155 citations · 955 across the 56 of their papers we have counts for
69 papers
On the Pseudo-Mixing of Kac's Walk
Natesh S. Pillai, Aaron Smith, Vinod Vaikuntanathan
Motivated by a conjecture of Vaikuntanathan and Zamir, we study the pseudo-mixing of Kac's walk on : whether short trajectories are indistinguishable from Haar meas…
Kac's walk on rotation matrices mixes in steps
Natesh S. Pillai, Aaron Smith
Kac's walk on the rotation group, introduced by Hastings in 1970, is an important high-dimensional Markov chain with applications in statistical physics, statistics, cryptography,…
Microergodicity implies orthogonality of Matérn fields on bounded domains in
Natesh S. Pillai
Matérn random fields are one of the most widely used classes of models in spatial statistics. The fixed-domain identifiability of covariance parameters for stationary Matérn Gaussi…
A Heavily Right Strategy for Statistical Inference with Dependent Studies in Arbitrary Dimensions
Tianle Liu, Xiao-Li Meng, Natesh S. Pillai
We leverage recent advances in heavy-tail approximations for global hypothesis testing with dependent studies to construct approximate confidence regions without modeling or estima…
No Free Lunch for Stochastic Gradient Langevin Dynamics
Natesh S. Pillai, Aaron Smith, Azeem Zaman
As sample sizes grow, scalability has become a central concern in the development of Markov chain Monte Carlo (MCMC) methods. One general approach to this problem, exemplified by t…
Privacy-Preserving Race/Ethnicity Estimation for Algorithmic Bias Measurement in the U.S
Saikrishna Badrinarayanan, Osonde Osoba, Miao Cheng +4
AI fairness measurements, including tests for equal treatment, often take the form of disaggregated evaluations of AI systems. Such measurements are an important part of Responsibl…
Policy Gradients for Optimal Parallel Tempering MCMC
Daniel Zhao, Natesh S. Pillai
Parallel tempering is a meta-algorithm for Markov Chain Monte Carlo that uses multiple chains to sample from tempered versions of the target distribution, enhancing mixing in multi…
Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descent
Tianle Liu, Promit Ghosal, Krishnakumar Balasubramanian +1
Stein Variational Gradient Descent (SVGD) is a nonparametric particle-based deterministic sampling algorithm. Despite its wide usage, understanding the theoretical properties of SV…
Optimal Scaling for the Proximal Langevin Algorithm in High Dimensions
Natesh S. Pillai
The Metropolis-adjusted Langevin (MALA) algorithm is a sampling algorithm that incorporates the gradient of the logarithm of the target density in its proposal distribution. In an…
A Bayesian Gaussian Process for Estimating a Causal Exposure Response Curve in Environmental Epidemiology
Boyu Ren, Xiao Wu, Danielle Braun +2
Motivated by environmental policy questions, we address the challenges of estimation, change point detection, and uncertainty quantification of a causal exposure-response function…
No Free Lunch for Approximate MCMC
James E. Johndrow, Natesh S. Pillai, Aaron Smith
It is widely known that the performance of Markov chain Monte Carlo (MCMC) can degrade quickly when targeting computationally expensive posterior distributions, such as when the sa…
Universality and least singular values of random matrix products: a simplified approach
Rohit Chaudhuri, Vishesh Jain, Natesh S. Pillai
In this note, we show how to provide sharp control on the least singular value of a certain translated linearization matrix arising in the study of the local universality of produc…
Rate-optimal refinement strategies for local approximation MCMC
Andrew D. Davis, Youssef Marzouk, Aaron Smith +1
Many Bayesian inference problems involve target distributions whose density functions are computationally expensive to evaluate. Replacing the target density with a local approxima…
Fast and memory-optimal dimension reduction using Kac's walk
Vishesh Jain, Natesh S. Pillai, Ashwin Sah +2
In this work, we analyze dimension reduction algorithms based on the Kac walk and discrete variants. (1) For points in , we design an optimal Johnson-Lindenstra…
Unbiased estimation of log normalizing constants with applications to Bayesian cross-validation
Maxime Rischard, Pierre E. Jacob, Natesh Pillai
Posterior distributions often feature intractable normalizing constants, called marginal likelihoods or evidence, that are useful for model comparison via Bayes factors. This has m…
Simple Conditions for Metastability of Continuous Markov Chains
Oren Mangoubi, Natesh S. Pillai, Aaron Smith
A family of Markov chains is said to exhibit with if its spectral gap (or some other…
Does Hamiltonian Monte Carlo mix faster than a random walk on multimodal densities?
Oren Mangoubi, Natesh S. Pillai, Aaron Smith
Hamiltonian Monte Carlo (HMC) is a very popular and generic collection of Markov chain Monte Carlo (MCMC) algorithms. One explanation for the popularity of HMC algorithms is their…
Bias correction in daily maximum and minimum temperature measurements through Gaussian process modeling
Maxime Rischard, Natesh Pillai, Karen A. McKinnon
The Global Historical Climatology Network-Daily database contains, among other variables, daily maximum and minimum temperatures from weather stations around the globe. It is long…
Diagnosing missing always at random in multivariate data
Iavor Bojinov, Natesh Pillai, Donald Rubin
Models for analyzing multivariate data sets with missing values require strong, often unassessable, assumptions. The most common of these is that the mechanism that created the mis…
Mixing Times for a Constrained Ising Process on the Two-Dimensional Torus at Low Density
Natesh S Pillai, Aaron Smith
We study a kinetically constrained Ising process (KCIP) associated with a graph and density parameter ; this process is an interacting particle system with state space $\{ 0…
Designs for estimating the treatment effect in networks with interference
Ravi Jagadeesan, Natesh Pillai, Alexander Volfovsky
In this paper we introduce new, easily implementable designs for drawing causal inference from randomized experiments on networks with interference. Inspired by the idea of matchin…
Optimal Scaling of the MALA algorithm with Irreversible Proposals for Gaussian targets
Michela Ottobre, Natesh S. Pillai, Konstantinos Spiliopoulos
It is well known in many settings that reversible Langevin diffusions in confining potentials converge to equilibrium exponentially fast. Adding irreversible perturbations to the d…
A Divide and Conquer Strategy for High Dimensional Bayesian Factor Models
Gautam Sabnis, Debdeep Pati, Barbara Engelhardt +1
We propose a distributed computing framework, based on a divide and conquer strategy and hierarchical modeling, to accelerate posterior inference for high-dimensional Bayesian fact…
Parallel local approximation MCMC for expensive models
Patrick Conrad, Andrew Davis, Youssef Marzouk +2
Performing Bayesian inference via Markov chain Monte Carlo (MCMC) can be exceedingly expensive when posterior evaluations invoke the evaluation of a computationally expensive model…