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multivariate normal distribution

CAE generated face on background of a MND

Latent space distribution of a CAE for face images – I – unenforced Multivariate Normal Distributions

The analysis of face images by a trained Autoencoder and the generation of face images from statistical vectors is a classical task in Machine Learning. In this post series I want to clarify the properties of vector distributions for face images generated by a trained standard Convolutional Autoencoder [CAE] in its latent space. The dataset primarily used is the CelebA… Read More »Latent space distribution of a CAE for face images – I – unenforced Multivariate Normal Distributions

Multivariate Normal Distributions – IV – Spectral decomposition of the covariance matrix and rotation of the coordinate system

In the preceding posts of this series we have considered a comprehensible definition and basic properties of a non-degenerate “Multivariate Normal Distribution” of vectors in the ℝn [N-MND]. In this post we will make a step in the direction of a numerical analysis of some given finite vector distribution with properties that indicate an underlying N-MND. We want to find… Read More »Multivariate Normal Distributions – IV – Spectral decomposition of the covariance matrix and rotation of the coordinate system

Linear transformed 3-dim Z-distribution

Multivariate Normal Distributions – II – Linear transformation of a random vector with independent standardized normal components

In Machine Learning we typically deal with huge, but finite vector distributions defined in the ℝn. At least in certain regions of the ℝn these distributions may approximate an underlying continuous distribution. In the first post of this series we worked with a special type of continuous vector distribution based on independent 1-dimensional standardized normal distributions for the vector components.… Read More »Multivariate Normal Distributions – II – Linear transformation of a random vector with independent standardized normal components

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 the literature two abbreviations are common: MNDs or MVNs. I will use both synonymously. To get an easy access I want to introduce MNDs as the result of a linear transformations applied to random vectors whose components can be described by independent 1-dimensional normal distributions. Afterward… Read More »Multivariate Normal Distributions – I – Basics and a random vector of independent Gaussians