Bayesian Deep ICE

Deep Independent Component Estimation (DICE) has many applications in modern day machine learning as a feature engineering extraction method. We provide a novel latent variable representation of independent component analysis that enables both point estimates via expectation-maximization (EM) and full posterior sampling via Markov Chain Monte Carlo (MCMC) algorithms. Our methodology also applies to flow-based methods for nonlinear feature extraction. We discuss how to implement conditional posteriors and envelope-based methods for optimization. Through this representation hierarchy, we unify a number of hitherto disjoint estimation procedures. We illustrate our methodology and algorithms on a numerical example. Finally, we conclude with directions for future research.