Bayesian cumulative shrinkage for infinite factorizations
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There are a variety of Bayesian models relying on representations in which the dimension of the parameter space is, itself, unknown. For example, in factor analysis the number of latent variables is, in general, not known and has to be inferred from the data. Although classical shrinkage priors are useful in these situations, incorporating cumulative shrinkage can provide a more effective option which progressively penalizes more complex expansions. A successful proposal within this setting is the multiplicative gamma process. However, such a process is limited in scope, and has some drawbacks in terms of shrinkage properties and interpretability. We overcome these issues via a novel class of convex mixtures of spike and slab distributions assigning increasing mass to the spike through an adaptive function which grows with model complexity. This prior has broader applicability, simple interpretation, parsimonious representation, and induces adaptive cumulative shrinkage of the terms associated with redundant, and potentially infinite, dimensions. Performance gains are illustrated in simulation studies.
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