68 citations · 353 across the 57 of their papers we have counts for
25 papers · 1 filter
Frequentist Regret Analysis of Gaussian Process Thompson Sampling via Fractional Posteriors
Somjit Roy, Prateek Jaiswal, Anirban Bhattacharya +2
We study Gaussian Process Thompson Sampling (GP-TS) for sequential decision-making over compact, continuous action spaces and provide a frequentist regret analysis based on fractio…
Consistent DAG selection for Bayesian causal discovery under general error distributions
Anamitra Chaudhuri, Anirban Bhattacharya, Yang Ni
We consider the problem of learning the underlying causal structure among a set of variables, which are assumed to follow a Bayesian network or, more specifically, a linear recursi…
Adaptive Resolution for Finite-Rank Gaussian Processes
Jaehoan Kim, Anirban Bhattacharya, Debdeep Pati
Finite-rank approximations are widely used to scale Gaussian process (GP) regression, but their posterior behavior can differ from that of the corresponding parent GP prior. We stu…
Robust Estimation in metric spaces: Achieving Exponential Concentration with a Fréchet Median
Jakwang Kim, Jiyoung Park, Anirban Bhattacharya
There is growing interest in developing statistical estimators that achieve exponential concentration around a population target even when the data distribution has heavier than ex…
Memory Efficient And Minimax Distribution Estimation Under Wasserstein Distance Using Bayesian Histograms
Peter Matthew Jacobs, Lekha Patel, Anirban Bhattacharya +1
We study Bayesian histograms for distribution estimation on under the Wasserstein distance in the i.i.d sampling regime. We newly show that when…
Statistical Guarantees for Transformation Based Models with Applications to Implicit Variational Inference
Sean Plummer, Shuang Zhou, Anirban Bhattacharya +2
Transformation-based methods have been an attractive approach in non-parametric inference for problems such as unconditional and conditional density estimation due to their unique…
Statistical optimality and stability of tangent transform algorithms in logit models
Indrajit Ghosh, Anirban Bhattacharya, Debdeep Pati
A systematic approach to finding variational approximation in an otherwise intractable non-conjugate model is to exploit the general principle of convex duality by minorizing the m…
Evidence bounds in singular models: probabilistic and variational perspectives
Anirban Bhattacharya, Debdeep Pati, Sean Plummer
The marginal likelihood or evidence in Bayesian statistics contains an intrinsic penalty for larger model sizes and is a fundamental quantity in Bayesian model comparison. Over the…
Nonasymptotic Laplace approximation under model misspecification
Anirban Bhattacharya, Debdeep Pati
We present non-asymptotic two-sided bounds to the log-marginal likelihood in Bayesian inference. The classical Laplace approximation is recovered as the leading term. Our derivatio…
Mass-shifting phenomenon of truncated multivariate normal priors
Shuang Zhou, Pallavi Ray, Debdeep Pati +1
We show that lower-dimensional marginal densities of dependent zero-mean normal distributions truncated to the positive orthant exhibit a mass-shifting phenomenon. Despite the trun…
On Statistical Optimality of Variational Bayes
Debdeep Pati, Anirban Bhattacharya, Yun Yang
The article addresses a long-standing open problem on the justification of using variational Bayes methods for parameter estimation. We provide general conditions for obtaining opt…
-Variational Inference with Statistical Guarantees
Yun Yang, Debdeep Pati, Anirban Bhattacharya
We propose a family of variational approximations to Bayesian posterior distributions, called -VB, with provable statistical guarantees. The standard variational approximation i…
Frequentist coverage and sup-norm convergence rate in Gaussian process regression
Yun Yang, Anirban Bhattacharya, Debdeep Pati
Gaussian process (GP) regression is a powerful interpolation technique due to its flexibility in capturing non-linearity. In this paper, we provide a general framework for understa…
Adaptive posterior convergence rates in non-linear latent variable models
Shuang Zhou, Debdeep Pati, Anirban Bhattacharya +1
Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In…
Bayesian fractional posteriors
Anirban Bhattacharya, Debdeep Pati, Yun Yang
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 func…
Sub-optimality of some continuous shrinkage priors
Anirban Bhattacharya, David B. Dunson, Debdeep Pati +1
Two-component mixture priors provide a traditional way to induce sparsity in high-dimensional Bayes models. However, several aspects of such a prior, including computational comple…
Optimal Bayesian estimation in stochastic block models
Debdeep Pati, Anirban Bhattacharya
With the advent of structured data in the form of social networks, genetic circuits and protein interaction networks, statistical analysis of networks has gained popularity over re…
Posterior contraction in Gaussian process regression using Wasserstein approximations
Anirban Bhattacharya, Debdeep Pati
We study posterior rates of contraction in Gaussian process regression with unbounded covariate domain. Our argument relies on developing a Gaussian approximation to the posterior…
Optimal Bayesian estimation in random covariate design with a rescaled Gaussian process prior
Debdeep Pati, Anirban Bhattacharya, Guang Cheng
In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the…
Tensor decompositions and sparse log-linear models
James E. Johndrow, Anirban Battacharya, David B. Dunson
Contingency table analysis routinely relies on log linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a low rank tensor f…
Dirichlet-Laplace priors for optimal shrinkage
Anirban Bhattacharya, Debdeep Pati, Natesh S. Pillai +1
Penalized regression methods, such as regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under spars…
Bayesian shrinkage
Anirban Bhattacharya, Debdeep Pati, Natesh S. Pillai +1
Penalized regression methods, such as regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under spars…
Posterior contraction in sparse Bayesian factor models for massive covariance matrices
Debdeep Pati, Anirban Bhattacharya, Natesh S. Pillai +1
Sparse Bayesian factor models are routinely implemented for parsimonious dependence modeling and dimensionality reduction in high-dimensional applications. We provide theoretical u…
Anisotropic function estimation using multi-bandwidth Gaussian processes
Anirban Bhattacharya, Debdeep Pati, David Dunson
In nonparametric regression problems involving multiple predictors, there is typically interest in estimating an anisotropic multivariate regression surface in the important predic…