{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[Table of Contents](./table_of_contents.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Multivariate Gaussians\n", "\n", "Modeling Uncertainty in Multiple Dimensions" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#format the book\n", "import book_format\n", "book_format.set_style()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The techniques in the last chapter are very powerful, but they only work with one variable or dimension. They provide no way to represent multidimensional data, such as the position and velocity of a dog in a field. Position and velocity are related to each other, and as we learned in the g-h chapter we should never throw away information. In this chapter we learn how to describe this relationship probabilistically. Through this key insight we will achieve markedly better filter performance." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multivariate Normal Distributions\n", "\n", "We've been using Gaussians for a scalar random variable, expressed as $\\mathcal{N}(\\mu, \\sigma^2)$. A more formal term for this is *univariate normal*, where univariate means 'one variable'. The probability distribution of the Gaussian is known as the *univariate normal distribution*.\n", "\n", "What might a *multivariate normal distribution* be? *Multivariate* means multiple variables. Our goal is to be able to represent a normal distribution with multiple dimensions. I don't necessarily mean spatial dimensions - if we track the position, velocity, and acceleration of an aircraft in (x, y, z) that gives us a nine dimensional problem. Consider a two dimensional case. It might be the *x* and *y* coordinates of a robot, it might be the position and velocity of a dog on the x-axis, or milk production and feed rate at a dairy. It doesn't really matter. We can see that for $N$ dimensions, we need $N$ means, which we will arrange in a column matrix (vector) like so:\n", "\n", "$$\n", "\\mu = \\begin{bmatrix}\\mu_1\\\\\\mu_2\\\\ \\vdots \\\\\\mu_n\\end{bmatrix}\n", "$$\n", "\n", "Let's say we believe that $x = 2$ and $y = 17$. We would have\n", "\n", "$$\n", "\\mu = \\begin{bmatrix}2\\\\17\\end{bmatrix} \n", "$$\n", "\n", "The next step is representing our variances. At first blush we might think we would also need N variances for N dimensions. We might want to say the variance for x is 10 and the variance for y is 4, like so. \n", "\n", "$$\\sigma^2 = \\begin{bmatrix}10\\\\4\\end{bmatrix}$$ \n", "\n", "This is incomplete because it does not consider the more general case. In the **Gaussians** chapter we computed the variance in the heights of students. That is a measure of how the heights vary relative to each other. If all students are the same height, then the variance is 0, and if their heights are wildly different, then the variance will be large. \n", "\n", "There is also a relationship between height and weight. In general, a taller person weighs more than a shorter person. Height and weight are *correlated*. We want a way to express not only what we think the variance is in the height and the weight, but also the degree to which they are correlated. In other words, we want to know how weight varies compared to the heights. We call that the *covariance*. \n", "\n", "Before we can understand multivariate normal distributions we need to understand the mathematics behind correlations and covariances." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Correlation and Covariance\n", "\n", "*Covariance* describes how much two variables vary together. Covariance is short for *correlated variances*. In other words, *variance* is a measure for how a population vary amongst themselves, and *covariance* is a measure for how much two variables change in relation to each other. For example, as height increases weight also generally increases. These variables are *correlated*. They are *positively correlated* because as one variable gets larger so does the other. As the outdoor temperature decreases home heating bills increase. These are *inversely correlated* or *negatively correlated* because as one variable gets larger the other variable lowers. The price of tea and the number of tail wags my dog makes have no relation to each other, and we say they are *uncorrelated* or *independent*- each can change independent of the other.\n", "\n", "Correlation allows prediction. If you are significantly taller than me I can predict that you also weigh more than me. As winter comes I predict that I will be spending more to heat my house. If my dog wags his tail more I don't conclude that tea prices will be changing.\n", "\n", "For example, here is a plot of height and weight of students on the school's track team. If a student is 68 inches tall I can predict they weigh roughly 160 pounds. Since the correlation is not perfect neither is my prediction. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "