Abstract
As a principled dimension reduction technique, factor models have been widely adopted in applications. However, conducting a proper Bayesian factor analysis can be subtle in high-dimensional settings since it requires both a careful prescription of the prior distribution and a suitable computational strategy. We analyze issues of posterior inconsistency and sensitivity under different priors for high-dimensional sparse normal factor models, and show why adopting the n-orthonormal factor assumption can resolve these issues and lead to a more robust and efficient Bayesian analysis. We also provide an efficient Gibbs sampler to conduct the required computation, and show that it can be orders of magnitude more efficient than compared existing algorithms.
Highlights
Factor models, which assume that the information in high-dimensional observations can be captured by a few latent factors, have been widely adopted in social science, economics, bioinformatics, and many other fields that need interpretable dimension reduction for their data
Under the SpSL-Indian Buffet process (IBP) prior with λ0 = 20 and λ1 = 0.1, we show in Figure 2 ten snapshots of the heat-map of |B| in a Gibbs sampling trajectory with all model parameters initialized at their true values
We focus on studying the connec√tion between posterior consistency and the factor assumption, and demonstrate why the n-orthonormal factor model is a natural choice under high dimensions
Summary
Factor models, which assume that the information in high-dimensional observations can be captured by a few latent factors, have been widely adopted in social science, economics, bioinformatics, and many other fields that need interpretable dimension reduction for their data. Compared to other methods for boosting MCMC (e.g., Fruehwirth-Schnatter and Lopes (2018)), our approach is mo√re straightforward and easier to implement For these reasons, we suggest to use the n-orthonormal factor model in place of the normal factor model before specifying priors and conducting the downstream Bayesian analysis in high-dimensional settings.
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