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Multivariate Normal Distributions

Aspects of Multivariate Normal Distributions and their relation to ML

Bivariate Normal Distribution from face data encoded by a CAE

Bivariate Normal Distribution – derivation of the covariance and correlation by integration of the probability density

In a previous post of this blog we have derived the functional form of a bivariate normal distribution [BND] of a two 1-dimensional random variables X and Y). By rewriting the probability density function [pdf] in terms of vectors (x, y)T and a matrix Σ-1 we recognized that a coefficient appearing in a central exponential of the pdf could be… Read More »Bivariate Normal Distribution – derivation of the covariance and correlation by integration of the probability density

Probability density function of a Bivariate Normal Distribution – derived from assumptions on marginal distributions and functional factorization

For a better understanding of ML experiments regarding a generator of human faces based on a convolutional autoencoder we need an understanding of multivariate and bivariate normal distributions and their probability densities. This post is about the probability density function of a bivariate normal distribution depending on two correlated random variables X and Y. Most derivations of the mathematical form… Read More »Probability density function of a Bivariate Normal Distribution – derived from assumptions on marginal distributions and functional factorization