68 citations · 319 across the 71 of their papers we have counts for
30 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…
Adaptive Divide and Conquer with Two Rounds of Communication
Niladri Kal, Botond Szabó, Rajarshi Guhaniyogi +2
We introduce a two-round adaptive communication strategy that enables rate-optimal estimation in the white noise model without requiring prior knowledge of the underlying smoothnes…
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…
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…
Adaptive posterior convergence in sparse high dimensional clipped generalized linear models
Biraj Subhra Guha, Debdeep Pati
We develop a framework to study posterior contraction rates in sparse high dimensional generalized linear models (GLM). We introduce a new family of GLMs, denoted by clipped GLM, w…
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…
Tail-adaptive Bayesian shrinkage
Se Yoon Lee, Peng Zhao, Debdeep Pati +1
Robust Bayesian methods for high-dimensional regression problems under diverse sparse regimes are studied. Traditional shrinkage priors are primarily designed to detect a handful o…
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…
Gaussian Processes with Errors in Variables: Theory and Computation
Shuang Zhou, Debdeep Pati, Tianying Wang +2
Covariate measurement error in nonparametric regression is a common problem in nutritional epidemiology and geostatistics, and other fields. Over the last two decades, this problem…
Bayesian Graph Selection Consistency Under Model Misspecification
Yabo Niu, Debdeep Pati, Bani Mallick
Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the…
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 model selection consistency and oracle inequality with intractable marginal likelihood
Yun Yang, Debdeep Pati
In this article, we investigate large sample properties of model selection procedures in a general Bayesian framework when a closed form expression of the marginal likelihood funct…
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…
Adaptive Bayesian Estimation of Conditional Densities
Andriy Norets, Debdeep Pati
We consider a non-parametric Bayesian model for conditional densities. The model is a finite mixture of normal distributions with covariate dependent multinomial logit mixing proba…