arXiv subjects

Antik Chakraborty

Publications and source records attributed to Antik Chakraborty.

10 recordsLinked to original sources

arXiv2026

Exact and Approximate MCMC for Doubly-intractable Probabilistic Graphical Models Leveraging the Underlying Independence Model

Bayesian inference for doubly-intractable pairwise exponential graphical models typically involves variations of the exchange algorithm or approximate Markov chain Monte Carlo (MCMC) samplers. However, existing methods for both classes of algorithms require either perfect samplers or sequential samplers for complex models, which are often either not available, or suffer from poor mixing, especially in high dimensions. We develop a method that does not require perfect or sequential sampling, and can be applied to both classes of methods: exact and approximate MCMC. The key to our approach is to utilize the tractable independence model underlying the intractable probabilistic graphical model for the purpose of constructing a finite sample unbiased Monte Carlo (and not MCMC) estimate of the Metropolis--Hastings ratio. This innovation turns out to be crucial for scalability in high dimensions. The method is demonstrated on the Ising model. Gradient-based alternatives to construct a proposal, such as Langevin and Hamiltonian Monte Carlo approaches, also arise as a natural corollary to our general procedure, and are demonstrated as well.

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arXiv2026

Empirical Bayes data integreation for multi-response regression

Motivated by applications in tissue-wide association studies (TWAS), we develop a flexible and theoretically grounded empirical Bayes approach for integrating %vector-valued outcomes data obtained from different sources. We propose a linear shrinkage estimator that effectively shrinks singular values of a data matrix. This problem is closely connected to estimating covariance matrices under a specific loss, for which we develop asymptotically optimal estimators. The basic linear shrinkage estimator is then extended to a local linear shrinkage estimator, offering greater flexibility. Crucially, the proposed method works under sparse/dense or low-rank/non low-rank parameter settings unlike well-known sparse or reduced rank estimators in the literature. Furthermore, the empirical Bayes approach offers greater scalability in computation compared to intensive full Bayes procedures. The method is evaluated through an extensive set of numerical experiments, and applied to a real TWAS data obtained from the Genotype-Tissue Expression (GTEx) project.

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arXiv2025

State Space Modeling of Mortgage Default Rates under Natural Hazard Shocks

Mortgage default rates, on the one hand, serve as a measure of economic health to support decision-making by insurance companies, and on the other hand, is a key risk factor in the asset-liability management (ALM) practice, as mortgage related assets constitute a significant proportion of insurers' investment portfolios. This paper studies the relationship between economic losses due to natural hazards and mortgage default rates. The topic is greatly relevant to the insurance industry, as excessive insurance losses from natural hazards can lead to a surge in mortgage defaults, creating compounded challenges for insurers. To this end, we apply a state-space modeling approach to decouple the effect of natural hazard losses on mortgage default rates after controlling for other economic determinants through the inclusion of latent variables. Moreover, we consider a sliced variant of the classical SSM to capture the subtle relationship that only emerges when natural hazard losses are sufficiently high. Our model verifies the significance of this relationship and provides insights into how natural hazard losses manifest as increased mortgage default rates.

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arXiv2025

Orthogonal calibration via posterior projections with applications to the Schwarzschild model

The orbital superposition method originally developed by Schwarzschild (1979) is used to study the dynamics of growth of a black hole and its host galaxy, and has uncovered new relationships between the galaxy's global characteristics. Scientists are specifically interested in finding optimal parameter choices for this model that best match physical measurements along with quantifying the uncertainty of such procedures. This renders a statistical calibration problem with multivariate outcomes. In this article, we develop a Bayesian method for calibration with multivariate outcomes using orthogonal bias functions thus ensuring parameter identifiability. Our approach is based on projecting the posterior to an appropriate space which allows the user to choose any nonparametric prior on the bias function(s) instead of having to model it (them) with Gaussian processes. We develop a functional projection approach using the theory of Hilbert spaces. A finite-dimensional analogue of the projection problem is also considered. We illustrate the proposed approach using a BART prior and apply it to calibrate the Schwarzschild model illustrating how a multivariate approach may resolve discrepancies resulting from a univariate calibration.

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arXiv2025

Likelihood Based Inference in Fully and Partially Observed Exponential Family Graphical Models with Intractable Normalizing Constants

Probabilistic graphical models that encode an underlying Markov random field are fundamental building blocks of generative modeling to learn latent representations in modern multivariate data sets with complex dependency structures. Among these, the exponential family graphical models are especially popular, given their fairly well-understood statistical properties and computational scalability to high-dimensional data based on pseudo-likelihood methods. These models have been successfully applied in many fields, such as the Ising model in statistical physics and count graphical models in genomics. Another strand of models allows some nodes to be latent, so as to allow the marginal distribution of the observable nodes to depart from exponential family to capture more complex dependence. These approaches form the basis of generative models in artificial intelligence, such as the Boltzmann machines and their restricted versions. A fundamental barrier to likelihood-based (i.e., both maximum likelihood and fully Bayesian) inference in both fully and partially observed cases is the intractability of the likelihood. The usual workaround is via adopting pseudo-likelihood based approaches, following the pioneering work of Besag (1974). The goal of this paper is to demonstrate that full likelihood based analysis of these models is feasible in a computationally efficient manner. The chief innovation lies in using a technique of Geyer (1991) utilizing the tractable independence model underlying an intractable graphical model, to estimate the normalizing constant, as well as its gradient. Extensive numerical results, supporting theory and comparisons with pseudo-likelihood based approaches demonstrate the applicability of the proposed method.

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arXiv2023

Nearest Neighbor Dirichlet Mixtures

There is a rich literature on Bayesian methods for density estimation, which characterize the unknown density as a mixture of kernels. Such methods have advantages in terms of providing uncertainty quantification in estimation, while being adaptive to a rich variety of densities. However, relative to frequentist locally adaptive kernel methods, Bayesian approaches can be slow and unstable to implement in relying on Markov chain Monte Carlo algorithms. To maintain most of the strengths of Bayesian approaches without the computational disadvantages, we propose a class of nearest neighbor-Dirichlet mixtures. The approach starts by grouping the data into neighborhoods based on standard algorithms. Within each neighborhood, the density is characterized via a Bayesian parametric model, such as a Gaussian with unknown parameters. Assigning a Dirichlet prior to the weights on these local kernels, we obtain a pseudo-posterior for the weights and kernel parameters. A simple and embarrassingly parallel Monte Carlo algorithm is proposed to sample from the resulting pseudo-posterior for the unknown density. Desirable asymptotic properties are shown, and the methods are evaluated in simulation studies and applied to a motivating data set in the context of classification.

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arXiv2022

Bayesian inference on high-dimensional multivariate binary responses

It has become increasingly common to collect high-dimensional binary response data; for example, with the emergence of new sampling techniques in ecology. In smaller dimensions, multivariate probit (MVP) models are routinely used for inferences. However, algorithms for fitting such models face issues in scaling up to high dimensions due to the intractability of the likelihood, involving an integral over a multivariate normal distribution having no analytic form. Although a variety of algorithms have been proposed to approximate this intractable integral, these approaches are difficult to implement and/or inaccurate in high dimensions. Our main focus is in accommodating high-dimensional binary response data with a small to moderate number of covariates. We propose a two-stage approach for inference on model parameters while taking care of uncertainty propagation between the stages. We use the special structure of latent Gaussian models to reduce the highly expensive computation involved in joint parameter estimation to focus inference on marginal distributions of model parameters. This essentially makes the method embarrassingly parallel for both stages. We illustrate performance in simulations and applications to joint species distribution modeling in ecology.

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arXiv2021

Bayesian semiparametric long memory models for discretized event data

We introduce a new class of semiparametric latent variable models for long memory discretized event data. The proposed methodology is motivated by a study of bird vocalizations in the Amazon rain forest; the timings of vocalizations exhibit self-similarity and long range dependence ruling out models based on Poisson processes. The proposed class of FRActional Probit (FRAP) models is based on thresholding of a latent process consisting of an additive expansion of a smooth Gaussian process with a fractional Brownian motion. We develop a Bayesian approach to inference using Markov chain Monte Carlo, and show good performance in simulation studies. Applying the methods to the Amazon bird vocalization data, we find substantial evidence for self-similarity and non-Markovian/Poisson dynamics. To accommodate the bird vocalization data, in which there are many different species of birds exhibiting their own vocalization dynamics, a hierarchical expansion of FRAP is provided in Supplementary Materials.

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arXiv2019

Bayesian sparse multiple regression for simultaneous rank reduction and variable selection

We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of regression coefficients which obviates the need to specify a prior on the rank, and shrinks the regression matrix towards low-rank and row-sparse structures. We provide theoretical support to the proposed methodology by proving minimax optimality of the posterior mean under the prediction risk in ultra-high dimensional settings where the number of predictors can grow sub-exponentially relative to the sample size. A one-step post-processing scheme induced by group lasso penalties on the rows of the estimated coefficient matrix is proposed for variable selection, with default choices of tuning parameters. We additionally provide an estimate of the rank using a novel optimization function achieving dimension reduction in the covariate space. We exhibit the performance of the proposed methodology in an extensive simulation study and a real data example.

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arXiv2016

Fast sampling with Gaussian scale-mixture priors in high-dimensional regression

We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed algorithm only requires matrix operations in the form of matrix multiplications and linear system solutions. We exhibit that the computational complexity of the proposed algorithm grows linearly with the dimension unlike existing algorithms relying on Cholesky factorizations with cubic orders of complexity. The algorithm should be broadly applicable in settings where Gaussian scale mixture priors are used on high dimensional model parameters. We provide an illustration through posterior sampling in a high dimensional regression setting with a horseshoe prior on the vector of regression coefficients.

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