{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"tags": [
"remove_cell"
]
},
"outputs": [],
"source": [
"# HIDDEN\n",
"import warnings\n",
"warnings.filterwarnings('ignore')\n",
"from datascience import *\n",
"from prob140 import *\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"plt.style.use('fivethirtyeight')\n",
"%matplotlib inline\n",
"from scipy import stats"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Multivariate Normal Density ##"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is reasonable to expect that if a random vector $\\mathbf{X}$ is multivariate normal then its components should have a joint density function. But we have to be careful about the components in order to discuss joint densities.\n",
"\n",
"For an example of what could go wrong, let $\\mathbf{Z} = [Z_1 ~ Z_2]^T$ consist of i.i.d. standard normal variables, and let $\\mathbf{X} = [Z_1 ~ 2Z_1]^T$. Then the components of $\\mathbf{X}$ don't have a joint density on the plane since all the probability is on the line $y = 2x$. We have a *degenerate* situation in which one component is a linear transformation of the other.\n",
"\n",
"Another example is $\\mathbf{X} = [Z_1 ~ Z_2 ~ Z_1+Z_2]^T$. The three components don't have a joint density in three dimensions, since the third component is a linear combination of the first two. \n",
"\n",
"For a data scientist, there is no benefit in carrying around variables that are deterministic functions of other variables in a dataset. So we will avoid degenerate cases such as those above. To do this, let's make an observation about the linear transformations involved.\n",
"\n",
"In both cases, if you write $\\mathbf{X}$ as $\\mathbf{AZ}$ then the matrix $\\mathbf{A}$ is not invertible, and the covariance matrix of $\\mathbf{X}$ is positive semi-definite instead of positive definite.\n",
"\n",
"Thus we are going to restrict the definition of multivariate normal vectors to **invertible** linear transformations of i.i.d. standard normal vectors and **positive definite** covariance matrices."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"tags": [
"remove-input",
"hide-output"
]
},
"outputs": [
{
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""
]
},
"execution_count": 1,
"metadata": {},
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}
],
"source": [
"# VIDEO: Multivariate Normal\n",
"from IPython.display import YouTubeVideo\n",
"\n",
"YouTubeVideo('lUd7UVydEoI')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The Density ###\n",
"\n",
"From now on, we will usually say \"density\" even when we mean \"joint density\". The dimension of the random vector will tell you how many coordinates the density function has.\n",
"\n",
"Let $\\boldsymbol{\\Sigma}$ be a positive definite matrix. An $n$-dimensional random vector $\\mathbf{X}$ has the *multivariate normal density with mean vector $\\boldsymbol{\\mu}$ and covariance matrix $\\boldsymbol{\\Sigma}$* if the joint density of the elements of $\\mathbf{X}$ is given by\n",
"\n",
"$$\n",
"f_\\mathbf{X}(\\mathbf{x}) ~ = ~ \\frac{1}{(\\sqrt{2\\pi})^n \\sqrt{\\det(\\boldsymbol{\\Sigma})} }\n",
"\\exp\\big{(}-\\frac{1}{2}(\\mathbf{x} - \\boldsymbol{\\mu})^T\\boldsymbol{\\Sigma}^{-1}(\\mathbf{x} - \\boldsymbol{\\mu})\\big{)}\n",
"$$\n",
"\n",
"We will say that the elements of $\\mathbf{X}$ are *jointly normal* or *jointly Gaussian*.\n",
"\n",
"You should check that the formula is correct when $n = 1$. In this case $\\boldsymbol{\\Sigma} = [\\sigma^2]$ is just a scalar. It is a number, not a larger matrix; its determinant is itself; its inverse is simply $1/\\sigma^2$. Also, $\\mathbf{x} = x$ and $\\boldsymbol{\\mu} = \\mu$ are just numbers. The formula above reduces to the familiar normal density function with mean $\\mu$ and variance $\\sigma^2$.\n",
"\n",
"You should also check that the formula is correct in the case when the elements of $\\mathbf{X}$ are i.i.d. standard normal. In that case $\\mathbf{\\mu} = \\mathbf{0}$ and $\\boldsymbol{\\Sigma} = \\mathbf{I}_n$, the $n$-dimensional identity matrix.\n",
"\n",
"When $n=2$ the multivariate normal distribution is called *bivariate* normal."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"tags": [
"remove-input",
"hide-output"
]
},
"outputs": [
{
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"execution_count": 3,
"metadata": {},
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}
],
"source": [
"# VIDEO: Multivariate Normal: Parameters\n",
"YouTubeVideo('ao4fqXghbmI')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In lab you went through a detailed development of the multivariate normal joint density function, starting with $\\mathbf{Z}$ consisting of two i.i.d. standard normal components and then taking linear combinations. It turns out that all non-degenerate multivariate normal random vectors can be generated in this way. In fact, there are three useful equivalent definitions of a random vector $\\mathbf{X}$ with the multivariate normal density."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"tags": [
"remove-input",
"hide-output"
]
},
"outputs": [
{
"data": {
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""
]
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"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
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],
"source": [
"# VIDEO: Multivariate Normal: Definition\n",
"\n",
"YouTubeVideo('owX4JKA-2F8')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Definition 1:** $\\mathbf{X} = \\mathbf{AZ} + \\mathbf{b}$ for some i.i.d. standard normal $\\mathbf{Z}$, an invertible $\\mathbf{A}$, and a column vector $\\mathbf{b}$.\n",
"\n",
"**Definition 2:** $\\mathbf{X}$ has the joint density above.\n",
"\n",
"**Definition 3:** Every linear combination of elements of $\\mathbf{X}$ is normally distributed.\n",
"\n",
"At the end of this section there is a note on establishing the equivalences. Parts of it are hard. Just accept that they are true, and let's examine the properties of the distribution.\n",
"\n",
"**The key to understanding the multivariate normal is Definition 1: every multivariate normal vector that has a density is an invertible linear transformation of i.i.d. standard normals.** Let's see what Definition 1 implies for the density."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"tags": [
"remove-input",
"hide-output"
]
},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# VIDEO: Multivariate Normal: Density\n",
"YouTubeVideo('tIvp_0HPeIo')"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"tags": [
"remove-input",
"hide-output"
]
},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# VIDEO: Quadratic Form\n",
"YouTubeVideo('rITtghijhb4')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Quadratic Form ###\n",
"The shape of the density is determined by the *quadratic form* $\\frac{1}{2}(\\mathbf{x} - \\boldsymbol{\\mu})^T\\boldsymbol{\\Sigma}^{-1}(\\mathbf{x} - \\boldsymbol{\\mu})$. The level surfaces are ellipsoids. In two dimensions these are the ellipses you saw in lab. \n",
"\n",
"Here is the joint density surface of standard normal variables $X_1$ and $X_2$ that are jointly normal with $Cov(X_1, X_2) = 0.8$. The call is `Plot_bivariate_normal(mu, cov)` where the mean vector `mu` is a list and the covariance matrix is a list of lists specifying the rows."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mu = [0, 0]\n",
"cov = [[1, 0.8], [0.8, 1]]\n",
"Plot_bivariate_normal(mu, cov)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note the elliptical contours, and that the probability is concentrated around a straight line. \n",
"\n",
"In more than two dimensions we can no longer draw joint density surfaces. But in three dimensions we can make i.i.d. draws from a multivariate normal joint density and plot the resulting points. Here is an example of the empirical distribution of 1000 observations of standard normal variables $X_1$, $X_2$, and $X_3$ that are jointly normal with $Cov(X_1, X_2) = 0.6$, $Cov(X_1, X_3) = 0.5$, and $Cov(X_2, X_3) = 0.2$. Note the elliptical cloud.\n",
"\n",
"The call is `Scatter_multivariate_normal(mu, cov, n)` where `n` is the number of points to generate. The function checks whether the specified matrix is positive semidefinite."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mu2 = [0, 0, 0]\n",
"cov2 = [[1, 0.6, 0.5], [0.6, 1, 0.2], [0.5, 0.2, 1]]\n",
"Scatter_multivariate_normal(mu2, cov2, 1000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To see how the quadratic form arises, let $\\mathbf{X}$ be multivariate normal. By Definition 1, $\\mathbf{X} = \\mathbf{AZ} + \\mathbf{b}$ for some invertible $\\mathbf{A}$ and vector $\\mathbf{b}$, and some i.i.d. standard normal $\\mathbf{Z}$. \n",
"\n",
"By multiplication of the marginals, the joint density of $\\mathbf{Z}$ is \n",
"\n",
"$$\n",
"f(\\mathbf{z}) ~ = ~ \\frac{1}{(\\sqrt{2\\pi})^n} \\exp\\big{(}-\\frac{1}{2}(z_1^2 + z_2^2 + \\cdots + z_n^2)\\big{)} ~ = ~ \\frac{1}{(\\sqrt{2\\pi})^n }\n",
"\\exp\\big{(}-\\frac{1}{2}\\mathbf{z}^T\\mathbf{z}\\big{)}\n",
"$$\n",
"\n",
"The preimage of $\\mathbf{x}$ under the linear transformation $\\mathbf{x} = \\mathbf{Az} + \\mathbf{b}$ is \n",
"\n",
"$$\n",
"\\mathbf{z} ~ = ~ \\mathbf{A}^{-1}(\\mathbf{x} - \\mathbf{b})\n",
"$$\n",
"\n",
"and so by change of variable the quadratic form in the density of $\\mathbf{X}$ is\n",
"\n",
"$$\n",
"\\frac{1}{2}\\mathbf{z}^T\\mathbf{z} ~ = ~ \n",
"\\frac{1}{2} (\\mathbf{x} - \\mathbf{b})^T (\\mathbf{A}^{-1})^T \\mathbf{A}^{-1}(\\mathbf{x} - \\mathbf{b}) ~ = ~\n",
"\\frac{1}{2} (\\mathbf{x} - \\mathbf{b})^T (\\mathbf{AA}^T)^{-1} (\\mathbf{x} - \\mathbf{b})\n",
"$$\n",
"\n",
"Let $\\mathbf{\\mu_X}$ be the mean vector of $\\mathbf{X}$. Because $\\mathbf{X} = \\mathbf{AZ} + \\mathbf{b}$, we have $\\mathbf{\\mu_X} = \\mathbf{b}$. \n",
"\n",
"The covariance matrix of $\\mathbf{Z}$ is $\\mathbf{I}_n$. So the covariance matrix of $\\mathbf{X}$ is\n",
"\n",
"$$\n",
"\\boldsymbol{\\Sigma}_\\mathbf{X} ~ = ~ \\mathbf{A} \\mathbf{I}_n \\mathbf{A}^T ~ = ~ \\mathbf{A} \\mathbf{A}^T\n",
"$$\n",
"\n",
"So the quadratic form in the density of $\\mathbf{X}$ becomes $\\frac{1}{2} (\\mathbf{x} - \\mathbf{\\mu_X})^T \\boldsymbol{\\Sigma}_\\mathbf{X}^{-1} (\\mathbf{x} - \\mathbf{\\mu_X})$."
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"source": [
"# VIDEO: Volume\n",
"YouTubeVideo('g_S0UeHYc2k')"
]
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"source": [
"### Constant of Integration ###\n",
"By linear change of variable, the density of $\\mathbf{X}$ is given by\n",
"$$\n",
"f_\\mathbf{X}(\\mathbf{x}) ~ = ~ f(\\mathbf{z}) \\cdot \\frac{1}{s}\n",
"$$\n",
"\n",
"where $\\mathbf{z}$ is the preimage of $\\mathbf{x}$ and $s$ is the volume of the parallelopiped formed by the transformed unit vectors. That is, $s = \\|\\det(\\mathbf{A})\\|$. Now\n",
"\n",
"$$\n",
"\\det(\\boldsymbol{\\Sigma}_\\mathbf{X}) ~ = ~ \\det(\\mathbf{AA}^T) ~ = ~ (\\det(\\mathbf{A}))^2\n",
"$$\n",
"\n",
"Therefore the constant of integration in the density of $\\mathbf{X}$ is\n",
"\n",
"$$\n",
"\\frac{1}{(\\sqrt{2\\pi})^n \\sqrt{\\det(\\boldsymbol{\\Sigma}_\\mathbf{X})} }\n",
"$$"
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"source": [
"We have shown how the joint density function arises and what its pieces represent. In the process, we have proved the Definition 1 implies Definition 2. Now let's establish that all three definitions are equivalent."
]
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"### The Equivalences ###\n",
"Here are some pointers for how to see the equivalences of the three definitions. One of the pieces is not easy to establish.\n",
"\n",
"Definition 1 is at the core of the properties of the multivariate normal. We will try to see why it is equivalent to the other two definitions.\n",
"\n",
"We have seen that Definition 1 implies Definition 2. \n",
"\n",
"To see that Definition 2 implies Definition 1, it helps to remember that a positive definite matrix $\\boldsymbol{\\Sigma}$ can be decomposed as $\\boldsymbol{\\Sigma} = \\mathbf{AA}^T$ for some lower triangular $\\mathbf{A}$ that has only positive elements on its diagonal and hence is invertible. This is called the *Cholesky decomposition*. Set $\\mathbf{Z} = \\mathbf{A}^{-1}(\\mathbf{X} - \\boldsymbol{\\mu})$ to see that Definition 1 implies Definition 2. \n",
"\n",
"So Definitions 1 and 2 are equivalent.\n",
"\n",
"You already know that linear combinations of independent normal variables are normal. If $\\mathbf{X}$ is an invertible linear transformation of i.i.d. standard normal variables $\\mathbf{Z}$, then any linear combination of elements of $\\mathbf{X}$ is also a linear combination of elements of $\\mathbf{Z}$ and hence is normal. This means that Definition 1 implies Definition 3.\n",
"\n",
"Showing that Definition 3 implies Definition 1 requires some math. Multivariate moment generating functions are one way to see why the result is true, if we accept that moment genrating functions determine distributions, but we won't go into that here. "
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