Sparse Bayesian infinite factor models.
- A. Bhattacharya, D. Dunson
- Computer ScienceBiometrika
- 1 June 2011
This work proposes 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, and develops an efficient Gibbs sampler that scales well as data dimensionality increases.
Dirichlet–Laplace Priors for Optimal Shrinkage
- A. Bhattacharya, D. Pati, N. Pillai, D. Dunson
- MathematicsJournal of the American Statistical Association
- 21 January 2014
This article proposes a new class of Dirichlet–Laplace priors, which possess optimal posterior concentration and lead to efficient posterior computation.
Fast sampling with Gaussian scale-mixture priors in high-dimensional regression.
- A. Bhattacharya, Antik Chakraborty, B. Mallick
- Computer ScienceBiometrika
- 15 June 2015
An efficient way to sample from a class of structured multivariate Gaussian distributions that only requires matrix multiplications and linear system solutions is proposed, unlike existing algorithms that rely on Cholesky factorizations with cubic complexity.
Scalable Bayesian Variable Selection Using Nonlocal Prior Densities in Ultrahigh-dimensional Settings.
- Minsuk Shin, A. Bhattacharya, V. Johnson
- Computer ScienceStatistica sinica
- 25 July 2015
It is found that Bayesian variable selection procedures based on nonlocal priors are competitive to all other procedures in a range of simulation scenarios, and this favorable performance is explained through a theoretical examination of their consistency properties.
Bayesian fractional posteriors
- A. Bhattacharya, D. Pati, Yun Yang
- MathematicsAnnals of Statistics
- 3 November 2016
We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a…
Posterior contraction in sparse Bayesian factor models for massive covariance matrices
- D. Pati, A. Bhattacharya, N. Pillai, D. Dunson
- Computer Science
- 16 June 2012
One of the major contributions is to develop a new class of continuous shrinkage priors and provide insights into their concentration around sparse vectors in inferring high-dimensional covariance matrices where the dimension can be larger than the sample size.
Simplex Factor Models for Multivariate Unordered Categorical Data
- A. Bhattacharya, D. Dunson
- Computer ScienceJournal of the American Statistical Association
- 31 January 2012
A novel class of simplex factor models is proposed that scales well with increasing dimension, with the number of factors treated as unknown, and an efficient proposal for updating the base probability vector in hierarchical Dirichlet models is developed.
Probabilistic Community Detection With Unknown Number of Communities
- J. Geng, A. Bhattacharya, D. Pati
- Computer ScienceJournal of the American Statistical Association
- 25 February 2016
A coherent probabilistic framework for simultaneous estimation of the number of communities and the community structure is proposed, adapting recently developed Bayesian nonparametric techniques to network models and developed concentration properties of nonlinear functions of Bernoulli random variables.
Bayesian shrinkage
- A. Bhattacharya, D. Pati, N. Pillai, D. Dunson
- Computer Science
- 25 December 2012
It is demonstrated that most used shrinkage priors, including the Bayesian Lasso, are suboptimal in high-dimensional set tings, and a new class of Dirichlet Laplace (DL) priors are proposed, which are optimal and lead to effici nt posterior computation exploiting results from normalized random measure theory.
Signal Adaptive Variable Selector for the Horseshoe Prior
- Pallavi Ray, A. Bhattacharya
- Mathematics
- 21 October 2018
In this article, we propose a simple method to perform variable selection as a post model-fitting exercise using continuous shrinkage priors such as the popular horseshoe prior. The proposed Signal…
...
...