Covariate-dependent dictionary learning and sparse coding
A dependent hierarchical beta process (dHBP) is developed as a prior for data that may be represented in terms of a sparse set of latent features (dictionary elements), with covariate-dependent feature usage. The dHBP is applicable to general covariates and data models, imposing that signals with similar covariates are likely to be manifested in terms of similar features. As an application, we consider the simultaneous sparse modeling of multiple images, with the covariate of a given image linked to its similarity to all other images (as applied in manifold learning). Efficient inference is performed using hybrid Gibbs, Metropolis-Hastings and slice sampling.