We study several properties of matrix variate beta type 3 distribution. We also derive probability density functions of the product of two independent random matrices when one of them is beta type 3. These densities are expressed in terms of Appell’s first hypergeometric function F1 and Humbert’s confluent hypergeometric functionΦ1 of matrix arguments. Further, a bimatrix variate generalization...

In stationary subspace analysis (SSA) one assumes that the observable p-variate time series is a linear mixture of k-variate nonstationary and (p−k)-variate series. The aim then to estimate unmixing matrix which transforms observed multivariate onto components. classical approach data are projected subspaces by minimizing Kullback–Leibler divergence between Gaussian distributions, method only d...

Abstract. Factorisation (also known as “factor separation”) is widely used in the analysis of numerical simulations. It allows changes properties a system to be attributed multiple variables associated with that system. There are many possible factorisation methods; here we discuss three previously proposed factorisations have been applied field climate modelling: linear factorisation, Stein an...

Modern datasets are becoming heterogeneous. To this end, we present in this paper MixedVariate Restricted Boltzmann Machines for simultaneously modelling variables of multiple types and modalities, including binary and continuous responses, categorical options, multicategorical choices, ordinal assessment and category-ranked preferences. Dependency among variables is modeled using latent binary...

This paper introduces a novel class of Bayesian models for multivariate time series analysis based on a synthesis of dynamic linear models and graphical models. The synthesis uses sparse graphical modelling ideas to introduce structured, conditional independence relationships in the time-varying, cross-sectional covariance matrices of multiple time series. We define this new class of models and...

Stochastic gradient optimization is a class of widely used algorithms for training machine learning models. To optimize an objective, it uses the noisy gradient computed from the random data samples instead of the true gradient computed from the entire dataset. However, when the variance of the noisy gradient is large, the algorithm might spend much time bouncing around, leading to slower conve...