Bayesian cumulative shrinkage for infinite factorizations.

Journal Article (Journal Article)

The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing complexity. In this article we propose a novel increasing shrinkage prior, called the cumulative shrinkage process, for the parameters that control the dimension in overcomplete formulations. Our construction has broad applicability and is based on an interpretable sequence of spike-and-slab distributions which assign increasing mass to the spike as the model complexity grows. Using factor analysis as an illustrative example, we show that this formulation has theoretical and practical advantages relative to current competitors, including an improved ability to recover the model dimension. An adaptive Markov chain Monte Carlo algorithm is proposed, and the performance gains are outlined in simulations and in an application to personality data.

Full Text

Duke Authors

Cited Authors

  • Legramanti, S; Durante, D; Dunson, DB

Published Date

  • September 2020

Published In

Volume / Issue

  • 107 / 3

Start / End Page

  • 745 - 752

PubMed ID

  • 32831355

Pubmed Central ID

  • PMC7430941

Electronic International Standard Serial Number (EISSN)

  • 1464-3510

International Standard Serial Number (ISSN)

  • 0006-3444

Digital Object Identifier (DOI)

  • 10.1093/biomet/asaa008


  • eng