  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.
