21120517.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "dw29NSYmFpyS"
   },
   "source": [
    "# Lab03: Linear Regression.\n",
    "\n",
    "- Student ID: 21120517\n",
    "- Student name: Nguyễn Thúc Minh Nhật"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "oHR1Zj5GFpyT"
   },
   "source": [
    "**How to do your homework**\n",
    "\n",
    "\n",
    "You will work directly on this notebook; the word `TODO` indicate the parts you need to do.\n",
    "\n",
    "You can discuss ideas with classmates as well as finding information from the internet, book, etc...; but *this homework must be your*.\n",
    "\n",
    "**How to submit your homework**\n",
    "\n",
    "Before submitting, rerun the notebook (`Kernel` ->` Restart & Run All`).\n",
    "\n",
    "Rename your notebook with `ID.ipynb` (for example, if your ID is 1234567, rename your notebook with `1234567.ipynb`) and submit it on moodle. In `ID.zip` must have only `ID.ipynb`\n",
    "\n",
    "**Contents:**\n",
    "\n",
    "- Linear Regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "REHkv-y8FpyU"
   },
   "source": [
    "### 1. The hypothesis set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "e75OMY0KFpyU"
   },
   "source": [
    "- Linear regression is a **linear** model, e.g. a model that assumes a linear relationship between the input variables (x) and the single output variable (y). More specifically, that y can be calculated from a linear combination of the input variables (x).\n",
    "- Generally, a linear model will make predictions by calculating a weighted sum of the input features (independent variables). \n",
    "$$ \\hat{y}=w_0+w_1x_1+w_2x_2+...+w_nx_n $$\n",
    "    - $\\hat{y}$ is the predicted value.\n",
    "    - $n$ is the number of features.\n",
    "    - $x_i$ is the $i^{th}$ feature value.\n",
    "    - $w_j$ is the $j^{th}$ model parameter (including the bias term $w_0$ and the feature weights $w_1,w_2,...w_n)$.\n",
    "$$\\hat{y}=h_{\\mathbf{w}}\\left(\\mathbf{x}\\right)=\\mathbf{w}^{T}\\cdot\\mathbf{x}$$\n",
    "    - $\\mathbf{w}$ is the model **parameter vector** (including the bias term $w_0$ and the feature weights $w_1,w_2,...w_n$).\n",
    "    - $\\mathbf{w}^T$ is a transpose  of $\\mathbf{w}$ (a row vector insteade of column vector).\n",
    "    - $\\mathbf{x}$ is the instance's **feature vector**, *containing* $x_0$ to $x_n$, with $x_0$ *always equal to* 1.\n",
    "    - $\\mathbf{w}^{T}\\cdot\\mathbf{x}$ is the dot product of $\\mathbf{w}^T$ and $\\mathbf{x}$.\n",
    "    - $h_{\\mathbf{w}}$ is the hypothesis function, using the parameters $\\mathbf{w}$.\n",
    "![Bias](Bias.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "5l8F4lnjFpyV"
   },
   "source": [
    "### 2. Performance measure and the learning goal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fdJNZ2q6FpyX"
   },
   "source": [
    "- Before we start to train the model, we need to determine how good the model fits the training data. There are a couple of ways to determine the level of quality, but we are going to use the most popular one and that is the **MSE** (Mean Square Error). We need to find the value for $\\mathbf{w}$ that will minimize the MSE:\n",
    "$$\\mathbf{w}=\\arg\\min MSE_{\\mathcal{D}_{train}}$$\n",
    "\n",
    "\n",
    "- MSE on the train set $\\mathcal{D}_{train}$ denoted as $\\left(\\mathbf{X},\\mathbf{y}\\right)$ including m samples $\\left\\{\\left(\\mathbf{x}_1,y_1\\right),\\left(\\mathbf{x}_2,y_2\\right),...\\left(\\mathbf{x}_m,y_m\\right)\\right\\}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "GTOZj7HfFpyY"
   },
   "source": [
    "$$MSE\\left(X,h_{\\mathbf{w}}\\right)=\\dfrac{1}{m}\\sum_{i=1}^{m}\\left(\\mathbf{w}^T\\cdot\\mathbf{x}_i - y_i\\right )^2$$\n",
    "$$MSE\\left(X,h_{\\mathbf{w}}\\right)=\\dfrac{1}{m}\\Vert\\mathbf{X}\\mathbf{w}-\\mathbf{y}\\Vert^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example below is a plot of an MSE function where the true target value is 100, and the predicted values range between -10,000 to 10,000. The MSE loss (Y-axis) reaches its minimum value at prediction (X-axis) = 100. The range is 0 to ∞.\n",
    "![Plot of MSE Loss (Y-axis) vs. Predictions (X-axis)](MSE.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ORU-9tCxFpyZ"
   },
   "source": [
    "- To find the value of $\\mathbf{w}$ that minimizes the MSE cost function, the most common way (*we have known since high school*) is to solve the derivative (gradient) equation. \n",
    "$$\\mathbf{\\hat{w}}=\\left(\\mathbf{X}^T  \\mathbf{X}\\right)^{\\dagger}  \\mathbf{X}^T  \\mathbf{y}$$\n",
    "  - $\\mathbf{\\hat{w}}$ is the value of $\\mathbf{w}$ that minimizes the cost function\n",
    "  - **Notice that** $\\mathbf{X}^T  \\mathbf{X}$ is not always invertible. $\\left(\\mathbf{X}^T  \\mathbf{X}\\right)^{\\dagger}$ is pseudo-inverse of $\\left(\\mathbf{X}^T \\mathbf{X}\\right)$ - a general case of inverse when the matrix is not invertible or not even square."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "6Tgy-tRYFpyZ"
   },
   "source": [
    "### 3. Implementation "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "qauCdk7LFpya"
   },
   "source": [
    "#### Import Library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "70Mis-p9Fpyd"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "import sklearn.datasets as datasets\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "nRr06hARFpyk"
   },
   "source": [
    "#### Create data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "g0K3G_SOFpyk"
   },
   "outputs": [],
   "source": [
    "X,y=datasets.make_regression(n_samples=100,n_features=1, noise=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "vBFWzeY3Fpyp"
   },
   "source": [
    "#### Load and visualize data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "4BpxLtG3Fpyq"
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize data \n",
    "\n",
    "plt.plot(X, y, 'ro')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "PLDAEVR8Fpyx"
   },
   "source": [
    "**TODO:** \n",
    "\n",
    "- Your observation about data: Dữ liệu được tạo ra theo mô hình hồi quy tuyến tính gồm 100 mẫu có một đặc trưng là 1 và độ nhiễu(noise) là 5, các mẫu trên mặt tọa độ tạo nên 1 đường thẳng tuy có hơi lệch nhỏ."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "mrb7peM1Fpyz"
   },
   "source": [
    "#### Training function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "DdPXTgoAFpyz"
   },
   "outputs": [],
   "source": [
    "def train_linear_regression(X, y):\n",
    "    '''\n",
    "    Trains Linear Regression on the dataset (X, y).\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    X : numpy array, shape (m, d + 1)\n",
    "        The matrix of input vectors (each row corresponds to an input vector); \n",
    "        the first column of this matrix is all ones (corresponding to x_0).\n",
    "    y : numpy array, shape (m, 1)\n",
    "        The vector of outputs.\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    w : numpy array, shape (d + 1, 1)\n",
    "        The vector of parameters of Linear Regression after training.\n",
    "    '''\n",
    "    # TODO\n",
    "    A = np.dot(X.T, X)\n",
    "    b = np.dot(X.T, y)\n",
    "    w = np.dot(np.linalg.pinv(A), b)\n",
    "    return w;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "wDgQ-5EDFpy5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "one_added_X.shape = (100, 2)\n",
      "y.shape = (100, 1)\n"
     ]
    }
   ],
   "source": [
    "# Construct one_added_X \n",
    "# TODO:\n",
    "# First column of one_added_X is all ones (corresponding to x_0).\n",
    "one_added_X = np.concatenate((np.ones((X.shape[0], 1)),X), axis=1)\n",
    "y = np.array([y]).T\n",
    "\n",
    "print ('one_added_X.shape =', one_added_X.shape)\n",
    "print ('y.shape =', y.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "nVhd2dvCFpzE"
   },
   "source": [
    "#### Train our model and visualize result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "y3YvmkEEFpzE"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.840508508893437, 2.4998523573640083)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w = train_linear_regression(one_added_X, y)\n",
    "\n",
    "# Visualize result\n",
    "predicted_ys = one_added_X.dot(w)\n",
    "\n",
    "plt.plot(X,y,'ro')\n",
    "\n",
    "x_min, x_max = plt.xlim()\n",
    "xs = np.array([x_min, x_max]).reshape(-1, 1)\n",
    "# Construct one_added_xs \n",
    "# TODO:\n",
    "# First column of one_added_xs is all ones (corresponding to x_0).\n",
    "ones_added_xs = np.concatenate((np.ones((xs.shape[0], 1)),xs), axis=1)\n",
    "\n",
    "\n",
    "predicted_ys = ones_added_xs.dot(w)\n",
    "plt.plot(xs, predicted_ys)\n",
    "plt.xlim(x_min, x_max)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "lTO6ilruFpzH"
   },
   "source": [
    "- **TODO**: Discuss about advantages and disadvantages of `Linear Regression`:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "BehaTobaFpzI"
   },
   "source": [
    "Advantages:\n",
    "- Linear Regression is simple to implement and easier to interpret the output coefficients.\n",
    "- When you know the relationship between the independent and dependent variable have a linear relationship, this algorithm is the best to use because of it’s less complexity compared to other algorithms.\n",
    "\n",
    "Disadvantages: \n",
    "- Outliers can have huge effects on the regression and boundaries are linear in this technique.\n",
    "- The second limitation of Linear Regression is its inability to represent complex models."
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "Lab01-LinearRegression.ipynb",
   "provenance": []
  },
  "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": "3.10.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}