Embedding and latent variable models using maximal correlation

Abstract

Finding low dimensional latent variable models is a useful technique in inferring unobserved affinity between unobserved co-occurrences. We explore using maximal correlation and the alternating conditional expectation algorithm to construct embeddings one dimensional at a time to maximally preserve the linear correlation in the embedding space. Each dimension is enforced to be orthogonal to all other dimensions to not encode redundant information. Intuitively, we want to map objects that frequently co-occur to be close in the embedding space. However, often there are unobserved or under-sampled pairs that skew the result. We derive simple regularization techniques to compensate for those outliers. Additionally, optimizing for the preservation of maximal correlations after processing lets us induce informative soft clustering and mixture models. Empirical results on natural language processing datasets show that our technique performs comparably to popular word embedding algorithms.