Variational Bayesian Learning of Cooperative Vector Quantizer Model - The Theory

This is the first part of a two-parted report on development of a statistical learning algorithm for a latent variable model referred to as cooperative vector quantizer model. This part presents the theory and mathematical derivations of a variational Bayesian learning algorithm for the model. The model has general applications in the field of machine learning and signal processing. For example it can be used to solve the problem of blind source separation or image separation. Our special interest is in its potential biological application in that we can use the model to simulate signal transduction components regulating gene expression as latent variables. The algorithm is capable of automatically and efficiently determining the number of latent variables of the model, estimating the distribution of the parameters and latent variables. Thus, we can use the model to address following biological questions regarding gene expression regulation: (1) What are the key signal transduction components regulating gene expression in a given kind of cell; (2) How many key components are needed to efficiently encode information for gene expression regulation; (3) What are the states of the key components for a given gene expression data point. Such information will provide insight for understanding the mechanism of information organization of cells, mechanism of diseases and drug effect/toxicity.