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Mathematics

Some math topics with relation to ML

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 [pdf] of a bivariate normal distribution of two correlated Gaussian random variables X and Y. Most derivations of the mathematical… Read More »Probability density function of a Bivariate Normal Distribution – derived from assumptions on marginal distributions and functional factorization

Surfaces of n-dimensional ellipsoids – I – quadratic form and matrix equation

Multidimensional ellipsoids are mathematically interesting figures per se. But there is a reason why they sometimes also appear in the context of Machine Learning experiments. One reason is that Multivariate Normal Distributions [MND] often describe the statistical distributions of properties which characterize natural objects we investigate by ML-methods. And the locations of constant probability density of MNDs are surfaces of… Read More »Surfaces of n-dimensional ellipsoids – I – quadratic form and matrix equation