Notebooks/Assignment_2_Model_Fitting_Tutorial_Solution.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "celltoolbar": "Slideshow",
    "colab": {
      "name": "Model Fitting Tutorial Solution",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true
    },
    "kernel": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "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": "3.7.8"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TyhpgBJW6zCw"
      },
      "source": [
        "# Assignment 2\n",
        "\n",
        "# Model Fitting: Linear regression, Multiple Linear Regression, Polynomial Regression and Bias-Variance tradeoff\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mrwOwyqe6zC9"
      },
      "source": [
        "___\n",
        "#Tutorial Objectives\n",
        "\n",
        "This is a Tutorial on fitting models to data. We will start with simple linear regression, using least squares optimization. In our way, we'll learn how to calculate the mean-squared error (MSE), explore how model parameters (slope) influence the MSE and learn how to find the optimal model parameter using least-squares optimization. Then, We'll finish our exploration of regression models by generalizing to multiple linear regression models in which we'll use Ordinary Least squares estimator.\n",
        "Happy Learning!\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q0PHSsIT6zC-"
      },
      "source": [
        "---\n",
        "# Setup"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WjOp-7X8UCmE"
      },
      "source": [
        "Let us begin with importing some libraries viz. numpy and matplotlib."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "both",
        "id": "FL9Vf3bd6zC_"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5EcvGT5X6zDB"
      },
      "source": [
        "# This is just a helper function that you will require in the following code. \n",
        "# So, make sure to run this code.\n",
        "def plot_observed_vs_predicted(x, y, y_hat, theta_hat):\n",
        "  \"\"\" Plot observed vs predicted data\n",
        "\n",
        "  Args:\n",
        "      x (ndarray): observed x values\n",
        "  y (ndarray): observed y values\n",
        "  y_hat (ndarray): predicted y values\n",
        "\n",
        "  \"\"\"\n",
        "  fig, ax = plt.subplots()\n",
        "  ax.scatter(x, y, label='Observed')  # our data scatter plot\n",
        "  ax.plot(x, y_hat, color='r', label='Fit')  # our estimated model\n",
        "  # plot residuals\n",
        "  ymin = np.minimum(y, y_hat)\n",
        "  ymax = np.maximum(y, y_hat)\n",
        "  ax.vlines(x, ymin, ymax, 'g', alpha=0.5, label='Residuals')\n",
        "  ax.set(\n",
        "      title=fr\"$\\hat{{\\theta}}$ = {theta_hat:0.2f}, MSE = {mse(x, y, theta_hat):.2f}\",\n",
        "      xlabel='x',\n",
        "      ylabel='y'\n",
        "  )\n",
        "  ax.legend()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rSWG07Z66zDC"
      },
      "source": [
        "---\n",
        "# Section 1: Mean Squared Error (MSE)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N63V_BB66zDD"
      },
      "source": [
        "**Linear regression** is an old but gold  optimization procedure that we are going to use for data fitting. Least squares (LS) optimization problems are those in which the objective function is a quadratic function of the\n",
        "parameter(s) being optimized.\n",
        "\n",
        "Suppose you have a set of measurements, $y_{n}$ (the \"dependent\" variable) obtained for different input values, $x_{n}$ (the \"independent\" or \"explanatory\" variable). Suppose we believe the measurements are proportional to the input values, but are corrupted by some (random) measurement errors, $\\epsilon_{n}$, that is:\n",
        "\n",
        "$$y_{n}= \\theta x_{n}+\\epsilon_{n}$$\n",
        "\n",
        "for some unknown slope parameter $\\theta.$ The least squares regression problem uses **mean squared error (MSE)** as its objective function, it aims to find the value of the parameter $\\theta$ by minimizing the average of squared errors:\n",
        "\n",
        "\\begin{align}\n",
        "\\min _{\\theta} \\frac{1}{N}\\sum_{n=1}^{N}\\left(y_{n}-\\theta x_{n}\\right)^{2}\n",
        "\\end{align}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ea7sKsoi6zDE"
      },
      "source": [
        "We will now explore how MSE is used in fitting a linear regression model to data. For illustrative purposes, we will create a simple synthetic dataset where we know the true underlying model. This will allow us to see how our estimation efforts compare in uncovering the real model (though in practice we rarely have this luxury).\n",
        "\n",
        "First we will generate some noisy samples $x$ from [0, 10) along the line $y = 1.5x$ as our dataset we wish to fit a model to."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P6vOiRzs6zDE",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "cellView": "code",
        "outputId": "cdaf2ac4-34fc-4060-a956-2029dcf46648"
      },
      "source": [
        "\n",
        "\n",
        "\n",
        "#this is a random number generator and setting a seed ensures that we get the same pseudonumber sequence.\n",
        "np.random.seed(121)\n",
        "\n",
        "# Let's set some parameters\n",
        "theta = 1.5\n",
        "n_samples = 50\n",
        "\n",
        "# Draw x and then calculate y\n",
        "x = 10 * np.random.rand(n_samples)  # sample from a uniform distribution over [0,10)\n",
        "noise = np.random.randn(n_samples)  # sample from a standard normal distribution\n",
        "y = theta * x + noise\n",
        "\n",
        "# Plot the results\n",
        "fig, ax = plt.subplots()\n",
        "ax.scatter(x, y)  # produces a scatter plot\n",
        "ax.set(xlabel='x', ylabel='y');"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7Ml9ygCj6zDF"
      },
      "source": [
        "Now that we have our dataset is much noisy,so  we can start trying to estimate the underlying model that produced it. We use MSE to evaluate how successful a particular slope estimate $\\hat{\\theta}$ is for explaining the data, with the closer to 0 the MSE is, the better our estimate fits the data."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BMc1xIZE6zDG"
      },
      "source": [
        "## Exercise 1: Compute MSE\n",
        "\n",
        "In this exercise you have to implement a method to compute the mean squared error i.e. MSE for a set of inputs $x$, measurements (outputs) $y$, and slope estimate $\\hat{\\theta}$. We will then compute and print the mean squared error for 4 different choices of theta"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "797eWFCN6zDG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c05961a4-f0c0-4900-8968-16ae9db496db"
      },
      "source": [
        "def mse(x, y, theta_hat):\n",
        "  \"\"\"Compute the mean squared error\n",
        "\n",
        "  Args:\n",
        "    x (ndarray): An array of shape (samples,) that contains the input values.\n",
        "    y (ndarray): An array of shape (samples,) that contains the corresponding\n",
        "      measurement values to the inputs.\n",
        "    theta_hat (float): An estimate of the slope parameter\n",
        "\n",
        "  Returns:\n",
        "    float: The mean squared error of the data with the estimated parameter.\n",
        "  \"\"\"\n",
        "  ####################################################\n",
        "  ## TODO for students: compute the mean squared error\n",
        "  # Fill out function and remove\n",
        "  # raise NotImplementedError(\"Student exercise: compute the mean squared error\")\n",
        "  ####################################################\n",
        "\n",
        "  # Compute the estimated y\n",
        "  y_hat = theta_hat*x\n",
        "\n",
        "  # Compute mean squared error\n",
        "  mse = np.mean((y-y_hat)**2)\n",
        "  \n",
        "  return mse\n",
        "\n",
        "\n",
        "# Uncomment below to test your function\n",
        "theta_hats = [0.8, 1.0, 1.6, 1.2]\n",
        "for theta_hat in theta_hats:\n",
        "  print(f\"theta_hat of {theta_hat} has an MSE of {mse(x, y, theta_hat):.2f}\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "theta_hat of 0.8 has an MSE of 17.08\n",
            "theta_hat of 1.0 has an MSE of 9.27\n",
            "theta_hat of 1.6 has an MSE of 1.14\n",
            "theta_hat of 1.2 has an MSE of 4.02\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-9QNjpy16zDK"
      },
      "source": [
        "The result should be:\n",
        "\n",
        "theta_hat of 0.8 has an MSE of 17.08\\\n",
        "theta_hat of 1.0 has an MSE of 9.27\\\n",
        "theta_hat of 1.6 has an MSE of 1.14\\\n",
        "theta_hat of 1.2 has an MSE of 4.02\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "If0FE8Z46zDK"
      },
      "source": [
        "We see that $\\hat{\\theta} = 1.6$ is our best estimate from the three we tried. Looking just at the raw numbers, however, isn't always satisfying, so let's visualize what our estimated model looks like over the data. \n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jqjlrHzN6zDL",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        },
        "cellView": "code",
        "outputId": "42301a29-bc10-4916-91f9-d0518808320a"
      },
      "source": [
        "\n",
        "# Execute this cell to visualize estimated models\n",
        "\n",
        "fig, axes = plt.subplots(ncols=4, figsize=(18, 4))\n",
        "for theta_hat, ax in zip(theta_hats, axes):\n",
        "\n",
        "  # True data\n",
        "  ax.scatter(x, y, label='Observed')  # our data scatter plot\n",
        "\n",
        "  # Compute and plot predictions\n",
        "  y_hat = theta_hat * x\n",
        "  ax.plot(x, y_hat, color='r', label='Fit')  # our estimated model\n",
        "\n",
        "  ax.set(\n",
        "      title= fr'$\\hat{{\\theta}}$= {theta_hat}, MSE = {mse(x, y, theta_hat):.2f}',\n",
        "      xlabel='x',\n",
        "      ylabel='y'\n",
        "  );\n",
        "\n",
        "axes[0].legend()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fcda5d9f278>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 79
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 1296x288 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3-nwKuGI3T3E"
      },
      "source": [
        "As you can see from the above graphs that we have the best fit for $\\hat{\\theta} = 1.6$ which is much close to the actual value i.e. 1.5"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sj9ji6s-6zDM"
      },
      "source": [
        "While visually exploring several estimates can be instructive, it's not the most efficient for finding the best estimate to fit our data. Another technique we can use is choose a reasonable range of parameter values and compute the MSE at several values in that interval. This allows us to plot the error against the parameter value (this is also called an **error landscape**, especially when we deal with more than one parameter). We can select the final $\\hat{\\theta}$ ($\\hat{\\theta}_{MSE}$) as the one which results in the lowest error."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GACGgKCK6zDN",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 308
        },
        "outputId": "75ad2b0b-50e8-4efa-eca4-cf8745c18291"
      },
      "source": [
        "# Execute this cell to loop over theta_hats, compute MSE, and plot results\n",
        "\n",
        "# Loop over different thetas, compute MSE for each\n",
        "theta_hat_grid = np.linspace(-2.0, 4.0)\n",
        "errors = np.zeros(len(theta_hat_grid))\n",
        "for i, theta_hat in enumerate(theta_hat_grid):\n",
        "  errors[i] = mse(x, y, theta_hat)\n",
        "\n",
        "# Find theta that results in lowest error\n",
        "best_error = np.min(errors)\n",
        "theta_hat = theta_hat_grid[np.argmin(errors)]\n",
        "\n",
        "\n",
        "# Plot results\n",
        "fig, ax = plt.subplots()\n",
        "ax.plot(theta_hat_grid, errors, '-o', label='MSE', c='C1')\n",
        "ax.axvline(theta, color='g', ls='--', label=r\"$\\theta_{True}$\")\n",
        "ax.axvline(theta_hat, color='r', ls='-', label=r\"$\\hat{{\\theta}}_{MSE}$\")\n",
        "ax.set(\n",
        "  title=fr\"Best fit: $\\hat{{\\theta}}$ = {theta_hat:.2f}, MSE = {best_error:.2f}\",\n",
        "  xlabel=r\"$\\hat{{\\theta}}$\",\n",
        "  ylabel='MSE')\n",
        "ax.legend();"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sArNWeP46zDN"
      },
      "source": [
        "Now here we can see that our best fit is $\\hat{\\theta}=1.55$ with an MSE of 0.95. This is really closer to the original true value $\\theta=1.5$!\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M35E18XB6zDO"
      },
      "source": [
        "---\n",
        "# Section 2: Least-squares optimization\n",
        "\n",
        "\n",
        "While the approach detailed above (computing MSE at various values of $\\hat\\theta$) quickly got us to a good estimate, it still relied on evaluating the MSE value across a grid of hand-specified values. If we didn't pick a good range to begin with, or with enough granularity, we might miss the best possible estimator. Let's go one step further, and instead of finding the minimum MSE from a set of candidate estimates, let's solve for it analytically.\n",
        "\n",
        "We can do this by minimizing the cost function. Mean squared error is a convex objective function, therefore we can compute its minimum using calculus. Please see video or appendix for this derivation! After computing the minimum, we find that:\n",
        "\n",
        "\\begin{align}\n",
        "\\hat\\theta = \\frac{\\vec{x}^\\top \\vec{y}}{\\vec{x}^\\top \\vec{x}}\n",
        "\\end{align}\n",
        "\n",
        "This is known as solving the normal equations. For different ways of obtaining the solution, see the notes on [Least Squares Optimization](https://www.cns.nyu.edu/~eero/NOTES/leastSquares.pdf) by Eero Simoncelli."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XNXOyhhX6zDP"
      },
      "source": [
        "### Exercise 2: Solve for the Optimal Estimator\n",
        "\n",
        "In this exercise, you have to write a function that finds the optimal $\\hat{\\theta}$ value using the least squares optimization approach (the equation above) to solve MSE minimization. It shoud take arguments $x$ and $y$ and return the solution $\\hat{\\theta}$.\n",
        "\n",
        "We will then use your function to compute $\\hat{\\theta}$ and plot the resulting prediction on top of the data. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yWv9XClk6zDP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "outputId": "96abbca1-d923-44c6-d9cf-d64fd15c48a5"
      },
      "source": [
        "def solve_normal_eqn(x, y):\n",
        "  \"\"\"Solve the normal equations to produce the value of theta_hat that minimizes\n",
        "    MSE.\n",
        "\n",
        "    Args:\n",
        "    x (ndarray): An array of shape (samples,) that contains the input values.\n",
        "    y (ndarray): An array of shape (samples,) that contains the corresponding\n",
        "      measurement values to the inputs.\n",
        "\n",
        "  Returns:\n",
        "    float: the value for theta_hat arrived from minimizing MSE\n",
        "  \"\"\"\n",
        "\n",
        "  ################################################################################\n",
        "  ## TODO for students: solve for the best parameter using least squares\n",
        "  # Fill out function and remove\n",
        "  #raise NotImplementedError(\"Student exercise: solve for theta_hat using least squares\")\n",
        "  ################################################################################\n",
        "\n",
        "  # Compute theta_hat analytically\n",
        "  theta_hat = x.T@y/(x.T@x)\n",
        "\n",
        "  return theta_hat\n",
        "\n",
        "\n",
        "# Uncomment below to test your function\n",
        "theta_hat = solve_normal_eqn(x, y)\n",
        "y_hat = theta_hat * x\n",
        "plot_observed_vs_predicted(x, y, y_hat, theta_hat)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "cellView": "both",
        "outputId": "5a46f798-31e1-4fbd-da7a-de8a270c5f7d",
        "id": "Pud5Vjaz6zDQ"
      },
      "source": [
        "\n",
        "\n",
        "*Example output:*\n",
        "![Solution Hint](https://drive.google.com/uc?export=view&id=1wSQyRMyHNKFSTaWtZdMxfDte3T_djcoj)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HhsFjt8nFePg"
      },
      "source": [
        "Now you see how good our model is at estimating $\\hat{\\theta}$. Its accurate upto 1 decimal places using least square optimization."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aRxJbvF9Lcrf"
      },
      "source": [
        "---\n",
        "# Section 3: Multiple Linear Regression\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DXzjcn-RLcrg"
      },
      "source": [
        "Now that we have considered the univariate case and how to produce confidence intervals for our estimator, we turn to the general linear regression case, where we can have more than one regressor, or feature, in our input.\n",
        "\n",
        "Recall that our original univariate linear model was given as\n",
        "\n",
        "\\begin{align}\n",
        "y = \\theta x + \\epsilon\n",
        "\\end{align}\n",
        "\n",
        "where $\\theta$ is the slope and $\\epsilon$ some noise. We can easily extend this to the multivariate scenario by adding another parameter for each additional feature\n",
        "\n",
        "\\begin{align}\n",
        "y = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + ... +\\theta_d x_d + \\epsilon\n",
        "\\end{align}\n",
        "\n",
        "where $\\theta_0$ is the intercept and $d$ is the number of features (it is also the dimensionality of our input).\n",
        "\n",
        "We can condense this succinctly using vector notation for a single data point\n",
        "\n",
        "\\begin{align}\n",
        "y_i = \\boldsymbol{\\theta}^{\\top}\\mathbf{x}_i + \\epsilon\n",
        "\\end{align}\n",
        "\n",
        "and fully in matrix form\n",
        "\n",
        "\\begin{align}\n",
        "\\mathbf{y} = \\mathbf{X}\\boldsymbol{\\theta} + \\mathbf{\\epsilon}\n",
        "\\end{align}\n",
        "\n",
        "where $\\mathbf{y}$ is a vector of measurements, $\\mathbf{X}$ is a matrix containing the feature values (columns) for each input sample (rows), and $\\boldsymbol{\\theta}$ is our parameter vector.\n",
        "\n",
        "This matrix $\\mathbf{X}$ is often referred to as the \"[design matrix](https://en.wikipedia.org/wiki/Design_matrix)\"."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LGOV7KmzLcri"
      },
      "source": [
        "For this tutorial we will focus on the two-dimensional case ($d=2$), which allows us to easily visualize our results. As an example, think of a situation where a scientist records the spiking response of a retinal ganglion cell to patterns of light signals that vary in contrast and in orientation. Then contrast and orientation values can be used as features / regressors to predict the cells response.\n",
        "\n",
        "In this case our model can be writen as:\n",
        "\n",
        "\\begin{align}\n",
        "y = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\epsilon\n",
        "\\end{align}\n",
        "\n",
        "or in matrix form where\n",
        "\n",
        "\\begin{align}\n",
        "\\mathbf{X} = \n",
        "\\begin{bmatrix}\n",
        "1 & x_{1,1} & x_{1,2} \\\\\n",
        "1 & x_{2,1} & x_{2,2} \\\\\n",
        "\\vdots & \\vdots & \\vdots \\\\\n",
        "1 & x_{n,1} & x_{n,2}\n",
        "\\end{bmatrix}, \n",
        "\\boldsymbol{\\theta} =\n",
        "\\begin{bmatrix}\n",
        "\\theta_0 \\\\\n",
        "\\theta_1 \\\\\n",
        "\\theta_2 \\\\\n",
        "\\end{bmatrix}\n",
        "\\end{align}\n",
        "\n",
        "For our actual exploration dataset we shall set $\\boldsymbol{\\theta}=[0, -2, -3]$ and draw $N=40$ noisy samples from $x \\in [-2,2)$. Note that setting the value of $\\theta_0 = 0$ effectively ignores the offset term."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "3UHzA5U4Lcrj",
        "outputId": "0dae637a-ef2f-4774-e796-bc04c921b7c7"
      },
      "source": [
        "# Execute this cell to simulate some data\n",
        "# Running this code is necessary for following exercise 3\n",
        "# Set random seed for reproducibility\n",
        "np.random.seed(1234)\n",
        "\n",
        "# Set parameters\n",
        "theta = [0, -2, -3]\n",
        "n_samples = 40\n",
        "\n",
        "# Draw x and calculate y\n",
        "n_regressors = len(theta)\n",
        "x0 = np.ones((n_samples, 1))\n",
        "x1 = np.random.uniform(-2, 2, (n_samples, 1))\n",
        "x2 = np.random.uniform(-2, 2, (n_samples, 1))\n",
        "X = np.hstack((x0, x1, x2))\n",
        "noise = np.random.randn(n_samples)\n",
        "y = X @ theta + noise\n",
        "\n",
        "\n",
        "ax = plt.subplot(projection='3d')\n",
        "ax.plot(X[:,1], X[:,2], y, '.')\n",
        "\n",
        "ax.set(\n",
        "    xlabel='$x_1$',\n",
        "    ylabel='$x_2$',\n",
        "    zlabel='y'\n",
        ")\n",
        "plt.tight_layout()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OZOCRt-fLcrk"
      },
      "source": [
        "Now that we have our dataset, we want to find an optimal vector of paramters $\\boldsymbol{\\hat\\theta}$. Recall our analytic solution to minimizing MSE for a single regressor:\n",
        "\n",
        "\\begin{align}\n",
        "\\hat\\theta = \\frac{\\sum_{i=1}^N x_i y_i}{\\sum_{i=1}^N x_i^2}.\n",
        "\\end{align}\n",
        "\n",
        "The same holds true for the multiple regressor case, only now expressed in matrix form\n",
        "\n",
        "\\begin{align}\n",
        "\\boldsymbol{\\hat\\theta} = (\\mathbf{X}^\\top\\mathbf{X})^{-1}\\mathbf{X}^\\top\\mathbf{y}.\n",
        "\\end{align}\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JvJSVuCLLcrm"
      },
      "source": [
        "### Exercise 3: Ordinary Least Squares Estimator\n",
        "\n",
        "In this exercise you will implement the OLS approach to estimating $\\boldsymbol{\\hat\\theta}$ from the design matrix $\\mathbf{X}$ and measurement vector $\\mathbf{y}$. You can use the `@` symbol for matrix multiplication, `.T` for transpose, and `np.linalg.inv` for matrix inversion.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "y9Um7BOvLcrm",
        "outputId": "98fe615e-1b93-4f37-f0bb-00cf0ba42b90"
      },
      "source": [
        "def ordinary_least_squares(X, y):\n",
        "  \"\"\"Ordinary least squares estimator for linear regression.\n",
        "\n",
        "  Args:\n",
        "    x (ndarray): design matrix of shape (n_samples, n_regressors)\n",
        "    y (ndarray): vector of measurements of shape (n_samples)\n",
        "\n",
        "  Returns:\n",
        "    ndarray: estimated parameter values of shape (n_regressors)\n",
        "  \"\"\"\n",
        "  ######################################################################\n",
        "  ## TODO for students: solve for the optimal parameter vector using OLS\n",
        "  # Fill out function and remove\n",
        "  #raise NotImplementedError(\"Student exercise: solve for theta_hat vector using OLS\")\n",
        "  ######################################################################\n",
        "\n",
        "  # Compute theta_hat using OLS\n",
        "  theta_hat = np.linalg.inv(X.T @ X) @ (X.T @ y)\n",
        "\n",
        "  return theta_hat\n",
        "\n",
        "\n",
        "# Uncomment below to test your function\n",
        "theta_hat = ordinary_least_squares(X, y)\n",
        "print(theta_hat)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[ 0.13861386 -2.09395731 -3.16370742]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EK0VeDiJLcrn"
      },
      "source": [
        "After filling in this function, you should see that $\\hat{\\theta}$ = [ 0.13861386, -2.09395731, -3.16370742]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S-R7Cvt-Lcro"
      },
      "source": [
        "Now that we have our $\\mathbf{\\hat\\theta}$, we can obtain $\\mathbf{\\hat y}$ and thus our mean squared error."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F-q4TJcpLcro",
        "outputId": "6a10c873-70ae-4081-e530-2a78fab1d720"
      },
      "source": [
        "# Compute predicted data\n",
        "theta_hat = ordinary_least_squares(X, y)\n",
        "y_hat = X @ theta_hat\n",
        "print(theta_hat)\n",
        "# Compute MSE\n",
        "print(f\"MSE = {np.mean((y - y_hat)**2):.2f}\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[ 0.13861386 -2.09395731 -3.16370742]\n",
            "MSE = 0.91\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CqxMU8Jo-sQS"
      },
      "source": [
        "The MSE should come out to be 0.91"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_X41s12NLcrp"
      },
      "source": [
        "Finally, the following code will plot a geometric visualization of the data points (blue) and fitted plane. Execute the following cell to visualize data and predicted plane."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "jPe5xVNOLcrp",
        "outputId": "0b5c4326-5fe1-4714-823d-8f7fbc8eb03a"
      },
      "source": [
        "# Execute this cell to visualize data and predicted plane\n",
        "\n",
        "theta_hat = ordinary_least_squares(X, y)\n",
        "xx, yy = np.mgrid[-2:2:50j, -2:2:50j]\n",
        "y_hat_grid = np.array([xx.flatten(), yy.flatten()]).T @ theta_hat[1:]\n",
        "y_hat_grid = y_hat_grid.reshape((50, 50))\n",
        "\n",
        "ax = plt.subplot(projection='3d')\n",
        "ax.plot(X[:, 1], X[:, 2], y, '.')\n",
        "ax.plot_surface(xx, yy, y_hat_grid, linewidth=0, alpha=0.5, color='C1',\n",
        "                cmap=plt.get_cmap('coolwarm'))\n",
        "\n",
        "for i in range(len(X)):\n",
        "  ax.plot((X[i, 1], X[i, 1]),\n",
        "          (X[i, 2], X[i, 2]),\n",
        "          (y[i], y_hat[i]),\n",
        "          'g-', alpha=.5)\n",
        "\n",
        "ax.set(\n",
        "    xlabel='$x_1$',\n",
        "    ylabel='$x_2$',\n",
        "    zlabel='y'\n",
        ")\n",
        "plt.tight_layout()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8GUflXBJiZEd"
      },
      "source": [
        "---\n",
        "# Section 4:  Polynomial Regression"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uFp1VvgoiZEe"
      },
      "source": [
        "So far today, you learned how to predict outputs from inputs by fitting a linear regression model. We can now model all sort of relationships, including in neuroscience!  \n",
        "\n",
        "One potential problem with this approach is the simplicity of the model. Linear regression, as the name implies, can only capture a linear relationship between the inputs and outputs. Put another way, the predicted outputs are only a weighted sum of the inputs. What if there are more complicated computations happening? Luckily, many more complex models exist (and you will encounter many more over the next 3 weeks). One model that is still very simple to fit and understand, but captures more complex relationships, is **polynomial regression**, an extension of linear regression.\n",
        "\n",
        "Since polynomial regression is an extension of linear regression, everything you learned so far will come in handy now! The goal is the same: we want to predict the dependent variable $y_{n}$ given the input values $x_{n}$. The key change is the type of relationship between inputs and outputs that the model can capture. \n",
        "\n",
        "Linear regression models predict the outputs as a weighted sum of the inputs:\n",
        "\n",
        "$$y_{n}= \\theta_0 + \\theta x_{n} + \\epsilon_{n}$$\n",
        "\n",
        "With polynomial regression, we model the outputs as a polynomial equation based on the inputs. For example, we can model the outputs as:\n",
        "\n",
        "$$y_{n}= \\theta_0 + \\theta_1 x_{n} + \\theta_2 x_{n}^2 + \\theta_3 x_{n}^3 + \\epsilon_{n}$$\n",
        "\n",
        "We can change how complex a polynomial is fit by changing the order of the polynomial. The order of a polynomial refers to the highest power in the polynomial. The equation above is a third order polynomial because the highest value x is raised to is 3. We could add another term ($+ \\theta_4 x_{n}^4$) to model an order 4 polynomial and so on.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PIoMpXHHiZEf"
      },
      "source": [
        "First, we will simulate some data to practice fitting polynomial regression models. We will generate random inputs $x$ and then compute y according to $y = x^2 - x - 2 $, with some extra noise both in the input and the output to make the model fitting exercise closer to a real life situation."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "id": "TIhFZoI9iZEf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "outputId": "5eb6403e-a79b-4027-d9ad-06d4a0476190"
      },
      "source": [
        "#@title\n",
        "#@markdown Execute this cell to simulate some data\n",
        "\n",
        "# setting a fixed seed to our random number generator ensures we will always\n",
        "# get the same psuedorandom number sequence\n",
        "np.random.seed(121)\n",
        "n_samples = 30\n",
        "x = np.random.uniform(-2, 2.5, n_samples)  # inputs uniformly sampled from [-2, 2.5)\n",
        "y =  x**2 - x - 2   # computing the outputs\n",
        "\n",
        "output_noise = 1/8 * np.random.randn(n_samples)\n",
        "y += output_noise  # adding some output noise\n",
        "\n",
        "input_noise = 1/2 * np.random.randn(n_samples)\n",
        "x += input_noise  # adding some input noise\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "ax.scatter(x, y)  # produces a scatter plot\n",
        "ax.set(xlabel='x', ylabel='y');"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "id": "zBzU3Q0VEWZI"
      },
      "source": [
        "#@title Helper Functions\r\n",
        "\r\n",
        "def plot_fitted_polynomials(x, y, theta_hat):\r\n",
        "  \"\"\" Plot polynomials of different orders\r\n",
        "\r\n",
        "  Args:\r\n",
        "    x (ndarray): input vector of shape (n_samples)\r\n",
        "    y (ndarray): vector of measurements of shape (n_samples)\r\n",
        "    theta_hat (dict): polynomial regression weights for different orders\r\n",
        "  \"\"\"\r\n",
        "\r\n",
        "  x_grid = np.linspace(x.min() - .5, x.max() + .5)\r\n",
        "\r\n",
        "  plt.figure()\r\n",
        "\r\n",
        "  for order in range(0, max_order + 1):\r\n",
        "    X_design = make_design_matrix(x_grid, order)\r\n",
        "    plt.plot(x_grid, X_design @ theta_hat[order]);\r\n",
        "\r\n",
        "  plt.ylabel('y')\r\n",
        "  plt.xlabel('x')\r\n",
        "  plt.plot(x, y, 'C0.');\r\n",
        "  plt.legend([f'order {o}' for o in range(max_order + 1)], loc=1)\r\n",
        "  plt.title('polynomial fits')\r\n",
        "  plt.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5VniylWhiZEg"
      },
      "source": [
        "## Section 4.1: Design matrix for polynomial regression\n",
        "\n",
        "Now we have the basic idea of polynomial regression and some noisy data, let's begin! The key difference between fitting a linear regression model and a polynomial regression model lies in how we structure the input variables.  \n",
        "\n",
        "For linear regression, we used $X = x$ as the input data. To add a constant bias (a y-intercept in a 2-D plot), we use $X = \\big[ \\boldsymbol 1, x \\big]$, where $\\boldsymbol 1$ is a column of ones.  When fitting, we learn a weight for each column of this matrix. So we learn a weight that multiples with column 1 - in this case that column is all ones so we gain the bias parameter ($+ \\theta_0$). We also learn a weight for every column, or every feature of x, as we learned in Section 1.\n",
        "\n",
        "This matrix $X$ that we use for our inputs is known as a **design matrix**. We want to create our design matrix so we learn weights for $x^2, x^3,$ etc. Thus, we want to build our design matrix $X$ for polynomial regression of order $k$ as:\n",
        "\n",
        "$$X = \\big[ \\boldsymbol 1 , x^1, x^2 , \\ldots , x^k \\big],$$\n",
        "\n",
        "where $\\boldsymbol{1}$ is the vector the same length as $x$ consisting of of all ones, and $x^p$ is the vector or matrix $x$ with all elements raised to the power $p$. Note that $\\boldsymbol{1} = x^0$ and $x^1 = x$ "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0KFmA0XOiZEg"
      },
      "source": [
        "### Exercise 5: Structure design matrix\n",
        "\n",
        "Create a function (`make_design_matrix`) that structures the design matrix given the input data and the order of the polynomial you wish to fit. We will print part of this design matrix for our data and order 5."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IyYXKLuFiZEh",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d0397a2e-deae-4f00-e75a-a0420aeeef0b"
      },
      "source": [
        "def make_design_matrix(x, order):\n",
        "  \"\"\"Create the design matrix of inputs for use in polynomial regression\n",
        "\n",
        "  Args:\n",
        "    x (ndarray): input vector of shape (n_samples)\n",
        "    order (scalar): polynomial regression order\n",
        "\n",
        "  Returns:\n",
        "    ndarray: design matrix for polynomial regression of shape (samples, order+1)\n",
        "  \"\"\"\n",
        "  ########################################################################\n",
        "  ## TODO for students: create the design matrix ##\n",
        "  # Fill out function and remove\n",
        "  #raise NotImplementedError(\"Student exercise: create the design matrix\")\n",
        "  ########################################################################\n",
        "\n",
        "  # Broadcast to shape (n x 1) so dimensions work\n",
        "  if x.ndim == 1:\n",
        "    x = x[:, None]\n",
        "\n",
        "  #if x has more than one feature, we don't want multiple columns of ones so we assign\n",
        "  # x^0 here\n",
        "  design_matrix = np.ones((x.shape[0], 1))\n",
        "\n",
        "  # Loop through rest of degrees and stack columns (hint: np.hstack)\n",
        "  for degree in range(1, order + 1):\n",
        "      design_matrix = np.hstack((design_matrix,x**degree))\n",
        "\n",
        "  return design_matrix\n",
        "\n",
        "\n",
        "# Uncomment to test your function\n",
        "order = 5\n",
        "X_design = make_design_matrix(x, order)\n",
        "print(X_design[0:2, 0:2])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ 1.         -1.51194917]\n",
            " [ 1.         -0.35259945]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6xu1BYUniZEh"
      },
      "source": [
        "You should see that the printed section of this design matrix is `[[ 1.         -1.51194917]\n",
        " [ 1.         -0.35259945]]`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X4m-Nrv6iZEi"
      },
      "source": [
        "## Section 4.2: Fitting polynomial regression models"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r6sbgiNAiZEi"
      },
      "source": [
        "Now that we have the inputs structured correctly in our design matrix, fitting a polynomial regression is the same as fitting a linear regression model! All of the polynomial structure we need to learn is contained in how the inputs are structured in the design matrix. We can use the same least squares solution we computed in previous exercises. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xAv7ijE1iZEi"
      },
      "source": [
        "### Exercise 6: Fitting polynomial regression models with different orders "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u4oa-3ZtiZEj"
      },
      "source": [
        "Here, we will fit polynomial regression models to find the regression coefficients ($\\theta_0, \\theta_1, \\theta_2,$ ...) by solving the least squares problem. Create a function `solve_poly_reg` that loops over different order polynomials (up to `max_order`), fits that model, and saves out the weights for each. You may invoke the `ordinary_least_squares` function. \n",
        "\n",
        "We will then qualitatively inspect the quality of our fits for each order by plotting the fitted polynomials on top of the data. In order to see smooth curves, we evaluate the fitted polynomials on a grid of $x$ values (ranging between the largest and smallest of the inputs present in the dataset)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "elmr54n1iZEj",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "cfdd37f6-b50d-4115-c903-972ae80c21f5"
      },
      "source": [
        "def solve_poly_reg(x, y, max_order):\n",
        "  \"\"\"Fit a polynomial regression model for each order 0 through max_order.\n",
        "\n",
        "  Args:\n",
        "    x (ndarray): input vector of shape (n_samples)\n",
        "    y (ndarray): vector of measurements of shape (n_samples)\n",
        "    max_order (scalar): max order for polynomial fits\n",
        "\n",
        "  Returns:\n",
        "    dict: fitted weights for each polynomial model (dict key is order)\n",
        "  \"\"\"\n",
        "\n",
        "  # Create a dictionary with polynomial order as keys,\n",
        "  # and np array of theta_hat (weights) as the values\n",
        "  theta_hats = {}\n",
        "\n",
        "  # Loop over polynomial orders from 0 through max_order\n",
        "  for order in range(max_order + 1):\n",
        "\n",
        "    ##################################################################################\n",
        "    ## TODO for students: Create design matrix and fit polynomial model for this order\n",
        "    # Fill out function and remove\n",
        "    #raise NotImplementedError(\"Student exercise: fit a polynomial model\")\n",
        "    ##################################################################################\n",
        "\n",
        "    # Create design matrix\n",
        "    X_design = make_design_matrix(x,order)\n",
        "\n",
        "    # Fit polynomial model\n",
        "    this_theta = ordinary_least_squares(X_design,y)\n",
        "\n",
        "    theta_hats[order] = this_theta\n",
        "\n",
        "  return theta_hats\n",
        "\n",
        "\n",
        "# Uncomment to test your function\n",
        "max_order = 5\n",
        "theta_hats = solve_poly_reg(x, y, max_order)\n",
        "plot_fitted_polynomials(x, y, theta_hats)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "812RkzdQiZEl"
      },
      "source": [
        "## Section 4.3: Evaluating fit quality\n",
        "\n",
        "As with linear regression, we can compute mean squared error (MSE) to get a sense of how well the model fits the data. \n",
        "\n",
        "We compute MSE as:\n",
        "\n",
        "$$ MSE = \\frac 1 N ||y - \\hat y||^2 = \\frac 1 N \\sum_{i=1}^N (y_i - \\hat y_i)^2 $$\n",
        "\n",
        "where the predicted values for each model are given by $ \\hat y = X \\hat \\theta$. \n",
        "\n",
        "*Which model (i.e. which polynomial order) do you think will have the best MSE?*"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zDCG0wFQiZEl"
      },
      "source": [
        "### Exercise 7: Compute MSE and compare models\n",
        "\n",
        "We will compare the MSE for different polynomial orders with a bar plot."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "both",
        "id": "68L7E73DiZEn",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 304
        },
        "outputId": "83ce00b2-b20a-4c45-faa1-f9f0c81a0cbb"
      },
      "source": [
        "# to_remove solution\n",
        "mse_list = []\n",
        "order_list = list(range(max_order + 1))\n",
        "\n",
        "for order in order_list:\n",
        "\n",
        "  X_design = make_design_matrix(x, order)\n",
        "\n",
        "  # Get prediction for the polynomial regression model of this order\n",
        "  y_hat = X_design @ theta_hats[order]\n",
        "\n",
        "  # Compute the residuals\n",
        "  residuals = y - y_hat\n",
        "\n",
        "  # Compute the MSE\n",
        "  mse = np.mean(residuals ** 2)\n",
        "\n",
        "  mse_list.append(mse)\n",
        "\n",
        "with plt.xkcd():\n",
        "  fig, ax = plt.subplots()\n",
        "  ax.bar(order_list, mse_list)\n",
        "  ax.set(title='Comparing Polynomial Fits', xlabel='Polynomial order', ylabel='MSE')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Wp7OHmrScRYY"
      },
      "source": [
        "---\n",
        "# Section 5: Bias-variance tradeoff\n",
        "\n",
        "Finding a good model can be difficult. One of the most important concepts to keep in mind when modeling is the **bias-variance tradeoff**. \n",
        "\n",
        "**Bias** is the difference between the prediction of the model and the corresponding true output variables you are trying to predict. Models with high bias will not fit the training data well since the predictions are quite different from the true data. These high bias models are overly simplified - they do not have enough parameters and complexity to accurately capture the patterns in the data and are thus **underfitting**.\n",
        "\n",
        "\n",
        "**Variance** refers to the variability of model predictions for a given input. Essentially, do the model predictions change a lot with changes in the exact training data used? Models with high variance are highly dependent on the exact training data used - they will not generalize well to test data. These high variance models are **overfitting** to the data.\n",
        "\n",
        "In essence:\n",
        "\n",
        "* High bias, low variance models have high train and test error.\n",
        "* Low bias, high variance models have low train error, high test error\n",
        "* Low bias, low variance models have low train and test error\n",
        "\n",
        "\n",
        "As we can see from this list, we ideally want low bias and low variance models! These goals can be in conflict though - models with enough complexity to have low bias also tend to overfit and depend on the training data more. We need to decide on the correct tradeoff.\n",
        "\n",
        "In this section, we will see the bias-variance tradeoff in action with polynomial regression models of different orders.\n",
        "\n",
        "Graphical illustration of bias and variance.\n",
        "(Source: http://scott.fortmann-roe.com/docs/BiasVariance.html)\n",
        "\n",
        "![bias-variance](https://www.cs.cornell.edu/courses/cs4780/2018fa/lectures/images/bias_variance/bullseye.png) \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "id": "qfA4F2NKcRYP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 518
        },
        "outputId": "f770766a-6120-4ede-ed64-3978c9b0c9d9"
      },
      "source": [
        "#@title Video 3: Bias Variance Tradeoff\n",
        "from IPython.display import YouTubeVideo\n",
        "video = YouTubeVideo(id=\"NcUH_seBcVw\", width=854, height=480, fs=1)\n",
        "print(\"Video available at https://youtube.com/watch?v=\" + video.id)\n",
        "video"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Video available at https://youtube.com/watch?v=NcUH_seBcVw\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "        <iframe\n",
              "            width=\"854\"\n",
              "            height=\"480\"\n",
              "            src=\"https://www.youtube.com/embed/NcUH_seBcVw?fs=1\"\n",
              "            frameborder=\"0\"\n",
              "            allowfullscreen\n",
              "        ></iframe>\n",
              "        "
            ],
            "text/plain": [
              "<IPython.lib.display.YouTubeVideo at 0x7fcda5fe4978>"
            ],
            "image/jpeg": "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\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 91
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "6wQpxDGIcRYX",
        "outputId": "297dc4bf-0275-467d-f149-e256ca97df0d"
      },
      "source": [
        "#@title\n",
        "#@markdown Execute this cell to simulate both training and test data\n",
        "\n",
        "### Generate training data\n",
        "np.random.seed(0)\n",
        "n_train_samples = 50\n",
        "x_train = np.random.uniform(-2, 2.5, n_train_samples) # sample from a uniform distribution over [-2, 2.5)\n",
        "noise = np.random.randn(n_train_samples) # sample from a standard normal distribution\n",
        "y_train =  x_train**2 - x_train - 2 + noise\n",
        "\n",
        "### Generate testing data\n",
        "n_test_samples = 20\n",
        "x_test = np.random.uniform(-3, 3, n_test_samples) # sample from a uniform distribution over [-2, 2.5)\n",
        "noise = np.random.randn(n_test_samples) # sample from a standard normal distribution\n",
        "y_test =  x_test**2 - x_test - 2 + noise\n",
        "\n",
        "## Plot both train and test data\n",
        "fig, ax = plt.subplots()\n",
        "plt.title('Training & Test Data')\n",
        "plt.plot(x_train, y_train, '.', markersize=15, label='Training')\n",
        "plt.plot(x_test, y_test, 'g+', markersize=15, label='Test')\n",
        "plt.legend()\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y');"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "id": "taRFZ_K0cRYa"
      },
      "source": [
        "#@title\n",
        "#@markdown Execute this cell to estimate theta_hats\n",
        "max_order = 5\n",
        "theta_hats = solve_poly_reg(x_train, y_train, max_order)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-7SLgIN0cRYb"
      },
      "source": [
        "### Exercise 8: Compute and compare train vs test error\n",
        "\n",
        "We will use MSE as our error metric again. Compute MSE on training data ($x_{train},y_{train}$) and test data ($x_{test}, y_{test}$) for each polynomial regression model (orders 0-5). Since you already developed code in T4 Exercise 4 for evaluating fit polynomials, we have ported that here into the function ``evaluate_poly_reg`` for your use.\n",
        "\n",
        "*Please think about after completing exercise before reading the following text! Do you think the order 0 model has high or low bias? High or low variance? How about the order 5 model?*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DaQfu1EdcRYc"
      },
      "source": [
        "def evaluate_poly_reg(x, y, theta_hats, max_order):\n",
        "    \"\"\" Evaluates MSE of polynomial regression models on data\n",
        "\n",
        "    Args:\n",
        "      x (ndarray): input vector of shape (n_samples)\n",
        "      y (ndarray): vector of measurements of shape (n_samples)\n",
        "      theta_hats (dict):  fitted weights for each polynomial model (dict key is order)\n",
        "      max_order (scalar): max order of polynomial fit\n",
        "\n",
        "    Returns\n",
        "      (ndarray): mean squared error for each order, shape (max_order)\n",
        "    \"\"\"\n",
        "\n",
        "    mse = np.zeros((max_order + 1))\n",
        "    for order in range(0, max_order + 1):\n",
        "      X_design = make_design_matrix(x, order)\n",
        "      y_hat = np.dot(X_design, theta_hats[order])\n",
        "      residuals = y - y_hat\n",
        "      mse[order] = np.mean(residuals ** 2)\n",
        "\n",
        "    return mse"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uIZCK0THcRYc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "28e69983-685f-4fc8-cff4-8280e78caffe"
      },
      "source": [
        "def compute_mse(x_train,x_test,y_train,y_test,theta_hats,max_order):\n",
        "  \"\"\"Compute MSE on training data and test data.\n",
        "\n",
        "  Args:\n",
        "    x_train(ndarray): training data input vector of shape (n_samples)\n",
        "    x_test(ndarray): test data input vector of shape (n_samples)\n",
        "    y_train(ndarray): training vector of measurements of shape (n_samples)\n",
        "    y_test(ndarray): test vector of measurements of shape (n_samples)\n",
        "    theta_hats(dict): fitted weights for each polynomial model (dict key is order)\n",
        "    max_order (scalar): max order of polynomial fit\n",
        "\n",
        "  Returns:\n",
        "    ndarray, ndarray: MSE error on training data and test data for each order\n",
        "  \"\"\"\n",
        "\n",
        "  #######################################################\n",
        "  ## TODO for students: calculate mse error for both sets\n",
        "  ## Hint: look back at tutorial 5 where we calculated MSE\n",
        "  # Fill out function and remove\n",
        "  #raise NotImplementedError(\"Student excercise: calculate mse for train and test set\")\n",
        "  #######################################################\n",
        "\n",
        "  mse_train = evaluate_poly_reg(x_train, y_train, theta_hats, max_order)\n",
        "  mse_test = evaluate_poly_reg(x_test, y_test, theta_hats, max_order)\n",
        "\n",
        "  return mse_train, mse_test\n",
        "\n",
        "\n",
        "#Uncomment below to test your function\n",
        "mse_train, mse_test = compute_mse(x_train, x_test, y_train, y_test, theta_hats, max_order)\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "width = .35\n",
        "\n",
        "ax.bar(np.arange(max_order + 1) - width / 2, mse_train, width, label=\"train MSE\")\n",
        "ax.bar(np.arange(max_order + 1) + width / 2, mse_test , width, label=\"test MSE\")\n",
        "\n",
        "ax.legend()\n",
        "ax.set(xlabel='Polynomial order', ylabel='MSE', title ='Comparing polynomial fits');"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z5xDhDQm6zDS"
      },
      "source": [
        "---\n",
        "# Congratulations!\n",
        "\n",
        "You have reached to the end of the tutorial. Yes, that was it. However, model fitting isn't limited to Linear Regression. Its very broad and seemingly endless. There are times when one model works in a particular scenario but fails for the other one, we have to tweak the parameters, optimize our algorithm and various other things to reach to our desired accuracy in predictions. <br> So, this was just an overview of how model fits into the input dataset, learns some parameters by itself and predict even for unseen inputs.\\\n",
        "Hope, you enjoyed and learnt from this!"
      ]
    }
  ]
}