add machine learning notebook

Author: gkarwchan

Machine_Learning.ipynb

@@ -0,0 +1,72 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Gradient Descent\n",
+    "\n",
+    "\n",
+    "## Cost Function\n",
+    "The cost function can be written as follows:\n",
+    "\n",
+    "\\begin{align}\n",
+    "J(\\theta_0, \\theta_1) = \\frac1{2m}\\  \\sum_{k=1}^m ( h_\\theta(x_i) - y_i )^2\n",
+    "\\end{align}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Gradient descent\n",
+    "\n",
+    "Repeat until convergence\n",
+    "\n",
+    "\\begin{align}\n",
+    "\\theta_j := \\theta_j - \\alpha \\frac{\\partial}{\\partial \\theta_j} J(\\theta_0, \\theta_1)\n",
+    "\\end{align}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Will become:  \n",
+    "\n",
+    "\\begin{align}\n",
+    "\\theta_0 := \\theta_0 - \\alpha \\frac1m \\sum_{k=1}^m ( h_\\theta(x_i) - y_i )  \\\\\n",
+    "\\theta_1 := \\theta_1 - \\alpha \\frac1m \\sum_{k=1}^m (( h_\\theta(x_i) - y_i ) x_i)\n",
+    "\\end{align}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "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": "3.6.8"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

README.md

@@ -9,6 +9,7 @@ We have the following tutorials:
 1. [Basic Descriptive Statistics](/descriptive_statistics.ipynb)
 2. [Linear Algebra](/linear_algebra.ipynb)
 3. [Probability](/Probability.ipynb)
+4. [Machine Learning](/Machine_Learning.ipynb)
 
 ## Datasets