{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Bayesian linear regression\n",
"\n",
"* [1. What is Bayesian linear regression?](#intro-blr)\n",
"* [2. Recap linear regression](#recap-lr)\n",
"* [3. Fundamental concepts](#fundamental-concepts)\n",
"* [4. Linear regression from a probabilistic perspective](#prob-lr)\n",
"* [5. Linear regression with basis functions](#lr-with-basis-functions)\n",
" * [5.1 Example basis functions](#example-basis-function)\n",
" * [5.2 The design matrix](#design-matrix)\n",
"* [6. Bayesian Linear Regression](#blr)\n",
" * [6.1 Step 1: Probabilistic Model](#prob-model)\n",
" * [6.2 Generating a dataset](#dataset)\n",
" * [6.3 Step 2: Posterior over the parameters](#param-posterior)\n",
" * [6.4 Visualizing the parameter posterior](#param-posterior-visualization)\n",
" * [6.5 Step 3: Posterior predictive distribution](#predictive-posterior)\n",
" * [6.6 Visualizing the predictive posterior](#predictive-posterior-visualization)\n",
"\n",
" \n",
"* [Sources and further reading](#sources)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Link to interactive demo\n",
"\n",
"[Click here](https://mybinder.org/v2/gh/zotroneneis/machine_learning_basics/HEAD?filepath=bayesian_linear_regression.ipynb) to run the notebook online (using Binder) without installing jupyter or downloading the code.\n",
"\n",
"\n",
"Sometimes, the GitHub version of the Jupyter notebook does not display the math formulas correctly. Please refer to the Binder version in case you think something might be off or missing.\n",
"\n",
"I also wrote a [blog post containing the contents of the notebook](https://alpopkes.com/posts/machine_learning/bayesian_linear_regression)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1. What is Bayesian linear regression (BLR)? \n",
"Bayesian linear regression is the *Bayesian* interpretation of linear regression. What does that mean? To answer this question we first have to understand the Bayesian approach. In most of the algorithms we have looked at so far we computed *point estimates* of our parameters. For example, in linear regression we chose values for the weights and bias that minimized our mean squared error cost function. In the Bayesian approach we don't work with exact values but with *probabilities*. This allows us to model the *uncertainty* in our parameter estimates. Why is this important?\n",
"\n",
"In nearly all real-world situations, our data and knowledge about the world is incomplete, indirect and noisy. Hence, uncertainty must be a fundamental part of our decision-making process. This is exactly what the Bayesian approach is about. It provides a formal and consistent way to reason in the presence of uncertainty. Bayesian methods have been around for a long time and are widely-used in many areas of science (e.g. astronomy). Although Bayesian methods have been applied to machine learning problems too, they are usually less well known to beginners. The major reason is that they require a good understanding of probability theory.\n",
"\n",
"In the following notebook we will work our way from linear regression to Bayesian linear regression, including the most important theoretical knowledge and code examples."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2. Recap linear regression \n",
"\n",
"- In linear regression, we want to find a function $f$ that maps inputs $x \\in \\mathbb{R}^D$ to corresponding function values $f(x) \\in \\mathbb{R}$. \n",
"- We are given an input dataset $D = \\big \\{ \\mathbf{x}_n, y_n \\big \\}_{n=1}^N$, where $y_n$ is a noisy observation value: $y_n = f(x_n) + \\epsilon$, with $\\epsilon$ being an i.i.d. random variable that describes measurement/observation noise\n",
"- Our goal is to infer the underlying function $f$ that generated the data such that we can predict function values at new input locations\n",
"- In linear regression, we model the underlying function $f$ using a linear combination of the input features:\n",
"\n",
"$$\n",
"\\begin{split}\n",
"y &= \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + ... + \\theta_d x_d \\\\\n",
"&= \\boldsymbol{x}^T \\boldsymbol{\\theta}\n",
"\\end{split}\n",
"$$\n",
" \n",
" \n",
"- For more details take a look at the [notebook on linear regression](https://github.com/zotroneneis/machine_learning_basics/blob/master/linear_regression.ipynb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3. Fundamental concepts \n",
"- One fundamental tool in Bayesian learning is [Bayes' theorem](https://en.wikipedia.org/wiki/Bayes%27_theorem)\n",
"- Bayes' theorem looks as follows:\n",
"$$\n",
"\\begin{equation}\n",
"p(\\boldsymbol{\\theta} | \\mathbf{x}, y) = \\frac{p(y | \\boldsymbol{x}, \\boldsymbol{\\theta})p(\\boldsymbol{\\theta})}{p(\\boldsymbol{x}, y)}\n",
"\\end{equation}\n",
"$$\n",
"- $p(y | \\boldsymbol{x}, \\boldsymbol{\\theta})$ is the *likelihood*. It describes the probability of the target values given the data and parameters.\n",
"- $p(\\boldsymbol{\\theta})$ is the *prior*. It describes our initial knowledge about which parameter values are likely and unlikely.\n",
"- $p(\\boldsymbol{x}, y)$ is the *evidence*. It describes the joint probability of the data and targets. \n",
"- $p(\\boldsymbol{\\theta} | \\boldsymbol{x}, y)$ is the *posterior*. It describes the probability of the parameters given the observed data and targets.\n",
" \n",
"- Another important tool you need to know about is the [Gaussian distribution](https://en.wikipedia.org/wiki/Normal_distribution). If you are not familiar with it I suggest you pause for a minute and understand its main properties before reading on.\n",
"\n",
"In general, Bayesian inference works as follows:\n",
"1. We start with some prior belief about a hypothesis $p(h)$\n",
"2. We observe some data, representating new evidence $e$\n",
"3. We use Bayes' theorem to update our belief given the new evidence: $p(h|e) = \\frac{p(e |h)p(h)}{p(e)}$ \n",
"\n",
"For more information take a look at the [Wikipedia article on Bayesian inference](https://en.wikipedia.org/wiki/Bayesian_inference)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 4. Linear regression from a probabilistic perspective \n",
"\n",
"In order to pave the way for Bayesian linear regression we will take a probabilistic spin on linear regression. Let's start by explicitly modelling the observation noise $\\epsilon$. For simplicity, we assume that $\\epsilon$ is normally distributed with mean $0$ and some known variance $\\sigma^2$: $\\epsilon \\sim \\mathcal{N}(0, \\sigma^2)$.\n",
"\n",
"As mentioned in the beginning, a simple linear regression model assumes that the target function $f(x)$ is given by a linear combination of the input features:\n",
"$$\n",
"\\begin{split}\n",
"y = f(\\boldsymbol{x}) + \\epsilon \\\\\n",
" = \\boldsymbol{x}^T \\boldsymbol{\\theta} + \\epsilon\n",
"\\end{split}\n",
"$$\n",
"\n",
"This corresponds to the following likelihood function: \n",
"$$p(y | \\boldsymbol{x}, \\boldsymbol{\\theta}) = \\mathcal{N}(\\boldsymbol{x}^T \\boldsymbol{\\theta}, \\sigma^2)$$\n",
"\n",
"Our goal is to find the parameters $\\boldsymbol{\\theta} = \\{\\theta_1, ..., \\theta_D\\}$ that model the given data best.\n",
"In standard linear regression we can find the best parameters using a least-squares, maximum likelihood (ML) or maximum a posteriori (MAP) approach. If you want to know more about these solutions take a look at the [notebook on linear regression](https://github.com/zotroneneis/machine_learning_basics/blob/master/linear_regression.ipynb) or at chapter 9.2 of the book [Mathematics for Machine Learning](https://mml-book.com)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 5. Linear regression with basis functions \n",
"The simple linear regression model above is linear not only with respect to the parameters $\\boldsymbol{\\theta}$ but also with respect to the inputs $\\boldsymbol{x}$. When $\\boldsymbol{x}$ is not a vector but a single value (that is, the dataset is one-dimensional) the model $y_i = x_i \\cdot \\theta$ describes straight lines with $\\theta$ being the slope of the line.\n",
"\n",
"The plot below shows example lines produced with the model $y = x \\cdot \\theta$, using different values for the slope $\\theta$ and intercept 0. \n",
"\n",
"\n",
"\n",
"Having a model which is linear both with respect to the parameters and inputs limits the functions it can learn significantly. We can make our model more powerful by making it *nonlinear* with respect to the inputs. After all, *linear regression* refers to models which are linear in the *parameters*, not necessarily in the *inputs* (linear in the parameters means that the model describes a function by a linear combination of input features).\n",
"\n",
"Making the model nonlinear with respect to the inputs is easy. We can adapt it by using a nonlinear transformation of the input features $\\phi(\\boldsymbol{x})$. With this adaptation our model looks as follows: \n",
"$$\n",
"\\begin{split}\n",
"y &= \\boldsymbol{\\phi}^T(\\boldsymbol{x}) \\boldsymbol{\\theta} + \\epsilon \\\\\n",
"&= \\sum_{k=0}^{K-1} \\theta_k \\phi_k(\\boldsymbol{x}) + \\epsilon\n",
"\\end{split}\n",
"$$\n",
"\n",
"Where $\\boldsymbol{\\phi}: \\mathbf{R}^D \\rightarrow \\mathbf{R}^K$ is a (non)linear transformation of the inputs $\\boldsymbol{x}$ and $\\phi_k: \\mathbf{R}^D \\rightarrow \\mathbf{R}$ is the $k-$th component of the *feature vector* $\\boldsymbol{\\phi}$:\n",
"\n",
"$$\n",
"\\boldsymbol{\\phi}(\\boldsymbol{x})=\\left[\\begin{array}{c}\n",
"\\phi_{0}(\\boldsymbol{x}) \\\\\n",
"\\phi_{1}(\\boldsymbol{x}) \\\\\n",
"\\vdots \\\\\n",
"\\phi_{K-1}(\\boldsymbol{x})\n",
"\\end{array}\n",
"\\right]\n",
"\\in \\mathbb{R}^{K}\n",
"$$\n",
"\n",
"\n",
"With our new nonlinear transformation the likelihood function is given by\n",
"\n",
"$$\n",
"p(y | \\boldsymbol{x}, \\boldsymbol{\\theta}) = \\mathcal{N}(\\boldsymbol{\\phi}^T(\\boldsymbol{x}) \\boldsymbol{\\theta},\\, \\sigma^2)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5.1 Example basis functions \n",
"\n",
"#### Linear regression\n",
"The easiest example for a basis function (for one-dimensional data) would be simple linear regression, that is, no non-linear transformation at all. In this case we would choose $\\phi_0(x) = 1$ and $\\phi_i(x) = x$. This would result in the following vector $\\boldsymbol{\\phi}(x)$:\n",
"\n",
"$$\n",
"\\boldsymbol{\\phi}(x)=\n",
"\\left[\n",
"\\begin{array}{c}\n",
"\\phi_{0}(x) \\\\\n",
"\\phi_{1}(x) \\\\\n",
"\\vdots \\\\\n",
"\\phi_{K-1}(x)\n",
"\\end{array}\n",
"\\right] = \n",
"\\left[\n",
"\\begin{array}{c}\n",
"1 \\\\\n",
"x \\\\\n",
"\\vdots \\\\\n",
"x\n",
"\\end{array}\n",
"\\right]\n",
"\\in \\mathbb{R}^{K}\n",
"$$\n",
"\n",
"#### Polynomial regression\n",
"Another common choice of basis function for the one-dimensional case is polynomial regression. For this we would set $\\phi_i(x) = x^i$ for $i=0, ..., K-1$. The corresponding feature vector $\\boldsymbol{\\phi}(x)$ would look as follows:\n",
"\n",
"$$\n",
"\\boldsymbol{\\phi}(x)=\n",
"\\left[\n",
"\\begin{array}{c}\n",
"\\phi_{0}(x) \\\\\n",
"\\phi_{1}(x) \\\\\n",
"\\vdots \\\\\n",
"\\phi_{K-1}(x)\n",
"\\end{array}\n",
"\\right] = \n",
"\\left[\n",
"\\begin{array}{c}\n",
"1 \\\\\n",
"x \\\\\n",
"x^2 \\\\\n",
"x^3 \\\\\n",
"\\vdots \\\\\n",
"x^{K-1}\n",
"\\end{array}\n",
"\\right]\n",
"\\in \\mathbb{R}^{K}\n",
"$$\n",
"\n",
"With this transformation we can lift our original one-dimensional input into a $K$-dimensional feature space. Our function $f$ can be any polynomial with degree $\\le K-1$: $f(x) = \\sum_{k=0}^{K-1} \\theta_k x^k$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5.2 The design matrix \n",
"To make it easier to work with the transformations $\\boldsymbol{\\phi}(\\boldsymbol{x})$ for the different input vectors $\\boldsymbol{x}$ we typically create a so called *design matrix* (also called *feature matrix*). Given our dataset $D = \\big \\{ \\mathbf{x}_n, y_n \\big \\}_{n=1}^N$ we define the design matrix as follows:\n",
"\n",
"$$\n",
"\\boldsymbol{\\Phi}:=\\left[\\begin{array}{c}\n",
"\\boldsymbol{\\phi}^{\\top}\\left(\\boldsymbol{x}_{1}\\right) \\\\\n",
"\\vdots \\\\\n",
"\\boldsymbol{\\phi}^{\\top}\\left(\\boldsymbol{x}_{N}\\right)\n",
"\\end{array}\\right]=\\left[\\begin{array}{ccc}\n",
"\\phi_{0}\\left(\\boldsymbol{x}_{1}\\right) & \\cdots & \\phi_{K-1}\\left(\\boldsymbol{x}_{1}\\right) \\\\\n",
"\\phi_{0}\\left(\\boldsymbol{x}_{2}\\right) & \\cdots & \\phi_{K-1}\\left(\\boldsymbol{x}_{2}\\right) \\\\\n",
"\\vdots & & \\vdots \\\\\n",
"\\phi_{0}\\left(\\boldsymbol{x}_{N}\\right) & \\cdots & \\phi_{K-1}\\left(\\boldsymbol{x}_{N}\\right)\n",
"\\end{array}\\right] \\in \\mathbb{R}^{N \\times K}\n",
"$$\n",
"\n",
"Note that the design matrix is of shape $N \\times K$. $N$ is the number of input examples and $K$ is the output dimension of the non-linear transformation $\\boldsymbol{\\phi}(\\boldsymbol{x})$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 6. Bayesian linear regression \n",
"What changes when we consider a Bayesian interpretation of linear regression? Our data stays the same as before: $D = \\big \\{ \\mathbf{x}_n, y_n \\big \\}_{n=1}^N$. Given the data $D$ we can define the set of all inputs as $\\mathcal{X} := \\{\\boldsymbol{x}_1, ..., \\boldsymbol{x}_n\\}$ and the set of all targets as $\\mathcal{Y} := \\{y_1, ..., y_n \\}$.\n",
"\n",
"In simple linear regression we compute point estimates of our parameters (e.g. using a maximum likelihood approach) and use these estimates to make predictions. Different to this, Bayesian linear regression estimates *distributions* over the parameters and predictions. This allows us to model the uncertainty in our predictions.\n",
"\n",
"To perform Bayesian linear regression we follow three steps:\n",
"1. We set up a probabilistic model that describes our assumptions how the data and parameters are generated\n",
"2. We perform inference for the parameters $\\boldsymbol{\\theta}$, that is, we compute the posterior probability distribution over the parameters\n",
"3. With this posterior we can perform inference for new, unseen inputs $y_*$. In this step we don't compute point estimates of the outputs. Instead, we compute the parameters of the posterior distribution over the outputs."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 6.1 Step 1: Probabilistic model \n",
"\n",
"We start by setting up a probabilistic model that describes our assumptions how the data and parameters are generated. For this, we place a prior $p(\\boldsymbol{\\theta})$ over our parameters which encodes what parameter values are plausible (before we have seen any data). Example: With a single parameter $\\theta$, a Gaussian prior $p(\\theta) = \\mathcal{N}(0, 1)$ says that parameter values are normally distributed with mean 0 and standard deviation 1. In other words: the parameter values are most likely to fall into the interval [−2,2] which is two standard deviations around the mean value.\n",
"\n",
"To keep things simple we will assume a Gaussian prior over the parameters: $p(\\boldsymbol{\\theta}) = \\mathcal{N}(\\boldsymbol{m}_0, \\boldsymbol{S}_0)$. Let's further assume that the likelihood function is Gaussian, too: $p(y \\mid \\boldsymbol{x}, \\boldsymbol{\\theta})=\\mathcal{N}\\left(y \\mid \\boldsymbol{\\phi}^{\\top}(\\boldsymbol{x}) \\boldsymbol{\\theta}, \\sigma^{2}\\right)$.\n",
"\n",
"Note: When considering the set of all targets $\\mathcal{Y} := \\{y_1, ..., y_n \\}$, the likelihood function becomes a multivariate Gaussian distribution: $p(\\mathcal{Y} \\mid \\mathcal{X}, \\boldsymbol{\\theta})=\\mathcal{N}\\left(\\boldsymbol{y} \\mid \\boldsymbol{\\Phi} \\boldsymbol{\\theta}, \\sigma^{2} \\boldsymbol{I}\\right)$\n",
"\n",
"The nice thing about choosing a Gaussian distribution for our prior is that the posterior distributions will be Gaussian, too (keyword [conjugate prior](https://en.wikipedia.org/wiki/Conjugate_prior))! \n",
"\n",
"We will start our `BayesianLinearRegression` class with the knowledge we have so far - our probabilistic model. As mentioned in the beginning we assume that the variance $\\sigma^2$ of the noise $\\epsilon$ is known. Furthermore, to allow plotting the data later on we will assume that it's two dimensional (d=2)."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from scipy.stats import multivariate_normal\n",
"import numpy as np\n",
"\n",
"class BayesianLinearRegression:\n",
" \"\"\" Bayesian linear regression\n",
" \n",
" Args:\n",
" prior_mean: Mean values of the prior distribution (m_0)\n",
" prior_cov: Covariance matrix of the prior distribution (S_0)\n",
" noise_var: Variance of the noise distribution\n",
" \"\"\"\n",
" \n",
" def __init__(self, prior_mean: np.ndarray, prior_cov: np.ndarray, noise_var: float):\n",
" self.prior_mean = prior_mean[:, np.newaxis] # column vector of shape (1, d)\n",
" self.prior_cov = prior_cov # matrix of shape (d, d)\n",
" # We initalize the prior distribution over the parameters using the given mean and covariance matrix\n",
" # In the formulas above this corresponds to m_0 (prior_mean) and S_0 (prior_cov)\n",
" self.prior = multivariate_normal(prior_mean, prior_cov)\n",
" \n",
" # We also know the variance of the noise\n",
" self.noise_var = noise_var # single float value\n",
" self.noise_precision = 1 / noise_var\n",
" \n",
" # Before performing any inference the parameter posterior equals the parameter prior\n",
" self.param_posterior = self.prior\n",
" # Accordingly, the posterior mean and covariance equal the prior mean and variance\n",
" self.post_mean = self.prior_mean # corresponds to m_N in formulas\n",
" self.post_cov = self.prior_cov # corresponds to S_N in formulas\n",
" \n",
" \n",
"# Let's make sure that we can initialize our model\n",
"prior_mean = np.array([0, 0])\n",
"prior_cov = np.array([[0.5, 0], [0, 0.5]])\n",
"noise_var = 0.2\n",
"blr = BayesianLinearRegression(prior_mean, prior_cov, noise_var)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 6.2 Generating a dataset \n",
"\n",
"Before going any further we need a dataset to test our implementation. Remember that we assume that our targets were generated by a function of the form $y = \\boldsymbol{\\phi}^T(\\boldsymbol{x}) \\boldsymbol{\\theta} + \\epsilon$ where $\\epsilon$ is normally distributed with mean $0$ and some known variance $\\sigma^2$: $\\epsilon \\sim \\mathcal{N}(0, \\sigma^2)$.\n",
"\n",
"To keep things simple we will work with one-dimensional data and simple linear regression (that is, no non-linear transformation of the inputs). Consequently, our data generating function will be of the form\n",
"$$ y = \\theta_0 + \\theta_1 \\, x + \\epsilon $$\n",
"\n",
"Note that we added a parameter $\\theta_0$ which corresponds to the intercept of the linear function. Until know we assumed $\\theta_0 = 0$. As mentioned earlier, $\\theta_1$ represents the slope of the linear function."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"def compute_function_labels(slope: float, intercept: float, noise_std_dev: float, data: np.ndarray) -> np.ndarray:\n",
" \"\"\"\n",
" Compute target values given function parameters and data.\n",
" \n",
" Args:\n",
" slope: slope of the function (theta_1)\n",
" intercept: intercept of the function (theta_0)\n",
" data: input feature values (x)\n",
" noise_std_dev: standard deviation of noise distribution (sigma)\n",
" \n",
" Returns:\n",
" target values, either true or corrupted with noise\n",
" \"\"\"\n",
" n_samples = len(data)\n",
" if noise_std_dev == 0: # Real function\n",
" return slope * data + intercept\n",
" else: # Noise corrupted\n",
" return slope * data + intercept + np.random.normal(0, noise_std_dev, n_samples)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# Set random seed to ensure reproducibility\n",
"seed = 42\n",
"np.random.seed(seed)\n",
"\n",
"# Generate true values and noise corrupted targets\n",
"n_datapoints = 1000\n",
"intercept = -0.7\n",
"slope = 0.9\n",
"noise_std_dev = 0.5\n",
"noise_var = noise_std_dev**2\n",
"lower_bound = -1.5\n",
"upper_bound = 1.5\n",
"\n",
"# Generate dataset\n",
"features = np.random.uniform(lower_bound, upper_bound, n_datapoints)\n",
"labels = compute_function_labels(slope, intercept, 0., features)\n",
"noise_corrupted_labels = compute_function_labels(slope, intercept, noise_std_dev, features)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
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