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contour ellipsoids of a projected MND

Multivariate Normal Distributions – I – Basics and a random vector of independent Gaussians

This post series is about mathematical aspects of so called “Multivariate Normal Distributions“. In respective literature two abbreviations are common: MNDs or MVNs. I will use both synonymously. To get an easy access, I want to introduce a MND as the result of a linear transformations applied to random vectors whose components can be described by independent 1-dimensional normal distributions.… Read More »Multivariate Normal Distributions – I – Basics and a random vector of independent Gaussians

Short ResNet training on CIFAR10 over 21 epochs

AdamW for a ResNet56v2 – V – weight decay and cosine shaped schedule of the learning rate

In this post series we try to find methods to reduce the number of epochs for the training of ResNets on image datasets. Our test case is CIFAR10. In this post we will test a modified cosine shaped schedule for a systematic and fast reduction of the learning rate LR. This supplements the approaches described in previous posts of this… Read More »AdamW for a ResNet56v2 – V – weight decay and cosine shaped schedule of the learning rate

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 a function g2(x,y for the probability density f a Bivariate Normal Distribution [BVD] of two 1-dimensional random variables X and Y). By rewriting the probability density function [pdf] in terms of vectors (x, y)T and a coupling matrix Σ-1 we recognized that a coefficient appearing in a central exponential of… 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 [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