Canonical Dual Approach to Binary Factor Analysis

Binary Factor Analysis (BFA) is a typical problem of Independent Component Analysis (ICA) where the signal sources are binary. Parameter learning and model selection in BFA are computationally intractable because of the combinatorial complexity. This paper aims at an efficient approach to BFA. For parameter learning, an unconstrained binary quadratic programming (BQP) is reduced to a canonical dual problem with low computational complexity; for model selection, we adopt the Bayesian Ying-Yang (BYY) framework to make model selection automatically during learning. In the experiments, the proposed approach cdual shows superior performance. Another BQP approximation round is also good in model selection and is more efficient. Two other methods, greedy and enum, are more accurate in BQP but fail to compete with cdual and round in BFA. We conclude that a good optimization is essential in a learning process, but the key task of learning is not simply optimization and an over-accurate optimization may not be preferred.