feat: 2109s ps4

cs2109s/labs/ps4/housing_data.csv

@@ -0,0 +1,91 @@
+floor_area_sqm,bedrooms,schools,asking_price
+60,2,3,480000.0
+63,2,4,450000.0
+65,2,1,480000.0
+65,2,4,360000.0
+66,2,5,350000.0
+67,2,0,400000.0
+67,2,1,430000.0
+67,2,2,450000.0
+67,2,3,410000.0
+67,2,4,390000.0
+67,2,5,390000.0
+67,2,6,390000.0
+68,2,1,460000.0
+68,2,2,400000.0
+68,2,3,370000.0
+68,2,4,360000.0
+68,2,6,370000.0
+68,2,7,400000.0
+68,2,8,370000.0
+69,2,3,420000.0
+70,2,3,510000.0
+70,2,8,370000.0
+73,2,5,370000.0
+73,2,7,380000.0
+83,2,1,590000.0
+83,3,1,650000.0
+83,3,2,550000.0
+83,3,3,550000.0
+83,3,4,580000.0
+84,3,3,560000.0
+86,3,2,560000.0
+88,3,3,510000.0
+89,3,1,610000.0
+90,3,3,500000.0
+90,3,4,520000.0
+90,3,5,490000.0
+91,3,0,550000.0
+91,3,3,620000.0
+92,3,1,490000.0
+92,3,2,590000.0
+92,3,3,490000.0
+92,3,4,510000.0
+92,3,5,490000.0
+92,3,6,490000.0
+92,3,7,510000.0
+93,3,0,490000.0
+93,3,1,660000.0
+93,3,2,540000.0
+93,3,3,550000.0
+93,3,4,490000.0
+93,3,5,510000.0
+93,3,6,490000.0
+93,3,7,490000.0
+94,3,2,590000.0
+94,3,3,550000.0
+94,3,4,490000.0
+94,3,5,540000.0
+95,3,1,700000.0
+95,3,2,620000.0
+95,3,3,530000.0
+95,3,4,540000.0
+96,3,2,600000.0
+96,3,7,480000.0
+97,3,1,660000.0
+97,3,2,600000.0
+97,3,4,440000.0
+98,3,5,450000.0
+104,3,1,720000.0
+105,3,0,630000.0
+105,3,1,670000.0
+105,3,2,670000.0
+105,4,1,610000.0
+108,3,1,780000.0
+109,3,2,700000.0
+110,3,3,670000.0
+110,3,4,660000.0
+111,3,3,640000.0
+112,3,1,700000.0
+112,3,2,660000.0
+112,3,3,670000.0
+112,3,4,650000.0
+113,3,1,640000.0
+113,3,2,590000.0
+113,3,3,600000.0
+113,3,4,590000.0
+113,3,5,590000.0
+115,3,1,720000.0
+115,3,2,700000.0
+119,4,3,690000.0
+124,3,1,770000.0

cs2109s/labs/ps4/imgs/bias_scatter.ipynb

@@ -0,0 +1,87 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "f64907f4",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# CODE TO GENERATE bias_scatter.png\n",
+    "import numpy as np\n",
+    "from sklearn.linear_model import LinearRegression"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "bf22eb4a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "X = np.array([1, 2, 3, 4, 5, 6]).reshape((-1, 1))\n",
+    "y = np.array([6, 7, 8, 8, 9, 11])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b185d8b9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "model_no_bias = LinearRegression(fit_intercept = False).fit(X, y)\n",
+    "model_with_bias = LinearRegression().fit(X, y)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "f5076cdc",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "X_with_zero = np.vstack([0, X]) # Added to show the lines passing through Feature=0\n",
+    "plt.scatter(X, y)\n",
+    "plt.plot(X_with_zero, model_no_bias.predict(X_with_zero), color = 'b', label=\"Without bias\")\n",
+    "plt.plot(X_with_zero, model_with_bias.predict(X_with_zero), color = 'r', label=\"With bias\")\n",
+    "plt.ylim(ymin=0)\n",
+    "plt.xlim(xmin=0, xmax=8)\n",
+    "plt.xlabel(\"Feature\")\n",
+    "plt.ylabel(\"Target\")\n",
+    "plt.legend(loc=\"center right\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e68dd023",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.9.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

cs2109s/labs/ps4/imgs/grad_desc_algorithm.tex

@@ -0,0 +1,24 @@
+% CODE TO GENERATE grad_desc_algorithm.tex
+\documentclass{article}
+\usepackage{algorithm2e}
+\usepackage{bm}
+\begin{document}
+\RestyleAlgo{ruled}
+\DontPrintSemicolon
+\begin{algorithm}[hbt!]
+    \caption{Gradient Descent for Linear Regression}
+    $w_0, w_1, \ldots, w_n \gets 0$\;
+    \For{$i\gets 1$ \KwTo $N$}{
+        $w'_0 \gets w_0 - \alpha\frac{\partial J(\boldsymbol{w})}{\partial w_0}$\;
+        $w'_1 \gets w_1 - \alpha\frac{\partial J(\boldsymbol{w})}{\partial w_1}$\;
+        $\vdots$\;
+        $w'_n \gets w_n - \alpha\frac{\partial J(\boldsymbol{w})}{\partial w_n}$\;
+        $w_0 \gets w'_0$\;
+        $w_1 \gets w'_1$\;
+        $\vdots$\;
+        $w_n \gets w'_n$\;
+        $loss \gets J(\boldsymbol{w})$\;
+    }
+\end{algorithm}
+
+\end{document}