arXiv subjects

Abhra Sarkar

Publications and source records attributed to Abhra Sarkar.

At least 19 recordsLinked to original sources

arXiv2026

Nonparametric Deconvolution and Denoising using Simulation Based Inference

Latent signals are often obscured by measurement noise, yet encode the underlying laws and dynamics of complex systems; learning both the signals and their distributions remains a central challenge in scientific inference. The noise is often non-negligible, and the likelihoods for expressive generative models are often intractable. We utilize a convolutional maximum mean discrepancy (convMMD) loss and propose a likelihood-free framework for nonparametric density deconvolution and empirical Bayes denoising under additive measurement error. Our method learns a latent generative model by matching the observed data distribution to the noise-convolved model distribution. This yields a differentiable, simulation-based objective for multivariate homoscedastic or heteroscedastic noise, compatible with expressive sieve classes such as Gaussian mixtures and normalizing flows. The learned density then serves as an empirical prior for posterior denoising of individual latent values. Theoretically, we extend convMMD from parametric to nonparametric estimation, proving finite-sample bounds for empirical sieve minimizers and $L_2$ convergence rates under Sobolev smoothness. These rates recover the classical inverse-problem dependence: polynomial for ordinary-smooth and logarithmic for super-smooth noises. Our method provides a practical, theoretically grounded approach to deconvolution and denoising under generative latent distribution models.

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arXiv2026

Convolutional Maximum Mean Discrepancy for Inference in Noisy Data

Modern data analyses frequently encounter settings where samples of variables are contaminated by measurement error. Ignoring measurement noise can substantially degrade statistical inference, while existing correction techniques are often computationally costly and inefficient. Recent advances in kernel methods, particularly those based on Maximum Mean Discrepancy (MMD), have enabled flexible, distribution-free inference, yet typically assume precise data and overlook contamination by measurement error. In this work, we introduce a novel framework for inference with samples corrupted by potentially heteroscedastic noise from a known distribution. Central to our approach is the convolutional MMD (convMMD), which compares distributions after noise convolution and retains metric validity under standard kernel conditions. We establish finite-sample deviation bounds that are unaffected by measurement error and prove an equivalence between testing under noise and kernel smoothing. Leveraging these insights, we introduce a convMMD-based estimator for inference with noisy, heteroscedastic observations. We establish its consistency and asymptotic normality, and provide an efficient implementation using stochastic gradient descent. We demonstrate the practical effectiveness of our approach through simulations and applications in astronomy and social sciences.

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arXiv2026

Bayesian Semiparametric Multivariate Density Regression with Coordinate-Wise Predictor Selection

We propose a flexible Bayesian approach for estimating the joint density of a multivariate outcome of interest in the presence of categorical covariates. Leveraging a Gaussian copula framework, our method effectively captures the dependence structure across different coordinates of the multivariate response. The conditional (on covariates) marginal (across outcomes) distributions are modeled as flexible mixtures with shared atoms across coordinates, while the mixture weights are allowed to vary with covariates through a novel Tucker tensor factorization-based structure, which enables the identification of coordinate-specific subsets of influential covariates. In particular, we replace the traditional mode matrices with coordinate-specific random partition models on the covariate levels, offering a flexible mechanism to aggregate covariate levels that exhibit similar effects on the response. Additionally, to handle settings with many covariates, we introduce a Markov chain Monte Carlo algorithm that scales with the number of aggregated levels rather than the original levels, significantly reducing memory requirements and improving computational efficiency. We demonstrate the method's numerical performance through simulation experiments and its practical applicability through the analysis of NHANES dietary data.

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arXiv2025

Bayesian Semiparametric Orthogonal Tucker Factorized Mixed Models for Multi-dimensional Longitudinal Functional Data

We introduce a novel longitudinal mixed model for analyzing complex multidimensional functional data, addressing challenges such as high-resolution, structural complexities, and computational demands. Our approach integrates dimension reduction techniques, including basis function representation and Tucker tensor decomposition, to model complex functional (e.g., spatial and temporal) variations, group differences, and individual heterogeneity while drastically reducing model dimensions. The model accommodates multiplicative random effects whose marginalization yields a novel Tucker-decomposed covariance-tensor framework. To ensure scalability, we employ semi-orthogonal mode matrices implemented via a novel graph-Laplacian-based smoothness prior with low-rank approximation, leading to an efficient posterior sampling method. A cumulative shrinkage strategy promotes sparsity and enables semiautomated rank selection. We establish theoretical guarantees for posterior convergence and demonstrate the method's effectiveness through simulations, showing significant improvements over existing techniques. Applying the method to Alzheimer's Disease Neuroimaging Initiative (ADNI) neuroimaging data reveals novel insights into local brain changes associated with disease progression, highlighting the method's practical utility for studying cognitive decline and neurodegenerative conditions.

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arXiv2024

BMRMM: An R Package for Bayesian Markov (Renewal) Mixed Models

We introduce the BMRMM package implementing Bayesian inference for a class of Markov renewal mixed models which can characterize the stochastic dynamics of a collection of sequences, each comprising alternative instances of categorical states and associated continuous duration times, while being influenced by a set of exogenous factors as well as a 'random' individual. The default setting flexibly models the state transition probabilities using mixtures of Dirichlet distributions and the duration times using mixtures of gamma kernels while also allowing variable selection for both. Modeling such data using simpler Markov mixed models also remains an option, either by ignoring the duration times altogether or by replacing them with instances of an additional category obtained by discretizing them by a user-specified unit. The option is also useful when data on duration times may not be available in the first place. We demonstrate the package's utility using two data sets.

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arXiv2024

Bayesian Semiparametric Longitudinal Inverse-Probit Mixed Models for Category Learning

Understanding how the adult human brain learns novel categories is an important problem in neuroscience. Drift-diffusion models are popular in such contexts for their ability to mimic the underlying neural mechanisms. One such model for gradual longitudinal learning was recently developed by Paulon et al. (2021). Fitting conventional drift-diffusion models, however, requires data on both category responses and associated response times. In practice, category response accuracies are often the only reliable measure recorded by behavioral scientists to describe human learning. However, To our knowledge, drift-diffusion models for such scenarios have never been considered in the literature. To address this gap, in this article, we build carefully on Paulon et al. (2021), but now with latent response times integrated out, to derive a novel biologically interpretable class of `inverse-probit' categorical probability models for observed categories alone. However, this new marginal model presents significant identifiability and inferential challenges not encountered originally for the joint model by Paulon et al. (2021). We address these new challenges using a novel projection-based approach with a symmetry-preserving identifiability constraint that allows us to work with conjugate priors in an unconstrained space. We adapt the model for group and individual-level inference in longitudinal settings. Building again on the model's latent variable representation, we design an efficient Markov chain Monte Carlo algorithm for posterior computation. We evaluate the empirical performance of the method through simulation experiments. The practical efficacy of the method is illustrated in applications to longitudinal tone learning studies.

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arXiv2023

Bayesian Nonparametric Common Atoms Regression for Generating Synthetic Controls in Clinical Trials

The availability of electronic health records (EHR) has opened opportunities to supplement increasingly expensive and difficult to carry out randomized controlled trials (RCT) with evidence from readily available real world data. In this paper, we use EHR data to construct synthetic control arms for treatment-only single arm trials. We propose a novel nonparametric Bayesian common atoms mixture model that allows us to find equivalent population strata in the EHR and the treatment arm and then resample the EHR data to create equivalent patient populations under both the single arm trial and the resampled EHR. Resampling is implemented via a density-free importance sampling scheme. Using the synthetic control arm, inference for the treatment effect can then be carried out using any method available for RCTs. Alternatively the proposed nonparametric Bayesian model allows straightforward model-based inference. In simulation experiments, the proposed method exhibits higher power than alternative methods in detecting treatment effects, specifically for non-linear response functions. We apply the method to supplement single arm treatment-only glioblastoma studies with a synthetic control arm based on historical trials.

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arXiv2022

Bayesian Semiparametric Markov Renewal Mixed Models for Vocalization Syntax

Studying the neurological, genetic and evolutionary basis of human vocal communication mechanisms is an important field of neuroscience. In the absence of high quality data on humans, mouse vocalization experiments in laboratory settings have been proven to be useful in providing valuable insights into mammalian vocal development and evolution, including especially the impact of certain genetic mutations. Data sets from mouse vocalization experiments usually consist of categorical syllable sequences along with continuous inter-syllable interval times for mice of different genotypes vocalizing under various contexts. Few statistical models have considered the inference for both transition probabilities and inter-state intervals. The latter is of particular importance as increased inter-state intervals can be an indication of possible vocal impairment. In this paper, we propose a class of novel Markov renewal mixed models that capture the stochastic dynamics of both state transitions and inter-state interval times. Specifically, we model the transition dynamics and the inter-state intervals using Dirichlet and gamma mixtures, respectively, allowing the mixture probabilities in both cases to vary flexibly with fixed covariate effects as well as random individual-specific effects. We apply our model to analyze the impact of a mutation in the Foxp2 gene on mouse vocal behavior. We find that genotypes and social contexts significantly affect the inter-state interval times but, compared to previous analyses, the influences of genotype and social context on the syllable transition dynamics are weaker.

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arXiv2022

Bayesian Semiparametric Multivariate Density Deconvolution via Stochastic Rotation of Replicates

We consider the problem of multivariate density deconvolution where the distribution of a random vector needs to be estimated from replicates contaminated with conditionally heteroscedastic measurement errors. We propose a conceptually straightforward yet fundamentally novel and highly robust approach to multivariate density deconvolution by stochastically rotating the replicates toward the corresponding true latent values. We also address the additionally significantly challenging problem of accommodating conditionally heteroscedastic measurement errors in this newly introduced framework. We take a Bayesian route to estimation and inference, implemented via an efficient Markov chain Monte Carlo algorithm, appropriately accommodating uncertainty in all aspects of our analysis. Asymptotic convergence guarantees for the method are also established. We illustrate the method's empirical efficacy through simulation experiments and its practical utility in estimating the long-term joint average intakes of different dietary components from their measurement error contaminated 24-hour dietary recalls.

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arXiv2022

Bayesian Tensor Factorized Vector Autoregressive Models for Inferring Granger Causality Patterns from High-Dimensional Multi-subject Panel Neuroimaging Data

Understanding the dynamics of functional brain connectivity patterns using noninvasive neuroimaging techniques is an important focus in human neuroscience. Vector autoregressive (VAR) processes and Granger causality analysis (GCA) have been extensively used for this purpose. While high-resolution multi-subject neuroimaging data are routinely collected now-a-days, the statistics literature on VAR models has remained heavily focused on small-to-moderate dimensional problems and single-subject data. Motivated by these issues, we develop a novel Bayesian random effects panel VAR model for multi-subject high-dimensional neuroimaging data. We begin with a single-subject model that structures the VAR coefficients as a three-way tensor, then reduces the dimensions by applying a Tucker tensor decomposition. A novel sparsity-inducing shrinkage prior allows data-adaptive rank and lag selection. We then extend the approach to a novel random effects model for multi-subject data that carefully avoids the dimensions getting exploded with the number of subjects but also flexibly accommodates subject-specific heterogeneity. We design a Markov chain Monte Carlo algorithm for posterior computation. Finally, GCA with posterior false discovery control is performed on the posterior samples. The method shows excellent empirical performance in simulation experiments. Applied to our motivating functional magnetic resonance imaging study, the approach allows the directional connectivity of human brain networks to be studied in fine detail, revealing meaningful but previously unsubstantiated cortical connectivity patterns.

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arXiv2022

Bayesian Mixed Multidimensional Scaling for Auditory Processing

The human brain distinguishes speech sounds by mapping acoustic signals into a latent perceptual space. This space can be estimated via multidimensional scaling (MDS), preserving the similarity structure in lower dimensions. However, individual and group-level heterogeneity, especially between native and non-native listeners, remains poorly understood. Prior approaches often ignore such variability or cannot capture shared structure, limiting principled comparisons. Moreover, the literature often focuses on latent distances rather than the underlying features themselves. To address these issues, we develop a Bayesian mixed MDS method that accounts for both subject- and group-level heterogeneity, allows for the recovery of unique, identifiable latent features, facilitating their biological interpretability, while also determining the effective dimensionality of the latent space in an automated, data-adaptive manner. Simulations and an auditory neuroscience application demonstrate how these features reconstruct observed distances and vary with individual and language background, revealing novel insights.

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arXiv2022

Bayesian Scalable Precision Factor Analysis for Massive Sparse Gaussian Graphical Models

We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance matrices as they admit a latent factor based representation that allows easy inference. The same is however not true for precision matrices due to the lack of computationally convenient representations which restricts inference to low-to-moderate dimensional problems. We address this remarkable gap in the literature by building on a latent variable representation for such decomposition for precision matrices. The construction leads to an efficient Gibbs sampler that scales very well to high-dimensional problems far beyond the limits of the current state-of-the-art. The ability to efficiently explore the full posterior space also allows the model uncertainty to be easily assessed. The decomposition crucially additionally allows us to adapt sparsity inducing priors to shrink the insignificant entries of the precision matrix toward zero, making the approach adaptable to high-dimensional small-sample-size sparse settings. Exact zeros in the matrix encoding the underlying conditional independence graph are then determined via a novel posterior false discovery rate control procedure. A near minimax optimal posterior concentration rate for estimating precision matrices is attained by our method under mild regularity assumptions. We evaluate the method's empirical performance through synthetic experiments and illustrate its practical utility in data sets from two different application domains.

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arXiv2022

Bayesian Semiparametric Hidden Markov Tensor Partition Models for Longitudinal Data with Local Variable Selection

We present a flexible Bayesian semiparametric mixed model for longitudinal data analysis in the presence of potentially high-dimensional categorical covariates. Building on a novel hidden Markov tensor decomposition technique, our proposed method allows the fixed effects components to vary between dependent random partitions of the covariate space at different time points. The mechanism not only allows different sets of covariates to be included in the model at different time points but also allows the selected predictors' influences to vary flexibly over time. Smooth time-varying additive random effects are used to capture subject specific heterogeneity. We establish posterior convergence guarantees for both function estimation and variable selection. We design a Markov chain Monte Carlo algorithm for posterior computation. We evaluate the method's empirical performances through synthetic experiments and demonstrate its practical utility through real world applications.

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arXiv2022

Bayesian Semiparametric Covariate Informed Multivariate Density Deconvolution

Estimating the marginal and joint densities of the long-term average intakes of different dietary components is an important problem in nutritional epidemiology. Since these variables cannot be directly measured, data are usually collected in the form of 24-hour recalls of the intakes. The problem of estimating the density of the latent long-term average intakes from their observed but error contaminated recalls then becomes a problem of multivariate deconvolution of densities. The underlying densities could potentially vary with the subjects' demographic characteristics such as sex, ethnicity, age, etc. The problem of density deconvolution in the presence of associated precisely measured covariates has, however, never been considered before, not even in the univariate setting. We present a flexible Bayesian semiparametric approach to covariate informed multivariate deconvolution. Building on recent advances in copula deconvolution and conditional tensor factorization techniques, our proposed method not only allows the joint and the marginal densities to vary flexibly with the associated predictors but also allows automatic selection of the most influential predictors. Importantly, the method also allows the density of interest and the density of the measurement errors to vary with potentially different sets of predictors. We design Markov chain Monte Carlo algorithms that enable efficient posterior inference, appropriately accommodating uncertainty in all aspects of our analysis. The empirical efficacy of the proposed method is illustrated through simulation experiments. Its practical utility is demonstrated in the afore-described nutritional epidemiology applications in estimating covariate-adjusted long term intakes of different dietary components. Supplementary materials include substantive additional details and R codes are also available online.

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arXiv2020

Bayesian Semiparametric Longitudinal Drift-Diffusion Mixed Models for Tone Learning in Adults

Understanding how adult humans learn non-native speech categories such as tone information has shed novel insights into the mechanisms underlying experience-dependent brain plasticity. Scientists have traditionally examined these questions using longitudinal learning experiments under a multi-category decision making paradigm. Drift-diffusion processes are popular in such contexts for their ability to mimic underlying neural mechanisms. Motivated by these problems, we develop a novel Bayesian semiparametric inverse Gaussian drift-diffusion mixed model for multi-alternative decision making in longitudinal settings. We design a Markov chain Monte Carlo algorithm for posterior computation. We evaluate the method's empirical performances through synthetic experiments. Applied to our motivating longitudinal tone learning study, the method provides novel insights into how the biologically interpretable model parameters evolve with learning, differ between input-response tone combinations, and differ between well and poorly performing adults.

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arXiv2019

Bayesian Copula Density Deconvolution for Zero-Inflated Data in Nutritional Epidemiology

Estimating the marginal and joint densities of the long-term average intakes of different dietary components is an important problem in nutritional epidemiology. Since these variables cannot be directly measured, data are usually collected in the form of 24-hour recalls of the intakes, which show marked patterns of conditional heteroscedasticity. Significantly compounding the challenges, the recalls for episodically consumed dietary components also include exact zeros. The problem of estimating the density of the latent long-time intakes from their observed measurement error contaminated proxies is then a problem of deconvolution of densities with zero-inflated data. We propose a Bayesian semiparametric solution to the problem, building on a novel hierarchical latent variable framework that translates the problem to one involving continuous surrogates only. Crucial to accommodating important aspects of the problem, we then design a copula-based approach to model the involved joint distributions, adopting different modeling strategies for the marginals of the different dietary components. We design efficient Markov chain Monte Carlo algorithms for posterior inference and illustrate the efficacy of the proposed method through simulation experiments. Applied to our motivating nutritional epidemiology problems, compared to other approaches, our method provides more realistic estimates of the consumption patterns of episodically consumed dietary components.

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arXiv2019

Bayesian Higher Order Hidden Markov Models

We consider the problem of flexible modeling of higher order hidden Markov models when the number of latent states and the nature of the serial dependence, including the true order, are unknown. We propose Bayesian nonparametric methodology based on tensor factorization techniques that can characterize any transition probability with a specified maximal order, allowing automated selection of the important lags and capturing higher order interactions among the lags. Theoretical results provide insights into identifiability of the emission distributions and asymptotic behavior of the posterior. We design efficient Markov chain Monte Carlo algorithms for posterior computation. In simulation experiments, the method vastly outperformed its first and higher order competitors not just in higher order settings, but, remarkably, also in first order cases. Practical utility is illustrated using real world applications.

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arXiv2016

Bayesian Semiparametric Mixed Effects Markov Chains

Studying the neurological, genetic and evolutionary basis of human vocal communication mechanisms using animal vocalization models is an important field of neuroscience. The data sets typically comprise structured sequences of syllables or `songs' produced by animals from different genotypes under different social contexts. We develop a novel Bayesian semiparametric framework for inference in such data sets. Our approach is built on a novel class of mixed effects Markov transition models for the songs that accommodates exogenous influences of genotype and context as well as animal-specific heterogeneity. We design efficient Markov chain Monte Carlo algorithms for posterior computation. Crucial advantages of the proposed approach include its ability to provide insights into key scientific queries related to global and local influences of the exogenous predictors on the transition dynamics via automated tests of hypotheses. The methodology is illustrated using simulation experiments and the aforementioned motivating application in neuroscience.

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