n",
    "You may want to use [this partial derivative of the log likelihood function](http://home.cc.umanitoba.ca/~godwinrt/7010/poissonregression.pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1.02288099e+68]\n",
      " [-9.54850997e+69]\n",
      " [-7.98111126e+69]\n",
      " [-4.42467458e+66]]\n"
     ]
    }
   ],
   "source": [
    "# \n",
    "\n",
    "data=pd.read_csv(\"nyc_bb_bicyclist_counts.csv\")\n",
    "n=data.shape[0]\n",
    "y=np.array(data['BB_COUNT']).reshape((n,1))\n",
    "hight=np.array(data['HIGH_T']).reshape((n,1))\n",
    "lowt=np.array(data['LOW_T']).reshape((n,1))\n",
    "precip=np.array(data['PRECIP']).reshape((n,1))\n",
    "x=np.hstack((np.ones((n,1)),hight,lowt,precip))\n",
    "\n",
    "\n",
    "\n",
    "w=np.array([1.,1.,1.,1.]).reshape((4,1))\n",
    "# print(w)\n",
    "learning_rate=0.00001\n",
    "num_iters=1000\n",
    "\n",
    "# print(x.T.dot(np.exp(x.dot(w))))\n",
    "\n",
    "# print(x.dot(w))\n",
    "\n",
    "for i in range(num_iters):\n",
    "    predict=np.exp(x.dot(w))\n",
    "    dw=x.T.dot((y-predict))\n",
    "    w+=(learning_rate/n)*dw\n",
    "\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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  "language_info": {
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
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}