35 citations · 108 across the 20 of their papers we have counts for
24 papers
Sample complexity bounds for categorical Markov random fields via Discrete Diffusions
Shivam Kumar, Nabarun Deb
Many applications in statistics, economics, and physics require sampling from high-dimensional categorical distributions with local dependence structures. Examples include finite m…
LDP for Tensor Forms
Reihaneh Malekian, Sohom Bhattacharya, Nabarun Deb +1
In this paper, we study the large deviation principle (LDP) for a tensor-weighted functional of i.i.d. random variables, when the sequence of tensors converges under a variant of t…
Normal approximations in nonparametric empirical Bayes
Jiafeng Chen, Nabarun Deb, Nikolaos Ignatiadis
Empirical Bayes analyses routinely model noisy measurements of latent parameters as normal, justifying this by an informal appeal to the central limit theorem (CLT). This paper put…
Parametric Mean-Field empirical Bayes in high-dimensional linear regression
Seunghyun Lee, Nabarun Deb
In this paper, we consider the problem of parametric empirical Bayes estimation of an i.i.d. prior in high-dimensional Bayesian linear regression, with random design. We obtain the…
Pivotal CLTs for Pseudolikelihood via Conditional Centering in Dependent Random Fields
Nabarun Deb
In this paper, we study fluctuations of conditionally centered statistics of the form where $(σ_1,\ldots ,σ_N)…
CLT in high-dimensional Bayesian linear regression with low SNR
Seunghyun Lee, Nabarun Deb, Sumit Mukherjee
We study central limit theorems for linear statistics in high-dimensional Bayesian linear regression with product priors. Unlike the existing literature where the focus is on poste…
Phase Transition in Nonparametric Minimax Rates for Covariate Shifts on Approximate Manifolds
Yuyao Wang, Nabarun Deb, Debarghya Mukherjee
We study nonparametric regression under covariate shift with structured data, where a small amount of labeled target data is supplemented by a large labeled source dataset. In many…
No-Regret Generative Modeling via Parabolic Monge-Ampère PDE
Nabarun Deb, Tengyuan Liang
We introduce a novel generative modeling framework based on a discretized parabolic Monge-Ampère PDE, which emerges as a continuous limit of the Sinkhorn algorithm commonly used in…
Fluctuations in random field Ising models
Seunghyun Lee, Nabarun Deb, Sumit Mukherjee
This paper establishes a CLT for linear statistics of the form with quantitative Berry-Esseen bounds, where is an observati…
Distribution-free Measures of Association based on Optimal Transport
Nabarun Deb, Promit Ghosal, Bodhisattva Sen
In this paper we propose and study a class of nonparametric, yet interpretable measures of association between two random vectors and taking values in an…
Trade-off Between Dependence and Complexity for Nonparametric Learning -- an Empirical Process Approach
Nabarun Deb, Debarghya Mukherjee
Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many…
Wasserstein Mirror Gradient Flow as the limit of the Sinkhorn Algorithm
Nabarun Deb, Young-Heon Kim, Soumik Pal +1
We prove that the sequence of marginals obtained from the iterations of the Sinkhorn algorithm or the iterative proportional fitting procedure (IPFP) on joint densities, converges…
Gibbs Measures with Multilinear Forms
Sohom Bhattacharya, Nabarun Deb, Sumit Mukherjee
In this paper, we study a class of multilinear Gibbs measures with Hamiltonian given by a generalized -statistic and with a general base measure. Expressing the asympto…
LDP for Inhomogeneous U-Statistics
Sohom Bhattacharya, Nabarun Deb, Sumit Mukherjee
In this paper we derive a Large Deviation Principle (LDP) for inhomogeneous U/V-statistics of a general order. Using this, we derive a LDP for two types of statistics: random multi…
Robustness and Efficiency of Rosenbaum's Rank-based Estimator in Randomized Trials: A Design-based Perspective
Aditya Ghosh, Nabarun Deb, Bikram Karmakar +1
Mean-based estimators of causal effects in randomized experiments may behave poorly if the potential outcomes have a heavy tail or contain outliers. An alternative estimator propos…
Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections
Nabarun Deb, Promit Ghosal, Bodhisattva Sen
Optimal transport maps between two probability distributions and on have found extensive applications in both machine learning and statistics. In practice, t…
Exact Detection Thresholds and Minimax Optimality of Chatterjee's Correlation Coefficient
Arnab Auddy, Nabarun Deb, Sagnik Nandy
Recently, Chatterjee (2021) introduced a new rank-based correlation coefficient which can be used to measure the strength of dependence between two random variables. This coefficie…
Pitman Efficiency Lower Bounds for Multivariate Distribution-Free Tests Based on Optimal Transport
Nabarun Deb, Bhaswar B. Bhattacharya, Bodhisattva Sen
Distribution-free tests such as the Wilcoxon rank sum test are popular for testing the equality of two univariate distributions. Among the important reasons for their popularity ar…
Kernel Partial Correlation Coefficient -- a Measure of Conditional Dependence
Zhen Huang, Nabarun Deb, Bodhisattva Sen
In this paper we propose and study a class of simple, nonparametric, yet interpretable measures of conditional dependence between two random variables and given a third var…
Detecting Structured Signals in Ising Models
Nabarun Deb, Rajarshi Mukherjee, Sumit Mukherjee +1
In this paper, we study the effect of dependence on detecting a class of signals in Ising models, where the signals are present in a structured way. Examples include Ising Models o…
Measuring Association on Topological Spaces Using Kernels and Geometric Graphs
Nabarun Deb, Promit Ghosal, Bodhisattva Sen
In this paper we propose and study a class of simple, nonparametric, yet interpretable measures of association between two random variables and taking values in general top…
Fluctuations in Mean-Field Ising models
Nabarun Deb, Sumit Mukherjee
In this paper, we study the fluctuations of the average magnetization in an Ising model on an approximately regular graph on vertices. In particular, if is \e…
Multivariate Rank-based Distribution-free Nonparametric Testing using Measure Transportation
Nabarun Deb, Bodhisattva Sen
In this paper, we propose a general framework for distribution-free nonparametric testing in multi-dimensions, based on a notion of multivariate ranks defined using the theory of m…
Two-component Mixture Model in the Presence of Covariates
Nabarun Deb, Sujayam Saha, Adityanand Guntuboyina +1
In this paper, we study a generalization of the two-groups model in the presence of covariates --- a problem that has recently received much attention in the statistical literature…