{ "cells": [ { "cell_type": "markdown", "id": "1dc8c8c2", "metadata": {}, "source": [ "## Bias, Variance and Automatic Differentiation" ] }, { "cell_type": "markdown", "id": "4ed5786d", "metadata": {}, "source": [ "Author: Omar Al-Ghattas" ] }, { "cell_type": "markdown", "id": "9904aaac", "metadata": {}, "source": [ "## Introduction" ] }, { "cell_type": "markdown", "id": "0dbf3c80", "metadata": {}, "source": [ "In this lab we will continue our discussion of bias and variance through a detailed example using simulated data. We will then cover the basics of automatic differentiation and `PyTorch`, and explore how these ideas can be used to solve problems in machine learning." ] }, { "cell_type": "markdown", "id": "52b3fc7a", "metadata": {}, "source": [ "### Acknowledgements:\n", "Autograd Theory:\n", "\n", " 1. https://people.cs.umass.edu/~domke/courses/sml2011/08autodiff_nnets.pdf\n", " 2. Mathematics for Machine Learning by Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong." ] }, { "cell_type": "markdown", "id": "ca6e03ec", "metadata": {}, "source": [ "## Bias-Variance Decomposition\n", "\n", "We first explore the concepts of bias and variance, as well as the idea of a bias-variance decomposition. We begin with a short mathematical explanation of bias and variance, and then reinforce the theory with code." ] }, { "cell_type": "markdown", "id": "c3335edd", "metadata": {}, "source": [ "We begin by discussing the Bias-Variance decomposition, a central theme in Statistics and Machine Learning. Assume that we are interested in estimating some population parameter $\\theta$, and we have access to a finite dataset $D = \\{X_1,\\dots, X_n\\}$, which we assume is independently sampled. To give a concrete example, suppose we are interested in estimating the average WAM of students in COMP9417, but we only have access to the WAM of a small subset of 22 randomly sampled students. The population here is all students in the course, and we must infer information about the true mean using only information about a small subset. \n", "\n", "When $\\theta$ denotes the population mean, one standard estimator to use is the sample-mean:\n", "\n", "$$\n", "\\hat{\\theta} = \\frac{1}{n} \\sum_{i=1}^n X_i.\n", "$$\n", "\n", "However, this is only one estimator, and we could use others, for example, the sample median:\n", "\n", "$$\n", "\\tilde{\\theta}=\\text{median}(X_1,\\dots,X_n)\n", "$$\n", "\n", "or, for a silly example, we could simply choose to estimate $\\theta$ by the second datapoint\n", "\n", "$$\n", "\\dot{\\theta} = X_2.\n", "$$\n", "\n", "These are all valid estimators of $\\theta$, but of course some are better than others (obviously $\\dot{\\theta}$ will be a useless estimator in almost all examples. Bias and Variance of estimators are two metrics we may use to quantify how good an estimator actually is. " ] }, { "cell_type": "markdown", "id": "6682cf6b", "metadata": {}, "source": [ "### Bias\n", "\n", "We first start with the mathematical definition and then explain the intuition behind that definition. Given an estimator $\\hat{\\theta}$ for population parameter $\\theta$, we define the bias of $\\hat{\\theta}$ as\n", "\n", "$$\n", "\\text{Bias}(\\hat{\\theta}) = \\mathbb{E}[\\hat{\\theta}] - \\theta,\n", "$$\n", "\n", "where $\\mathbb{E}$ denotes expectation. The bias simply measures how far away the expected value of our estimator is from the truth. An estimator with zero bias is called an unbiased estimator. All else equal, an unbiased estimator is better than a biased estimator." ] }, { "cell_type": "markdown", "id": "9c0f97c1", "metadata": {}, "source": [ "### Variance\n", "\n", "The variance of an estimator $\\hat{\\theta}$, is denoted by $\\text{Var}(\\hat{\\theta})$ and is defined in the usual way\n", "\n", "$$\n", "\\text{Var}(\\hat{\\theta}) = \\mathbb{E} [ ( \\hat{\\theta} - \\mathbb{E}[\\hat{\\theta} ] )^2]\n", "$$" ] }, { "cell_type": "markdown", "id": "589d1762", "metadata": {}, "source": [ "### Interpretation - An important point\n", "An important question arises here: what does it mean to take an expectation (or variance) of an estimator $\\hat{\\theta}$? How do we compute these values? For the purpose of this lab, we will side-step the proper mathematical definitions and try to answer this question in a more intuitive sense. We can think of our dataset $D$ as being just one of infinitely many datasets. Let's imagine that we have access to a black-box $B$ that we can query datasets from. We label these datasets: $D_1,D_2,\\dots, D_{\\infty}$, and for simplicity we assume that each dataset consists of the same number $n$ of samples. For clarity, we have:\n", "\n", "\\begin{align*}\n", "D_1 &= \\{ X^{(1)}_1, X^{(1)}_2,\\dots,X^{(1)}_n \\} \\\\\n", "D_2 &= \\{ X^{(2)}_1, X^{(2)}_2,\\dots,X^{(2)}_n\\}\\\\\n", "D_3 &= \\{ X^{(3)}_1, X^{(3)}_2,\\dots,X^{(3)}_n\\}\\\\\n", "& \\vdots\n", "\\end{align*}\n", "\n", "Now, assume that we have chosen an estimator $\\hat{\\theta}$. This estimator is a function of the dataset, so for each dataset, we can compute a new estimate. For example, if we wish to use the sample mean, then our estimate for each dataset would just be the sample-mean of each dataset:\n", "\n", "\\begin{align*}\n", "\\hat{\\theta}_1 &= \\overline{X}_1 = \\frac{1}{n} \\sum_{i=1}^n X_i^{(1)}\\\\\n", "\\hat{\\theta}_2 &= \\overline{X}_2 = \\frac{1}{n} \\sum_{i=1}^n X_i^{(2)}\\\\\n", "& \\vdots\n", "\\end{align*}\n", "\n", "and so on. Now, we can think of the quantity $\\mathbb{E}[\\hat{\\theta}]$ as being the average value of $\\hat{\\theta}$ over an infinite number of datasets. Similarly, we can think of $\\text{Var}(\\hat{\\theta})$ as the variance of $\\hat{\\theta}$ over an infinite number of datasets. \n", "\n", "Note that this is a purely theoretical construction because we do not have access to a black-box $B$ that allows us to generate multiple datasets (in fact we will usually only have access to a single dataset), and secondly even if we did have access to $B$, we cannot sample an infinite number of datasets. This theoretical construction does however help us understand the benefits of different estimators and has led to the proposal of many important algorithms in machine learning that have had great empirical success." ] }, { "cell_type": "markdown", "id": "59c057e2", "metadata": {}, "source": [ "### Bias-Variance for Learning Functions\n", "Up to this point, you should have understood the basic concepts underlying the bias-variance decomposition. We now tie this back into the machine learning framework. In a general (supervised) learning problem, we have access to a dataset $D$ which consists not only of feature vectors $X$, but also response values $y$, so that \n", "\n", "$$\n", "D = \\{(x_1,y_1),\\dots,(x_n, y_n)\\}.\n", "$$\n", "\n", "We assume that there exists some true (but unobservable) function $f$ that takes as input a feature vector $X$ and outputs a response $y$. We will also assume that the observed responses are corrupted by some additive noise. In other words, our assumption is that:\n", "\n", "$$\n", "y = f(x) + \\epsilon, \\qquad \\epsilon \\sim (0,\\sigma^2),\n", "$$\n", "\n", "where the notation $\\epsilon \\sim (0,\\sigma^2)$ means that $\\epsilon$ is a random variable with zero mean and variance $\\sigma^2$. One way to think about $\\epsilon$ is that it represents measurement error. For example, if we are measuring temperature on a given day using a thermometer, then our measurement might consist of the `true` temperature, $f(x)$, plus some noise due to the usage of a cheap theormometer. The most common assumption is that $\\epsilon$ is normally distributed, so we write: $\\epsilon \\sim N(0,\\sigma^2)$.\n", "\n", "Now, the goal of learning is to use the data $D$ to find an estimate of $f$, which we call $\\hat{f}$, so that $f$ and $\\hat{f}$ are as close as possible in some sense. One common way to do this is to learn a $\\hat{f}$ that minimizes the Mean Squared Error (MSE) between $y$ and $\\hat{f}$. So far in this course, we have seen many ways of computing such an estimate $\\hat{f}$, for example, linear regression, SVMs, Neural Networks, etc. It turns out that regardless of how you choose to construct your estimate, there exists a decomposition of the MSE (the expected squared error of $\\hat{f}$ on a previously unseen example, i.e. test MSE), called the Bias Variance Decomposition:\n", "\n", "$$\n", "\\mathbb{E} [(y- \\hat{f}(x))^2] = \\left ( \\text{Bias}(\\hat{f}(x)) \\right)^2 + \\text{Var}(\\hat{f}(x)) + \\sigma^2,\n", "$$\n", "\n", "where as before, we have \n", "\n", "$$\n", "\\text{Bias}(\\hat{f}(x)) = \\mathbb{E} [\\hat{f}(x)] - f(x).\n", "$$\n", "\n", "In other words, the MSE of $\\hat{f}$ may be decomposed into a sum of three terms:\n", "\n", "1. (Squared) Bias: As discussed earlier, bias captures how far an estimate is from its target. Intuitively, simple algorithms (i.e. those with few parameters, such as linear models) will have high bias, since the 'true' function $f$ is rarely linear). We will see that models with low flexibility (linear models) tend to have high bias, and those with high flexibility (neural nets will have low bias).\n", "\n", "2. Variance: this captures how sensitive the learning method is to changes in the dataset. i.e. given two datasets $D_1$, $D_2$, how different are the corresonding estimates $\\hat{f}_1(x)$ and $\\hat{f}_2(x)$? We will see that flexible learning algorithms, such as neural nets, will have high variance. Intuitively, since neural nets are so powerful, they can fit pretty much any decision surface, so estimates on different datasets can vary greatly.\n", "\n", "3. $\\sigma^2$: this is called the irreducible error, and since our responses contain noise, this is the error we have to live with in our predictions, regardless of the learning algorithm we use.\n", "\n", "It is important to understand why these factors contribute to the overall test error. A learning algorithm with high bias is unlikely to be able to fit the true function, and so will do poorly when asked to make a prediction on a new test point (underfitting). A learning algorithm with high variance will have a lot of flexibility, and so will fit the training data very well, but this does not necessarily mean it will be able to generalise well (overfitting).\n", "\n", "It turns out that there is a trade-off between bias and variance. That is, learning algorithms that have low bias will tend to have high variance, and vice versa. In machine learning, we wish to find models that minimise MSE, and so we have to choose models that achieve the right balance between these two competing criteria." ] }, { "cell_type": "markdown", "id": "fcb92533", "metadata": {}, "source": [ "### Illustrating the Bias-Variance Decomposition\n", "In order to illustrate these concepts and hopefully make them more understandable, we will now work through an extended example in code. The idea is to assume we have access to the blackbox $B$, from which we will generate multiple datasets from, and build models of increasing complexity from. To start with, consider the function:\n", "\n", "$$\n", "f(x) = 0.001 x^3\n", "$$\n", "\n", "We next write a function to sample noisy examples from this function, with noise taken to be Normally distributed with mean zero and standard deviation $\\sigma=0.1$. We will assume that the input values $x$ are uniformly distributed from $x=1$ to $x=10$, and this choice is completely arbitrary." ] }, { "cell_type": "code", "execution_count": 1, "id": "2a45b3fe", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from sklearn.linear_model import LinearRegression\n", "from sklearn.preprocessing import PolynomialFeatures" ] }, { "cell_type": "markdown", "id": "896e5bab", "metadata": {}, "source": [ "\n", " \n", "#### Exercise: \n", "Code up the true function and name this implementation `f`. Then define another function called `f_sampler(f, n, sigma)` that:\n", "1. generates $n$ random uniform $(0,10)$ evaluation point values, called $x_1,\\dots, x_n$\n", "2. generates $n$ random normal $(0,\\sigma^2)$ noise variables, called $\\epsilon_1,\\dots, \\epsilon_n$\n", "3. generate $n$ noisy observations from $f$, called $y_1,\\dots,y_n$ where $y_i = f(x_i) + \\epsilon_i$.\n", "\n", "Finally, plot the true function in blue, and a scatter of the $n$ points in red on the same plot." ] }, { "cell_type": "code", "execution_count": 1, "id": "7949728d", "metadata": {}, "outputs": [ { "ename": "SyntaxError", "evalue": "invalid syntax (1132108883.py, line 6)", "output_type": "error", "traceback": [ "\u001b[0;36m Input \u001b[0;32mIn [1]\u001b[0;36m\u001b[0m\n\u001b[0;31m xvals = ###\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n" ] } ], "source": [ "# true function\n", "f = lambda x: 0.001 * x**3\n", "\n", "def f_sampler(f, n=100, sigma=0.1): \n", " # sample points from function f with Gaussian noise (0,sigma**2)\n", " xvals = ###\n", " yvals = ###\n", " \n", " # build dataset D\n", " D = np.zeros(shape=(n, 2))\n", " D[:,0] = xvals; D[:,1] = yvals; \n", " \n", " return D" ] }, { "cell_type": "code", "execution_count": 3, "id": "8c6b11aa", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fsamples = f_sampler(f, 100, sigma=0.2)\n", "\n", "xx = np.linspace(1,10,1000)\n", "plt.plot(xx, f(xx), label=\"truth\")\n", "plt.scatter(*fsamples.T, color=\"red\", label=\"samples\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "f23d00af", "metadata": {}, "source": [ "We can generate an infinite number of datasets (we have access to the blackbox) in this way. Let's consider 9 different datasets, call them $D_1,\\dots,D_9$. Note that they are all generated from the same $f(x)$, which is the blue function in the plots, but due to the randomness in the noise, each of the datasets is different. In a learning problem, we will only have access to the dataset of the form $(x_i, y_i), i=1,\\dots, n$ and the goal is to try to recover $f$ from this data. We usually denote our estimate of $f$ by putting a hat on the parameter of interest, i.e. $\\hat{f}$. \n", "\n", "To estimate $f$, we usually try to put assumptions on the form of the unkown $f$. In the linear regression case for example, we make the simplifying assumption that $f(x)$ is a linear function." ] }, { "cell_type": "code", "execution_count": 4, "id": "35c8af90", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(3,3, figsize=(10,10))\n", "np.random.seed(10)\n", "for i, ax in enumerate(ax.flat):\n", " ax.plot(xx, f(xx), label=\"truth\")\n", " fsamples = f_sampler(f, 25, sigma=0.2)\n", " ax.scatter(*fsamples.T, color=\"red\", label=\"samples\")\n", " ax.set_title(f\"$D_{i+1}$\")\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "cf68a254", "metadata": {}, "source": [ "To understand bias and variance, the idea now will be to fit a model to each of the datasets, and see how the fits vary from dataset to dataset. A simple model to begin with is linear regression (with a single feature $x$). This model has high bias because it has a very strict assumption on the shape of the model, regardless of the data. It has low variance because models fit on different datasets will not vary too much. We can see this empirically for the 9 generated datasets, and we will plot the fitted models in green on each plot in the grid." ] }, { "cell_type": "code", "execution_count": 5, "id": "00b344dc", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(3,3, figsize=(10,10))\n", "np.random.seed(10)\n", "\n", "mods = np.zeros((9, 2)) # store models\n", "for i, ax in enumerate(ax.flat):\n", " ax.plot(xx, f(xx), label=\"truth\")\n", " fsamples = f_sampler(f, 25, sigma=0.2)\n", " ax.scatter(*fsamples.T, color=\"red\", label=\"samples\")\n", " ax.set_title(f\"$D_{i+1}$\")\n", " \n", " # build model\n", " X = fsamples[:,0].reshape(-1,1)\n", " y = fsamples[:,1].reshape(-1,1)\n", " mod = LinearRegression().fit(X, y)\n", " lr = lambda x: mod.intercept_[0] + mod.coef_[0]*x\n", " # additonal dtype argument here avoids a depracation warning\n", " mods[i] = np.array([mod.intercept_[0], mod.coef_[0]], dtype='object')\n", " ax.plot(xx, lr(xx), color=\"green\", label=\"$\\\\hat{f}$\")\n", " if i==1: ax.legend()\n", " \n", "fig.suptitle(\"$features: x$\", fontsize=16)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "84acbf55", "metadata": {}, "source": [ "Note that the fitted model does not vary much from dataset to dataset. Linear models with a single feature do not have much ability to fit complicated trends in the data (they must be a straight line), and so will exhibit low variance, and high bias. Let's compute these quantities for our toy example at a single point, say $x_0 = 5$. \n", "\n", "The bias is the expected value of the model at $x_0$ minus the true value of $f$ at $x_0$, i.e. $f(x_0)$. Recall that in order to compute the expected value at $x_0$, we must be able to sample an infinite number of datasets, fit a model, then average. Here we will use the average of the predictions of the 9 models at $x_0$ as a proxy. To compute variance, we compute the variance of the predictions of all 9 models at $x_0$. We can see from the plot that linear regression has high bias, and low variance. Compare this picture to the picture we looked at earlier with the bias/variance targets." ] }, { "cell_type": "code", "execution_count": 6, "id": "6cd1abe2", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x0 = 5\n", "x0_preds = np.zeros(9)\n", "plt.plot(xx, f(xx))\n", "for i in range(9):\n", " lr = lambda x: mods[i,0]+mods[i,1]*x\n", " plt.plot(xx, lr(xx), color=\"green\", alpha=0.4)\n", " \n", " x0_preds[i] = lr(x0)\n", "plt.axvline(x0, color=\"red\")\n", "plt.annotate(f'Bias Squared: {round((np.mean(x0_preds)-f(x0))**2,4)}', (6, 0.05), size=12, color='black')\n", "plt.annotate(f'Variance: {round(np.var(x0_preds),4)}', (6, -0.05), size=12, color='black')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "d2149439", "metadata": {}, "source": [ "The above plot shows the $9$ fitted models (in blue), and the true function $f$ in blue. We see that $x_0=5$, all $9$ models seem to do quite poorly as they are unable to fit the curvature in the true model. The bias here is high because the estimate is consistently far away from the truth. Note however that all $9$ models more or less predict the same value for $x_0$, and so exhibit very lower variance." ] }, { "cell_type": "markdown", "id": "948aa86c", "metadata": {}, "source": [ "We can now investigate a more complex model by adding polynomial features to the linear regression. As we add higher order terms, we will be able to fit more complicated (curvy) functions. $\\hat{y} = a + bx + cx^2$" ] }, { "cell_type": "markdown", "id": "6f9745bb", "metadata": {}, "source": [ "\n", " \n", "#### Exercise: \n", "Re-do the previous analysis, but now use both $x$ and $x^2$ when fitting the linear regression model. Create the same grid of plots as before but with your new model, and plot the bias and variance. What do you notice?\n", "\n", "Hint: see the sklearn documentation here to get a better idea of how to fit a linear model with two covariates: https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html" ] }, { "cell_type": "markdown", "id": "0f2e738a", "metadata": {}, "source": [ "\n", " \n", "#### Exercise: \n", "Add more polynomial features: $a + bx + cx^2 + dx^3+ex^4 + fx^5 + g x^6$ and re-run the experiment. Comment on your results." ] }, { "cell_type": "markdown", "id": "02851009", "metadata": {}, "source": [ "We see that as the complexity increases, so too does the variance. As we increase the complexity of the model, it has more and more flexibility to fit complex functions. The problem is that for different datasets, the models end up fitting the noise in the data. The high variance comes from the fact that for different datasets, we can get wildly different models. So there is a tradeoff here, which is known as the bias variance decomposition. If we want to reduce test error, then we want to be able to reduce the bias AND reduce the variance, but as we reduce bias sufficiently, the variance begins to increase." ] }, { "cell_type": "markdown", "id": "9312da6b", "metadata": {}, "source": [ "\n", " \n", "#### Advanced Exercise: \n", "Let's consider a more interesting function:\n", "\n", "$$\n", "f(x) = 0.00002 x^3 + 0.2 \\cos(x^{1.2}).\n", "$$\n", "\n", "1. Generate 80 datasets from $f$ using $\\sigma=0.1$ each of size $n=100$.\n", "2. For each dataset, fit 9 models: the first model being a linear regression with degree 1, the second having both $x$ and $x^2$, and the final model having $x,\\dots, x^9$ as features.\n", "3. Create a 3x3 grid of plots, each sub-plot corresponding to a given degree (1-9). On each sub-plot, plot the true function in red, the 80 fitted functions in blue, and the average of the 80 fitted functions in yellow.\n", "4. Now, using the above data, try to visualise the bias and variance at each of the points on the $x$-axis.\n", "5. Comment." ] }, { "cell_type": "markdown", "id": "eb7e8cd6", "metadata": {}, "source": [ "## Automatic Differentiation and a short intro to PyTorch\n", "\n", "As discussed in the first tutorial, numerical techniques such as gradient descent are very important in machine learning, because they allow us to solve optimisation problems on the computer. This is particularly important when a closed form solution does not exist (we cannot write down a neat solution for the problem), or when computing the explicit solution is too expensive.\n", "\n", "In this course, we will rely mainly on PyTorch when doing anything involving gradients. Pytorch is technically an `automatic differentiation (autodiff)` library, which means that it is able to compute gradients of functions numerically. PyTorch is primarily used for deep learning (which requires a form of differentiation called backpropagation), and we will see it again in later weeks (you may also want to use it for your project if doing something deep learning related).\n", "\n", "The basic idea behind automatic differentiation is to decompose a function into simpler components and then apply the chain rule in a smart way. Let us consider a simple example to demonstrate the power of autodiff.\n", "\n", "Consider the following complicated looking function:\n", "\n", "$$\n", "f(x) = \\exp (\\exp(x) + \\exp(2x)) + \\sin(\\exp(x) + \\exp(2x)).\n", "$$\n", "\n", "This looks quite complicated, but with a bit of work we can show that the derivative of $f$ is\n", "\n", "$$\n", "f'(x) = \\exp (\\exp(x) + \\exp(2x))(\\exp(x) + 2\\exp(2x)) + \\cos(\\exp(x) + \\exp(2x))(\\exp(x) + 2\\exp(2x))\n", "$$\n", "\n", "For those of you that attempted this by hand, you should see that the standard differentiation approach is somewhat wasteful, since we have the same factor $(\\exp(x) + \\exp(2x))$ in both expressions. Let's consider a more algorithmic approach. Define the following intermediate variables:\n", "\n", "\\begin{align*}\n", "a &= \\exp(x)\\\\\n", "b &= a^2\\\\\n", "c &= a+b\\\\\n", "d &= \\exp(c)\\\\\n", "e &= \\sin(c)\\\\\n", "f &= d+e\n", "\\end{align*}" ] }, { "cell_type": "markdown", "id": "43d9e416", "metadata": {}, "source": [ "This may look strange at first, but we are basically rewriting $f(x)$ as an iterative procedure. We can represent this in graph form, using a structure known as a computational graph:" ] }, { "cell_type": "markdown", "id": "06e43666", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "id": "85070e61", "metadata": {}, "source": [ "The square nodes are computation nodes, they implement the functions they are named after, and the circular nodes are variable nodes, which store the intermediate variables. Viewing $g$ in this way allows us to compute the gradient in an iterative manner. We compute the derivatives of the intermediate variables with respect to their inputs:\n", "\\begin{align*}\n", "\\frac{\\partial a}{\\partial x} &= \\exp(x)\\\\\n", "\\frac{\\partial b}{\\partial a} &= 2 a\\\\\n", "\\frac{\\partial c}{\\partial a} &= 1 = \\frac{\\partial c}{\\partial b}\\\\\n", "\\frac{\\partial d}{\\partial c} &= \\exp(c)\\\\\n", "\\frac{\\partial e}{\\partial c} &= \\cos(c)\\\\\n", "\\frac{\\partial f}{\\partial d} &= 1 = \\frac{\\partial f}{\\partial e}\n", "\\end{align*}" ] }, { "cell_type": "markdown", "id": "ac7f5bac", "metadata": {}, "source": [ "The goal is to compute $\\frac{\\partial g}{\\partial x}$, we can do so by working our way backwards through the computation graph from the output node (node $f$) to the input node (node $x$). We first introduce the following notation $\\text{child}(y)$ to denote the children of a node $y$. For example $\\text{child}(c) = \\{d, e\\}$. Then, for any node $y$ in the graph, the chain rule tells us that\n", "\n", "$$\n", "\\frac{\\partial f}{\\partial y} = \\sum_{z \\in \\text{child}(y)} \\frac{\\partial f}{\\partial z} \\frac{\\partial z}{\\partial y}\n", "$$\n", "\n", "Let's apply this formula, we already have the partial derivatives of $f$ with respect to $d,e$ from above, so we start with $c$:\n", "\n", "\\begin{align*}\n", "\\frac{\\partial f}{\\partial c} &= \\frac{\\partial f}{\\partial d}\\frac{\\partial d}{\\partial c} + \\frac{\\partial f}{\\partial e}\\frac{\\partial e}{\\partial c} = 1 \\times \\exp(c) + 1 \\times \\cos (c)\\\\\n", "\\frac{\\partial f}{\\partial b} &= \\frac{\\partial f}{\\partial c}\\frac{\\partial c}{\\partial b} =\\frac{\\partial f}{\\partial c} \\times 1\\\\\n", "\\frac{\\partial f}{\\partial a} &= \\frac{\\partial f}{\\partial b}\\frac{\\partial b}{\\partial a} + \\frac{\\partial f}{\\partial b}\\frac{\\partial b}{\\partial a} = \n", "\\frac{\\partial f}{\\partial b} \\times 2 a + \\frac{\\partial f}{\\partial c} \\times 1\\\\\n", "\\frac{\\partial f}{\\partial x} &= \\frac{\\partial f}{\\partial a} \\frac{\\partial a}{\\partial x} = \\frac{\\partial f}{\\partial a} \\times \\exp(x)\n", "\\end{align*}\n" ] }, { "cell_type": "markdown", "id": "fde9aca0", "metadata": {}, "source": [ "Observe that the computation required for calculating the derivative is proportional to the computation required to calculate the function. You can visualise this process as if each node in the computational graph stores the derivatives of itself with respect to any child nodes, then to compute the gradient of the graph, we start from the output and work our way backwards, at each step re-using gradients computed earlier in the process. As you become more familiar with backpropagation, you should see that the two concepts are identical. Let's finalise our understanding by looking at a toy example using Pytorch. " ] }, { "cell_type": "markdown", "id": "ee1d91b2", "metadata": {}, "source": [ "Since we have an excplicit form for the gradient, the goal will be to compare our explicit form to the solution computed numerically with PyTorch. Note that this is numerical differentiation, not symbolic, so the value of the gradient will change as we vary the input. We will compare the two results at the end." ] }, { "cell_type": "code", "execution_count": 16, "id": "85ea34d1", "metadata": {}, "outputs": [], "source": [ "import torch # run \"! pip3 install torch\" in jupyter if you do not have torch\n", "\n", "def func(x):\n", " t = np.exp(x) + np.exp(2*x)\n", " return np.exp(t) + np.sin(t)\n", "\n", "def grad_func(x):\n", " t1 = np.exp(x) + np.exp(2*x)\n", " t2 = np.exp(x) + 2*np.exp(2*x)\n", " return t2 * (np.exp(t1) + np.cos(t1))\n", "\n", "def sequential_func(x):\n", " inp = torch.tensor([[x]], dtype=torch.float64, requires_grad=True)\n", " a = torch.exp(inp)\n", " b = torch.pow(a, 2)\n", " c = a + b\n", " d = torch.exp(c)\n", " e = torch.sin(c)\n", " f = d + e\n", " f.backward()\n", " return inp.grad.item()" ] }, { "cell_type": "code", "execution_count": 23, "id": "207ba7b7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "explicit gradient: 59.578079470554506\n", "autograd gradient: 59.57807947055451\n" ] } ], "source": [ "x_input = 0.2\n", "print(\"explicit gradient: \", grad_func(x_input))\n", "print(\"autograd gradient: \", sequential_func(x_input))" ] }, { "cell_type": "markdown", "id": "7ac3279d", "metadata": {}, "source": [ "### Gradient Descent using PyTorch" ] }, { "cell_type": "markdown", "id": "53eb1220", "metadata": {}, "source": [ "We will now work through an extended example of performing gradient descent for a linear regression problem. We will first code this up manually using the results derived in tutorial 1. We will then sanity check our result by comparing it to the `sklearn` solution. We then implement gradient descent for the linear regression problem by hand, and finish off by re-implementing the model in `PyTorch`. Of course, for more complex models, such as deep neural nets, we will only be able to use `PyTorch` to compute answers efficiently." ] }, { "cell_type": "markdown", "id": "0144e2d0", "metadata": {}, "source": [ "First, let's generate some synthetic data for our problem:" ] }, { "cell_type": "code", "execution_count": 24, "id": "061a1111", "metadata": {}, "outputs": [], "source": [ "np.random.seed(6)\n", "\n", "n = 100 # number of samples\n", "p = 5 # dimension of problem\n", "sigma = 0.2 # noise standard deviation\n", "X = np.random.normal(0, 1, size=(n,p)) # design matrix\n", "betastar = np.random.randint(-4, 2, p) # true beta\n", "noise = np.random.normal(0, sigma, size=(n))\n", "y = X @ betastar + noise # our data" ] }, { "cell_type": "markdown", "id": "fa2b4415", "metadata": {}, "source": [ "#### Approach 1: by hand (using `NumPy`)\n", "We know from Tutorial 1 that the optimal solution (the one that minimizes MSE) is given by:\n", "\n", "$$\n", "\\hat{\\beta} = (X^TX)^{-1}X^T y.\n", "$$\n", "\n", "We can easily code this up in `NumPy` and compare it to the true $\\beta^*$." ] }, { "cell_type": "code", "execution_count": 25, "id": "83aeb201", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "beta hat using numpy: [ 0.97783793 0.01438534 -1.99131507 -3.9788805 -0.02356845]\n", " true beta: [ 1 0 -2 -4 0]\n" ] } ], "source": [ "betahat_np = np.linalg.inv(X.T @ X) @ X.T @ y\n", "print(\"beta hat using numpy: \", betahat_np)\n", "print(\" true beta: \", betastar)" ] }, { "cell_type": "markdown", "id": "2be2a1df", "metadata": {}, "source": [ "#### Approach 2: using `sklearn`\n", "In Lab 1 we have already explored the linear model object in `sklearn`." ] }, { "cell_type": "code", "execution_count": 26, "id": "69d69b0f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "beta hat using sklearn: [ 0.97783793 0.01438534 -1.99131507 -3.9788805 -0.02356845]\n", " true beta: [ 1 0 -2 -4 0]\n" ] } ], "source": [ "from sklearn.linear_model import LinearRegression\n", "betahat_sk = LinearRegression(fit_intercept=False).fit(X,y).coef_ \n", "print(\"beta hat using sklearn: \", betahat_sk)\n", "print(\" true beta: \", betastar)" ] }, { "cell_type": "markdown", "id": "4bbb6c76", "metadata": {}, "source": [ "#### Approach 3: gradient descent by hand\n", "Recall that in gradient descent, we iteratively update the weight vector by doing:\n", "\n", "$$\n", "\\hat{\\beta}^{(k+1)} = \\hat{\\beta}^{(k)} - \\eta \\nabla_{\\beta} L(\\hat{\\beta}^{(k)}).\n", "$$\n", "\n", "From Tutorial 1, we know that \n", "\n", "$$\n", "\\nabla_\\beta L(\\beta) = -2 X^T y + 2X^TX\\beta,\n", "$$\n", "\n", "We will take $\\eta=0.001$ as the step size, and we'll run gradient descent for T=50 iterations, and we'll initialize $\\hat{\\beta}^{(0)} = 0_p$, the zero vector in $p$ dimensions." ] }, { "cell_type": "code", "execution_count": 27, "id": "8e3026ee", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "beta hat using GD by hand: [ 0.97707459 0.01357098 -1.99153047 -3.97745021 -0.02467584]\n", " true beta: [ 1 0 -2 -4 0]\n" ] } ], "source": [ "eta = 0.001\n", "T = 50\n", "\n", "def grad_loss(b, X, y):\n", " return -2 * X.T @ y + 2 * X.T @ X @ b\n", "\n", "betas = np.zeros(shape=(T, p)) # store the beta vec at each iteration\n", "\n", "for t in range(1, T):\n", " betas[t,:] = betas[t-1,:] - eta * grad_loss(betas[t-1,:], X, y)\n", " \n", "print(\"beta hat using GD by hand: \", betas[T-1,:])\n", "print(\" true beta: \", betastar)" ] }, { "cell_type": "markdown", "id": "eb61f235", "metadata": {}, "source": [ "#### Approach 4: gradient descent with `PyTorch`\n", "We now make use of `PyTorch` to compute the gradients - had we started here we would have had to do absolutely no calculus to compute the gradients required in approach 3, we would simply specify the objective we wish to optimize and let `PyTorch` do the rest. Obviously this is extremely useful when doing calculus by hand is hard (or impossible).\n", "\n", "In `PyTorch` we use tensors rather than `NumPy`arrays. You can think of tensors as you do arrays; the only difference is that tensors allow you to compute gradients as we saw before. It is important to note here that in the following code, there is no equivalent of the `grad_loss` function, which is taken care of by the autodiff." ] }, { "cell_type": "code", "execution_count": 28, "id": "077baa33", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "beta hat using PyTorch: tensor([ 0.9772, 0.0137, -1.9915, -3.9776, -0.0245])\n", " true beta: [ 1 0 -2 -4 0]\n" ] } ], "source": [ "X_tensor = torch.from_numpy(X).float() # X data tensor\n", "y_tensor = torch.from_numpy(y).float() # y data tensor\n", "beta_tensor = torch.zeros(p, requires_grad=True) # this is our parameter vector beta\n", "eta = 0.1\n", "T = 50\n", "\n", "for _ in range(T):\n", " yhat = X_tensor @ beta_tensor # prediction of model\n", " residual = yhat - y_tensor # residual tensor (errors)\n", " loss = (residual**2).mean() # mean squared error tensor\n", "\n", " loss.backward() # this call computes gradients of `loss` w.r.t. any params (beta)tensor\n", " \n", " with torch.no_grad():\n", " # we do not want this calculation to be part of the gradient computation\n", " beta_tensor -= eta * beta_tensor.grad\n", " \n", " # remove current gradients from being stored (important if you want to recompute gradients)\n", " beta_tensor.grad.zero_()\n", "\n", "print(\"beta hat using PyTorch: \", beta_tensor.data)\n", "print(\" true beta: \", betastar)" ] }, { "cell_type": "markdown", "id": "8a395bd5", "metadata": {}, "source": [ "#### Approach 5: gradient descent with `PyTorch` but better\n", "In approach 4, we used PyTorch but the computation was somewhat ad hoc. We now repeat the exercise but make use of more `PyTorch` functionality. \n", "\n", "Some things to note:\n", "1. For any problem you wish to solve using `PyTorch`, you should first specify a `model` which inherits from the `Module` class and defines the model of computation you wish to work with. Importantly, this class always contains a `forward` function that describes how an input should make its way through the computational graph.\n", "\n", "2. `PyTorch` already has a host of useful machine learning functions that can be imported. Many of these live in the `nn` module, which is short for `neural nets`.\n", "\n", "3. `PyTorch` already has a large number of optimizers (other numerical methods apart from GD) that we can use. These live in the `optim` module\n", "\n", "4. Throughout the course we will use similar classes to define various models." ] }, { "cell_type": "code", "execution_count": 29, "id": "4e08be6b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "beta hat using PyTorch w model: tensor([ 0.9772, 0.0137, -1.9915, -3.9776, -0.0245])\n", " true beta: [ 1 0 -2 -4 0]\n" ] } ], "source": [ "from torch import nn, optim\n", "\n", "# create the linear regression model class\n", "class LinearRegressionTorch(nn.Module):\n", " def __init__(self):\n", " super().__init__()\n", " \n", " # need to wrap the params of the model in nn.Parameter\n", " self.beta_tensor = nn.Parameter(torch.zeros(p, requires_grad=True))\n", " \n", " def forward(self, X):\n", " return X @ self.beta_tensor\n", "\n", "model = LinearRegressionTorch() # create a model instance\n", "loss_func = nn.MSELoss() # choose MSE loss\n", "optimizer = optim.SGD(model.parameters(), lr=eta) # choose Stochastic GD\n", "\n", "for _ in range(50):\n", " yhat = model.forward(X_tensor)\n", " loss = loss_func(y_tensor, yhat)\n", " loss.backward()\n", " optimizer.step() # no need to manually update\n", " optimizer.zero_grad()\n", "\n", "print(\"beta hat using PyTorch w model: \", model.beta_tensor.data)\n", "print(\" true beta: \", betastar)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.7" } }, "nbformat": 4, "nbformat_minor": 5 }