{ "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": [ "from __future__ import division, print_function\n", "%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", 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