# Sparse Bayesian infinite factor models.

@article{Bhattacharya2011SparseBI, title={Sparse Bayesian infinite factor models.}, author={Anirban Bhattacharya and David B. Dunson}, journal={Biometrika}, year={2011}, volume={98 2}, pages={ 291-306 } }

We focus on sparse modelling of high-dimensional covariance matrices using Bayesian latent factor models. We propose a multiplicative gamma process shrinkage prior on the factor loadings which allows introduction of infinitely many factors, with the loadings increasingly shrunk towards zero as the column index increases. We use our prior on a parameter-expanded loading matrix to avoid the order dependence typical in factor analysis models and develop an efficient Gibbs sampler that scales well…

## 334 Citations

Bayesian group factor analysis with structured sparsity

- Mathematics, Computer ScienceJ. Mach. Learn. Res.
- 2016

A structured Bayesian group factor analysis model is developed that extends the factor model to multiple coupled observation matrices and allows for both dense and sparse latent factors so that covariation among either all features or only a subset of features can be recovered.

Bayesian group latent factor analysis with structured sparsity

- Mathematics, Biology
- 2014

A structured Bayesian group factor analysis model is developed that extends the factor model to multiple coupled observation matrices and allows for both dense and sparse latent factors so that covariation among either all features or only a subset of features can both be recovered.

Sparse Bayesian Factor Analysis when the Number of Factors is Unknown

- Mathematics
- 2018

Despite the popularity of sparse factor models, little attention has been given to formally address identifiability of these models beyond standard rotation-based identification such as the positive…

Bayesian group latent factor analysis with structured sparse priors

- Mathematics
- 2014

Latent factor models are the canonical statistical tool for exploratory analyses of low-dimensional linear structure for an observation matrix with p features across n samples. We develop a Bayesian…

Robust Sparse Bayesian Infinite Factor Models

- Mathematics
- 2020

Most of previous works and applications of Bayesian factor model have assumed the normal likelihood regardless of its validity. We propose a Bayesian factor model for heavy-tailed high-dimensional…

Bayesian cumulative shrinkage for infinite factorizations.

- Mathematics, MedicineBiometrika
- 2020

This article proposes a novel increasing shrinkage prior, called the cumulative shrinkage process, for the parameters that control the dimension in overcomplete formulations, and shows that this formulation has theoretical and practical advantages relative to current competitors, including an improved ability to recover the model dimension.

Bayesian Precision Factor Analysis for High-dimensional Sparse Gaussian Graphical Models

- 2021

Gaussian graphical models are popular tools for studying the dependence relationships between different random variables. We propose a novel approach to Gaussian graphical models that relies on…

Clustering multivariate data using factor analytic Bayesian mixtures with an unknown number of components

- Computer Science, MathematicsStat. Comput.
- 2020

This work considers a set of eight parameterizations, giving rise to parsimonious representations of the covariance matrix per cluster, which are compared to similar models estimated using the expectation–maximization algorithm on simulated and real datasets.

Bayesian Gaussian Copula Factor Models for Mixed Data

- Mathematics, MedicineJournal of the American Statistical Association
- 2013

A novel class of Bayesian Gaussian copula factor models that decouple the latent factors from the marginal distributions is proposed and new theoretical and empirical justifications for using this likelihood in Bayesian inference are provided.

Expandable factor analysis

- Mathematics, MedicineBiometrika
- 2017

This work proposes expandable factor analysis for scalable inference in factor models when the number of factors is unknown, relying on a continuous shrinkage prior for efficient maximum a posteriori estimation of a low-rank and sparse loadings matrix.

## References

SHOWING 1-10 OF 41 REFERENCES

Default Prior Distributions and Efficient Posterior Computation in Bayesian Factor Analysis

- Computer Science, MedicineJournal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
- 2009

A default, heavy-tailed prior distribution specification is proposed, which is induced through parameter expansion while facilitating efficient posterior computation and an approach to allow uncertainty in the number of factors is developed.

BAYESIAN MODEL ASSESSMENT IN FACTOR ANALYSIS

- Computer Science
- 2004

This work explores reversible jump MCMC methods that build on sets of parallel Gibbs sampling-based analyses to generate suitable empirical proposal distributions and that address the challenging problem of finding efficient proposals in high-dimensional models.

Parsimonious Bayesian Factor Analysis when the Number of Factors is Unknown

- Mathematics
- 2010

We introduce a new and general set of identifiability conditions for factor models which handles the ordering problem associated with current common practice. In addition, the new class of…

Bayesian factor regression models in the''large p

- Computer Science
- 2003

Bayesian factor regression models with many explanatory variables are discussed, and sparse latent factor models are introduced to induce sparsity in factor loadings matrices to provide a novel approach to variable selection with very many predictors.

Factor analysis and outliers: A Bayesian approach

- Computer Science
- 1999

A Gibbs sampling approach is suggested for a multivariate outlier model in extension of the approach of Verdinelli and Wasserman (1991) and the approach is demonstrated for the language data set of Fuller (1987).

Bayesian factor analysis with fat-tailed factors and its exact marginal likelihood

- Computer Science, MathematicsJ. Multivar. Anal.
- 2009

The exact marginal likelihood is derived and enables us to evaluate posterior model probabilities without inducing the above problems.

Infinite Sparse Factor Analysis and Infinite Independent Components Analysis

- Computer ScienceICA
- 2007

Four variants of the nonparametric Bayesian extension of Independent Components Analysis are described, with Gaussian or Laplacian priors on X and the one or two-parameter IBPs, and Bayesian inference under these models is demonstrated using a Markov Chain Monte Carlo algorithm.

Bayesian estimation and test for factor analysis model with continuous and polytomous data in several populations.

- Mathematics, MedicineThe British journal of mathematical and statistical psychology
- 2001

A Bayesian approach for the multisample factor analysis model with continuous and polytomous variables is developed and it is shown that the conditional distributions involved in the implementation are the familiar uniform, gamma, normal, univariate truncated normal and Wishart distributions.

Regularized estimation of large covariance matrices

- Mathematics
- 2008

This paper considers estimating a covariance matrix of p variables from n observations by either banding the sample covariance matrix or estimating a banded version of the inverse of the covariance.…

Bayesian Selection on the Number of Factors in a Factor Analysis Model

- Mathematics
- 2002

This paper considers a Bayesian approach for selecting the number of factors in a factor analysis model with continuous and polvtomous variables. A procedure for computing the important statistic in…