Computing based on probabilistic principal component analysis model

An effective solution to problems of multivariate data analysis requires the use of complex probabilistic models, among which the probabilistic model of principal component analysis (PPCA) occupies a worthy place. It allows one to adequately describe real data, formally formulate and solve the problem of choosing its parameters. Practical application of PPCA is associated with a large number of laborious computations. The article discusses techniques for significantly reducing the time spent in calculating the density of the multivariate normal distribution. For this, the expediency of using the Cholesky expansion for the covariance matrix and Woodbury identity for its PPCA factorization is substantiated. A brief description of the experiments is given, which makes it possible to evaluate the real time characteristics of the algorithms and to reveal the conditions for their effective application. Along the way, recommendations are given on the implementation of individual operations.