arXiv subjects

Sunrit Chakraborty

Publications and source records attributed to Sunrit Chakraborty.

7 recordsLinked to original sources

arXiv2026

Learning Mixtures of Nonparametric and Convolutional Measures on Effectively Low-dimensional Affine Spaces

In this paper, we develop a finite mixture of convolutional distributions, a statistical model to analyze continuous data distributed approximately on a mixture of low-dimensional affine subspaces. The observations are assumed independent and identically distributed from the mixture of distributions, where each component arises from a convolution of a distribution supported on a low-dimensional subspace with a suitable noise kernel. We discuss theoretical properties of such class of models, including identifiability under very general conditions - in particular, showing that the minimal representation for such mixtures is uniquely identifiable in a semi-parametric setting. We further study the posterior contraction rates for the parameters for a parametrized class of such models where the supports of the component mixing measures are assumed to be convex polytopes under a suitable well-specified Bayesian regime. This still requires developing novel inverse bounds for problems involving a nested mixture structure, where the mixture kernel is itself another continuous mixture. Our approach for both the identifiability theory and posterior contraction rates is to exploit the geometric structure of the underlying support of the latent measures. Apart from applications in end-member analysis, spectral unmixing and topic models, this study provides a grounded framework for subspace clustering with the goal of exploring conditions for learning multiple latent low-dimensional structures. We illustrate our findings through careful simulation study, which also includes developing new algorithms for such class of models

math.ST↗

arXiv2026

From Collapse to Improvement: Statistical Perspectives on the Evolutionary Dynamics of Iterative Training on Contaminated Sources

The problem of model collapse has presented new challenges in iterative training of generative models, where such training with synthetic data leads to an overall degradation of performance. This paper looks at the problem from a statistical viewpoint, illustrating that one can actually hope for improvement when models are trained on data contaminated with synthetic samples, as long as there is some amount of fresh information from the true target distribution. In particular, we consider iterative training on samples sourced from a mixture of the true target and synthetic distributions. We analyze the entire iterative evolution in a next-token prediction language model, capturing how the interplay between the mixture weights and the sample size controls the overall long-term performance. With non-trivial mixture weight of the true distribution, even if it decays over time, simply training the model in a contamination-agnostic manner with appropriate sample sizes can avoid collapse and even recover the true target distribution under certain conditions. Simulation studies support our findings and also show that such behavior is more general for other classes of models.

stat.ML↗

arXiv2025

Dirichlet moment tensors and the correspondence between admixture and mixture of product models

Understanding posterior contraction behavior in Bayesian hierarchical models is of fundamental importance, but progress in this question is relatively sparse in comparison to the theory of density estimation. In this paper, we study two classes of hierarchical models for grouped data, where observations within groups are exchangeable. Using moment tensor decomposition of the distribution of the latent variables, we establish a precise equivalence between the class of Admixture models (such as Latent Dirichlet Allocation) and the class of Mixture of products of multinomial distributions. This correspondence enables us to leverage the result from the latter class of models, which are more well-understood, so as to arrive at the identifiability and posterior contraction rates in both classes under conditions much weaker than in existing literature. For instance, our results shed light on cases where the topics are not linearly independent or the number of topics is misspecified in the admixture setting. Finally, we analyze individual documents' latent allocation performance via the borrowing of strength properties of hierarchical Bayesian modeling. Many illustrations and simulations are provided to support the theory.

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arXiv2024

FLIPHAT: Joint Differential Privacy for High Dimensional Sparse Linear Bandits

High dimensional sparse linear bandits serve as an efficient model for sequential decision-making problems (e.g. personalized medicine), where high dimensional features (e.g. genomic data) on the users are available, but only a small subset of them are relevant. Motivated by data privacy concerns in these applications, we study the joint differentially private high dimensional sparse linear bandits, where both rewards and contexts are considered as private data. First, to quantify the cost of privacy, we derive a lower bound on the regret achievable in this setting. To further address the problem, we design a computationally efficient bandit algorithm, \textbf{F}orgetfu\textbf{L} \textbf{I}terative \textbf{P}rivate \textbf{HA}rd \textbf{T}hresholding (FLIPHAT). Along with doubling of episodes and episodic forgetting, FLIPHAT deploys a variant of Noisy Iterative Hard Thresholding (N-IHT) algorithm as a sparse linear regression oracle to ensure both privacy and regret-optimality. We show that FLIPHAT achieves optimal regret in terms of privacy parameters $ε, δ$, context dimension $d$, and time horizon $T$ up to a linear factor in model sparsity and logarithmic factor in $d$. We analyze the regret by providing a novel refined analysis of the estimation error of N-IHT, which is of parallel interest.

stat.ML↗

arXiv2024

Learning Topic Hierarchies by Tree-Directed Latent Variable Models

We study a parametric family of latent variable models, namely topic models, equipped with a hierarchical structure among the topic variables. Such models may be viewed as a finite mixture of the latent Dirichlet allocation (LDA) induced distributions, but the LDA components are constrained by a latent hierarchy, specifically a rooted and directed tree structure, which enables the learning of interpretable and latent topic hierarchies of interest. A mathematical framework is developed in order to establish identifiability of the latent topic hierarchy under suitable regularity conditions, and to derive bounds for posterior contraction rates of the model and its parameters. We demonstrate the usefulness of such models and validate its theoretical properties through a careful simulation study and a real data example using the New York Times articles.

math.ST↗

arXiv2023

Thompson Sampling for High-Dimensional Sparse Linear Contextual Bandits

We consider the stochastic linear contextual bandit problem with high-dimensional features. We analyze the Thompson sampling algorithm using special classes of sparsity-inducing priors (e.g., spike-and-slab) to model the unknown parameter and provide a nearly optimal upper bound on the expected cumulative regret. To the best of our knowledge, this is the first work that provides theoretical guarantees of Thompson sampling in high-dimensional and sparse contextual bandits. For faster computation, we use variational inference instead of Markov Chain Monte Carlo (MCMC) to approximate the posterior distribution. Extensive simulations demonstrate the improved performance of our proposed algorithm over existing ones.

stat.ML↗

arXiv2021

Scalable nonparametric Bayesian learning for heterogeneous and dynamic velocity fields

Analysis of heterogeneous patterns in complex spatio-temporal data finds usage across various domains in applied science and engineering, including training autonomous vehicles to navigate in complex traffic scenarios. Motivated by applications arising in the transportation domain, in this paper we develop a model for learning heterogeneous and dynamic patterns of velocity field data. We draw from basic nonparameric Bayesian modeling elements such as hierarchical Dirichlet process and infinite hidden Markov model, while the smoothness of each homogeneous velocity field element is captured with a Gaussian process prior. Of particular focus is a scalable approximate inference method for the proposed model; this is achieved by employing sequential MAP estimates from the infinite HMM model and an efficient sequential GP posterior computation technique, which is shown to work effectively on simulated data sets. Finally, we demonstrate the effectiveness of our techniques to the NGSIM dataset of complex multi-vehicle interactions.

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