NB_CII-ML_is_difficult.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Notebook 1: Why is Machine Learning difficult?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview \n",
    "\n",
    "In this notebook, we will get our hands dirty trying to gain intuition about why machine learning is difficult. \n",
    "\n",
    "Our task is going to be a simple one, fitting data with polynomials of different order. Formally, this goes under the name of polynomial regression. Here we will do a series of exercises that are intended to give the reader intuition about the major challenges that any machine learning algorithm faces.\n",
    "\n",
    "## Learning Goal\n",
    "\n",
    "We will explore how our ability to predict depends on the number of data points we have, the \"noise\" in the data, and our knowledge about relevant features. The goal is to build intuition about why prediction is difficult and discuss general strategies for overcoming these difficulties.\n",
    "\n",
    "\n",
    "## The Prediction Problem\n",
    "\n",
    "Consider a probabilistic process that gives rise to labeled data $(x,y)$. The data is generated by drawing samples from the equation\n",
    "$$\n",
    "    y_i= f(x_i) + \\eta_i,\n",
    "$$\n",
    "where $f(x_i)$ is some fixed, but (possibly unknown) function, and $\\eta_i$ is a Gaussian, uncorrelate noise variable such that\n",
    "$$\n",
    "\\langle \\eta_i \\rangle=0 \\\\\n",
    "\\langle \\eta_i \\eta_j \\rangle = \\delta_{ij} \\sigma\n",
    "$$\n",
    "We will refer to the $f(x_i)$ as the **true features** used to generate the data. \n",
    "\n",
    "To make prediction, we will consider a family of functions $g_\\alpha(x;\\theta_\\alpha)$ that depend on some parameters $\\theta_\\alpha$. These functions respresent the **model class** that we are using to try to model the data and make predictions. The $g_\\alpha(x;\\theta_\\alpha)$ encode the class of **features** we are using to represent the data.\n",
    "\n",
    "To learn the parameters $\\boldsymbol{\\theta}$, we will train our models on a **training data set** and then test the effectiveness of the model on a <i>different</i> dataset, the **test data set**. The reason we must divide our data into a training and test dataset is that the point of machine learning is to make accurate predictions about new data we have not seen. As we will see below, models that give the best fit to the training data do not necessarily make the best predictions on the test data. This will be a running theme that we will encounter repeatedly in machine learning.  \n",
    "\n",
    "\n",
    "For the remainder of the notebook, we will focus on polynomial regression. Our task is to model the data with polynomials and make predictions about the new data that we have not seen.\n",
    "We will consider two qualitatively distinct situations: \n",
    "<ul>\n",
    "<li> In the first case, the process that generates the underlying data is in the model class we are using to make predictions. For polynomial regression, this means that the functions $f(x_i)$ are themselves polynomials.\n",
    "<li>In the second case, our data lies outside our model class. In the case of polynomial regression, this could correspond to the case where the $f(x_i)$ is a 10-th order polynomial but $g_\\alpha(x;\\theta_\\alpha)$ are polynomials of order 1 or 3.\n",
    "</ul>\n",
    "\n",
    "In the exercises and discussion we consider 3 model classes:\n",
    "<ul>\n",
    "<li> the case where the $g_\\alpha(x;\\theta_\\alpha)$ are all polynomials up to order 1 (linear models),\n",
    "<li> the case where the $g_\\alpha(x;\\theta_\\alpha)$ are all polynomials up to order 3,\n",
    "<li> the case where the $g_\\alpha(x;\\theta_\\alpha)$ are all polynomials up to order 10.\n",
    "</ul>\n",
    "\n",
    "To measure our ability to predict, we will learn our parameters by fitting our training dataset and then making predictions on our test data set. One common measure of predictive  performance of our algorithm is to compare the predictions,$\\{y_j^\\mathrm{pred}\\}$, to the true values $\\{y_j\\}$. A commonly employed measure for this is the sum of the mean square-error (MSE) on the test set:\n",
    "$$\n",
    "MSE= \\frac{1}{N_\\mathrm{test}}\\sum_{j=1}^{N_\\mathrm{test}} (y_j^\\mathrm{pred}-y_j)^2\n",
    "$$\n",
    "We will return to this in later notebooks. For now, we will try to get a qualitative picture by examining plots on test and training data.\n",
    "\n",
    "## Fitting vs. predicting when the data is in the model class\n",
    "\n",
    "\n",
    "We start by considering the case:\n",
    "$$\n",
    "f(x)=2x.\n",
    "$$\n",
    "Then the data is clearly generated by a model that is contained within all three model classes we are using to make predictions (linear models, third order polynomials, and tenth order polynomials). \n",
    "\n",
    "\n",
    "Run the code for the following cases:\n",
    "<ul> \n",
    "<li> For $f(x)=2x$, $N_{\\mathrm{train}}=10$ and $\\sigma=0$ (noiseless case), train the three classes of models (linear, third-order polynomial, and tenth order polynomial) for a training set when $x_i  \\in [0,1]$. Make graphs comparing fits for different order of polynomials. Which model fits the data the best?   \n",
    "<br><span style=\"color:blue\">  \n",
    "All three models provide a good fit to the data.\n",
    "</spin>\n",
    "    \n",
    "![NB1_1.png](https://raw.githubusercontent.com/DBustamante98/ML/main/NB1_1.png)        \n",
    "\n",
    "<li> Do you think that the data that has the least error on the training set will also make the best predictions? Why or why not? Can you try to discuss and formalize your intuition? What can go right and what can go wrong?\n",
    "<br><span style=\"color:blue\">  \n",
    "Noise or random fluctuations in the training data is picked up and learned as concepts by the model. Overfitting happens when a model learns the detail and noise in the training data to the extent that it negatively impacts the performance of the model on new data.    \n",
    "</spin> \n",
    "<li>Check your answer by seeing how well your fits predict newly generated test data (including on data outside the range you fit on, for example $x \\in [0,1.2]$) using the code below. How well do you do on points in the range of $x$ where you trained the model? How about points outside the original training data set? \n",
    "<br><span style=\"color:blue\">    \n",
    "Without noise, the predictions are good for new inputs outside the training range.\n",
    "</spin> \n",
    " \n",
    "![NB1_2.png](https://github.com/DBustamante98/ML/blob/main/NB1_2.png?raw=true)        \n",
    "\n",
    "<li>Repeat the exercises above for $f(x)=2x$, $N_{\\mathrm{train}}=10$, and $\\sigma=1$. What changes?\n",
    "<br><span style=\"color:blue\">      \n",
    "When we train a model with small datasets that have noise, the model generally memorizes the training dataset instead of learning general features of our data. For this reason, the model will perform well on the training set and poor on new data.  \n",
    "<br><br>Simple models (like the linear function) cannot represent complicated patterns in the data, so they are forced to ignore the fluctuations and to focus on the larger trends.\n",
    "</spin>  \n",
    "    \n",
    "![NB1_3.png](https://github.com/DBustamante98/ML/blob/main/NB1_3.png?raw=true)        \n",
    "\n",
    "<li>Repeat the exercises above for $f(x)=2x$, $N_{\\mathrm{train}}=100$, and $\\sigma=1$. What changes?\n",
    "<br><span style=\"color:blue\">          \n",
    "Increasing the amount of data in the training set increases the data-to-noise ratio, reducing overfitting.\n",
    "</spin>  \n",
    "    \n",
    "![NB1_4.png](https://github.com/DBustamante98/ML/blob/main/NB1_4.png?raw=true)         \n",
    "    \n",
    "<li> Summarize what you have learned about the relationship between model complexity (number of parameters), goodness of fit on training data, and the ability to predict well.\n",
    "<br><span style=\"color:blue\">          \n",
    "Using a complex model can result in overfitting. Increasing a model’s complexity (the number of fitting parameters)\n",
    "will usually yield better results on the training data. However, when the training data size is small and the data are\n",
    "noisy, the result is overfitting and this can substantially degrade the predictive performance of the model.\n",
    "</spin>  \n",
    "\n",
    "</ul>\n",
    "\n",
    "\n",
    "## Fitting vs. predicting when the data is not in the model class\n",
    "Thus far, we have considered the case where the data is generated using a model contained in the model class. Now consider  $f(x)=2x-10x^5+15x^{10}$. *Notice that the for linear and third-order polynomial the true model $f(x)$ is not contained in model class $g_\\alpha(x)$* .\n",
    "\n",
    "<ul>\n",
    "<li> Repeat the exercises above fitting and predicting for $f(x)=2x-10x^5+15x^{10}$ for $N_{\\mathrm{train}}=10,100$ and $\\sigma=0,1$. Record your observations.\n",
    "<br><span style=\"color:blue\">              \n",
    "In the noiseless case, the tenth order model performs the best for data generated from a tenth order polynomial. In the presence of noise, the tenth order polynomial can capture both the global trends and noise-generated patterns at the same time (overfitting). In this case, we can use less expressive models with fewer parameters, or we can collect more data so that the likelihood that the noise appears patterned decreases. When we increase the size of the training dataset, the tenth order polynomial gives both the best fits and the most predictive power.\n",
    "</spin> \n",
    "    \n",
    "![NB1_5.png](https://github.com/DBustamante98/ML/blob/main/NB1_5.png?raw=true)             \n",
    "    \n",
    "<li> Do better fits lead to better predictions?\n",
    "<br><span style=\"color:blue\">                  \n",
    "When the training data size is too small and does not contain enough data samples to accurately represent all possible input data values, then we have overfitting. In this case, the machine learning model gives accurate predictions for training data but not for new data. We can prevent overfitting by diversifying and scaling the training data set.\n",
    "</spin>    \n",
    "<li> What is the relationship between the true model for generating the data and the model class that has the most predictive power? How is this related to the model complexity? How does this depend on the number of data points $N_{\\mathrm{train}}$ and $\\sigma$?\n",
    "<br><span style=\"color:blue\">                     \n",
    "When the amount of training data is limited, one can often get better predictive performance by using a less expressive model (a lower order polynomial) rather than the more complex model (the tenth order polynomial). Even though the correct model is guaranteed to have better predictive performance for an infinite amount of training data (less bias), the training errors stemming from finite-size sampling (variance) can cause simpler models to outperform the\n",
    "more complex model when sampling is limited.    \n",
    "</spin>    \n",
    "    \n",
    "<li> Summarize what you think you learned about the relationship of knowing the true model class and predictive power.\n",
    "<br><span style=\"color:blue\">                     \n",
    "When the model is very complex, the gap between training and generalization/test error is very high (overfitting).\n",
    "When the model is very simple, the model will have a sufficiently high training error (underfitting).\n",
    "</spin> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When the model memorizes the noise and fits too closely to the training set, the model becomes “overfitted,” and it is unable to generalize well to new data.\n",
    "\n",
    "A small dataset provides a poor description of our problem and it may result in a difficult problem to learn.\n",
    "\n",
    "**Advantages of polynomial regression**\n",
    "You can model non-linear relationships between variables.\n",
    "There is a large range of different functions that you can use for fitting.\n",
    "Good for exploration purposes: you can test for the presence of curvature and its inflections.\n",
    "\n",
    "**Disadvantages of polynomial regression**\n",
    "Even a single outlier in the data plot can seriously mess up the results.\n",
    "PR models are prone to overfitting. If enough parameters are used, you can fit anything. \n",
    "As a consequence of the previous, PR models might not generalize well outside of the data used."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training the models:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#This is Python Notebook to walk through polynomial regression examples\n",
    "#We will use this to think about regression\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "from sklearn import datasets, linear_model\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "from matplotlib import pyplot as plt, rcParams\n",
    "fig = plt.figure(figsize=(8, 6))\n",
    "\n",
    "# The Training Data\n",
    "N_train=100\n",
    "sigma_train=1\n",
    "\n",
    "# Train on integers\n",
    "x=np.linspace(0.01,0.95,N_train)\n",
    "# Draw Gaussian random noise\n",
    "s = sigma_train*np.random.randn(N_train)\n",
    "\n",
    "#linear\n",
    "y=2*x+s\n",
    "\n",
    "# Tenth Order\n",
    "y=2*x-10*x**5+15*x**10+s\n",
    "\n",
    "p1=plt.plot(x, y, \"o\", ms=8, alpha=0.5, label='Training')\n",
    "\n",
    "# Linear Regression : create linear regression object\n",
    "clf = linear_model.LinearRegression()\n",
    "\n",
    "# Train the model using the training set\n",
    "# Note: sklearn requires a design matrix of shape (N_train, N_features). Thus we reshape x to (N_train, 1):\n",
    "clf.fit(x[:, np.newaxis], y)\n",
    "\n",
    "# Use fitted linear model to predict the y value:\n",
    "xplot=np.linspace(0.02,0.98,200) # grid of points, some are in the training set, some are not\n",
    "linear_plot=plt.plot(xplot, clf.predict(xplot[:, np.newaxis]), label='Linear')\n",
    "\n",
    "# Polynomial Regression\n",
    "poly3 = PolynomialFeatures(degree=3)\n",
    "# Construct polynomial features\n",
    "X = poly3.fit_transform(x[:,np.newaxis])\n",
    "clf3 = linear_model.LinearRegression()\n",
    "clf3.fit(X,y)\n",
    "\n",
    "\n",
    "Xplot=poly3.fit_transform(xplot[:,np.newaxis])\n",
    "poly3_plot=plt.plot(xplot, clf3.predict(Xplot), label='Poly 3')\n",
    "\n",
    "# Fifth order polynomial in case you want to try it out\n",
    "#poly5 = PolynomialFeatures(degree=5)\n",
    "#X = poly5.fit_transform(x[:,np.newaxis])\n",
    "#clf5 = linear_model.LinearRegression()\n",
    "#clf5.fit(X,y)\n",
    "\n",
    "#Xplot=poly5.fit_transform(xplot[:,np.newaxis])\n",
    "#plt.plot(xplot, clf5.predict(Xplot), 'r--',linewidth=1)\n",
    "\n",
    "poly10 = PolynomialFeatures(degree=10)\n",
    "X = poly10.fit_transform(x[:,np.newaxis])\n",
    "clf10 = linear_model.LinearRegression()\n",
    "clf10.fit(X,y)\n",
    "\n",
    "Xplot=poly10.fit_transform(xplot[:,np.newaxis])\n",
    "poly10_plot=plt.plot(xplot, clf10.predict(Xplot), label='Poly 10')\n",
    "\n",
    "plt.legend(loc='best')\n",
    "plt.ylim([-7,7])\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "Title=\"N=%i, $\\sigma=%.2f$\"%(N_train,sigma_train)\n",
    "plt.title(Title+\" (train)\")\n",
    "\n",
    "\n",
    "# Linear Filename\n",
    "filename_train=\"train-linear_N=%i_noise=%.2f.pdf\"%(N_train, sigma_train)\n",
    "\n",
    "# Tenth Order Filename\n",
    "#filename_train=\"train-o10_N=%i_noise=%.2f.pdf\"%(N_train, sigma_train)\n",
    "\n",
    "# Saving figure and showing results\n",
    "plt.savefig(filename_train)\n",
    "plt.grid()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Testing the fitted models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "format": "tab",
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate Test Data\n",
    "%matplotlib inline\n",
    "# Number of test data\n",
    "N_test=100\n",
    "sigma_test=sigma_train\n",
    "\n",
    "# Generate random grid points (x) in the interval [0, max_x]:\n",
    "# Note some points will be drawn outside the training interval\n",
    "max_x=1.2\n",
    "x_test=max_x*np.random.random(N_test)\n",
    "\n",
    "# Draw random Gaussian noise\n",
    "s_test = sigma_test*np.random.randn(N_test)\n",
    "\n",
    "# Linear\n",
    "y_test=2*x_test+s_test\n",
    "# Tenth order\n",
    "y_test=2*x_test-10*x_test**5+15*x_test**10+s_test\n",
    "\n",
    "# Make design matrices for prediction\n",
    "x_plot=np.linspace(0,max_x, 200)\n",
    "X3 = poly3.fit_transform(x_plot[:,np.newaxis])\n",
    "X10 = poly10.fit_transform(x_plot[:,np.newaxis])\n",
    "\n",
    "############## PLOTTING RESULTS ##########\n",
    "\n",
    "fig = plt.figure(figsize=(8, 6))\n",
    "\n",
    "p1=plt.plot(x_test, y_test, 'o', ms=10, alpha=0.5, label='test data')\n",
    "p2=plt.plot(x_plot,clf.predict(x_plot[:,np.newaxis]), lw=2, label='linear')\n",
    "p3=plt.plot(x_plot,clf3.predict(X3), lw=2, label='3rd order')\n",
    "p10=plt.plot(x_plot,clf10.predict(X10), lw=2, label='10th order')\n",
    "\n",
    "\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.legend(loc='best')\n",
    "Title=\"N=%i, $\\sigma=%.2f$\"%(N_test,sigma_test)\n",
    "plt.title(Title+\" (pred.)\")\n",
    "plt.tight_layout()\n",
    "plt.ylim((-6,12))\n",
    "\n",
    "# Linear Filename\n",
    "filename_test=\"pred-linear_N=%i_noise=%.2f.pdf\"%(N_test, sigma_test)\n",
    "\n",
    "# Tenth Order Filename\n",
    "#filename_test=Title+\"pred-o10.pdf\"\n",
    "\n",
    "# Saving figure and showing results\n",
    "plt.savefig(filename_test)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}