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Saptarshi Chakraborty

Publications and source records attributed to Saptarshi Chakraborty.

At least 19 recordsLinked to original sources
arXiv2026

Robust Linear Predictions: Analyses of Uniform Concentration, Fast Rates and Model Misspecification

The problem of linear predictions has been extensively studied for the past century under pretty generalized frameworks. Recent advances in the robust statistics literature allow us to analyze robust versions of classical linear models through the prism of Median of Means (MoM). Combining these approaches in a piecemeal way might lead to ad-hoc procedures, and the restricted theoretical conclusions that underpin each individual contribution may no longer be valid. To meet these challenges coherently, in this study, we offer a unified robust framework that includes a broad variety of linear prediction problems on a Hilbert space, coupled with a generic class of loss functions. Notably, we do not require any assumptions on the distribution of the outlying data points ($\mathcal{O}$) nor the compactness of the support of the inlying ones ($\mathcal{I}$). Under mild conditions on the dual norm, we show that for misspecification level $ε$, these estimators achieve an error rate of $O(\max\left\{|\mathcal{O}|^{1/2}n^{-1/2}, |\mathcal{I}|^{1/2}n^{-1} \right\}+ε)$, matching the best-known rates in literature. This rate is slightly slower than the classical rates of $O(n^{-1/2})$, indicating that we need to pay a price in terms of error rates to obtain robust estimates. Additionally, we show that this rate can be improved to achieve so-called "fast rates" under additional assumptions.

stat.ML↗
arXiv2026

Why Fe doping kills photoluminescence in CsPbCl$_3$ but not in CsPbBr$_3$: Role of midgap Fe 3$d$ states and electron-phonon coupling

Understanding the impact of transition-metal doping on the optoelectronic properties of halide perovskite nanocrystals is essential for their rational design in photonic applications. We establish the microscopic origin of photoluminescence (PL) quenching in Fe-doped CsPbCl$_3$ using spin-polarized density functional theory calculations. The emergence of Fe 3$d$ midgap states creates efficient electron-trapping centres that drive nonradiative recombination, accounting for the reduced PL intensity. Extending this analysis to Fe-doped CsPbX$_3$ (X = Cl, Br), we show experimentally that although PL intensity is suppressed in both systems relative to their pristine counterparts, their high-doping behaviour diverges: CsPbCl$_3$ becomes completely non-emissive, whereas CsPbBr$_3$ retains a finite, saturated PL intensity. Despite this contrast, electronic structure calculations reveal nearly identical midgap states in both materials, indicating that electronic effects alone cannot explain the distinct PL responses. Phonon calculations likewise fail to capture this difference. In contrast, electron-phonon coupling calculations based on the deformation potential approach reveal significantly stronger coupling in Fe-doped CsPbCl$_3$, enabling efficient dissipation of electronic excitation energy into lattice vibrations and leading to complete PL quenching. These results identify electron-phonon coupling as the key factor governing halide-dependent PL quenching and provide a unified microscopic framework for dopant-induced nonradiative processes in halide perovskites.

cond-mat.mtrl-sci↗
arXiv2026

A New Framework for Convex Clustering in Kernel Spaces: Finite Sample Bounds, Consistency and Performance Insights

Convex clustering is a well-regarded clustering method, resembling the similar centroid-based approach of Lloyd's $k$-means, without requiring a predefined cluster count. It starts with each data point as its centroid and iteratively merges them. Despite its advantages, this method can fail when dealing with data exhibiting linearly non-separable or non-convex structures. To mitigate the limitations, we propose a kernelized extension of the convex clustering method. This approach projects the data points into a Reproducing Kernel Hilbert Space (RKHS) using a feature map, enabling convex clustering in this transformed space. This kernelization not only allows for better handling of complex data distributions but also produces an embedding in a finite-dimensional vector space. We provide a comprehensive theoretical underpinning for our kernelized approach, proving algorithmic convergence and establishing finite sample bounds for our estimates. The effectiveness of our method is demonstrated through extensive experiments on both synthetic and real-world datasets, showing superior performance compared to state-of-the-art clustering techniques. This work marks a significant advancement in the field, offering an effective solution for clustering in non-linear and non-convex data scenarios.

stat.ML↗
arXiv2026

A Review of Statistical Methods for Spontaneous Reporting System Data Mining: Signal Detection and Beyond

Postmarketing safety surveillance relies on data from spontaneous reporting systems (SRS) such as FAERS, EudraVigilance and VigiBase, and commonly uses SRS data mining methods to assess the associations between drugs and adverse events (AEs). Traditionally, these analyses have focused on signal detection framed as a binary decision problem, whereas more recent work has emphasized more nuanced inference involving signal strength estimation and uncertainty quantification. In this paper, we review contemporary SRS data mining approaches and their statistical underpinnings for safety assessment using data from major pharmacovigilance databases worldwide. In addition to methodological review, we provide practical guidance on data preprocessing for such analysis, including construction of SRS contingency tables using only aggregated AE-drug counts, as are publicly available from databases such as VigiBase and EudraVigilance. We illustrate the guidance via opioid-related datasets obtained from FAERS and VigiBase, complied with subsequent downstream SRS data analyses.

stat.AP↗
arXiv2026

Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data

Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional structure common in real data, such as that arising in natural images. In this work, we study the statistical convergence of score-based diffusion models for learning an unknown distribution $μ$ from finitely many samples. Under mild regularity conditions on the forward diffusion process and the data distribution, we derive finite-sample error bounds on the learned generative distribution, measured in the Wasserstein-$p$ distance. Unlike prior results, our guarantees hold for all $p \ge 1$ and require only a finite-moment assumption on $μ$, without compact-support, manifold, or smooth-density conditions. Specifically, given $n$ i.i.d.\ samples from $μ$ with finite $q$-th moment and appropriately chosen network architectures, hyperparameters, and discretization schemes, we show that the expected Wasserstein-$p$ error between the learned distribution $\hatμ$ and $μ$ scales as $\mathbb{E}\, \mathbb{W}_p(\hatμ,μ) = \widetilde{O}\!\left(n^{-1 / d^\ast_{p,q}(μ)}\right),$ where $d^\ast_{p,q}(μ)$ is the $(p,q)$-Wasserstein dimension of $μ$. Our results demonstrate that diffusion models naturally adapt to the intrinsic geometry of data and mitigate the curse of dimensionality, since the convergence rate depends on $d^\ast_{p,q}(μ)$ rather than the ambient dimension. Moreover, our theory conceptually bridges the analysis of diffusion models with that of GANs and the sharp minimax rates established in optimal transport. The proposed $(p,q)$-Wasserstein dimension also extends the notion of classical Wasserstein dimension to distributions with unbounded support, which may be of independent theoretical interest.

stat.ML↗
arXiv2026

Efficient Logistic Regression with Mixture of Sigmoids

This paper studies the Exponential Weights (EW) algorithm with an isotropic Gaussian prior for online logistic regression. We show that the near-optimal worst-case regret bound $O(d\log(Bn))$ for EW, established by Kakade and Ng (2005) against the best linear predictor of norm at most $B$, can be achieved with total worst-case computational complexity $O(B^3 n^5)$. This substantially improves on the $O(B^{18}n^{37})$ complexity of prior work achieving the same guarantee (Foster et al., 2018). Beyond efficiency, we analyze the large-$B$ regime under linear separability: after rescaling by $B$, the EW posterior converges as $B\to\infty$ to a standard Gaussian truncated to the version cone. Accordingly, the predictor converges to a solid-angle vote over separating directions and, on every fixed-margin slice of this cone, the mode of the corresponding truncated Gaussian is aligned with the hard-margin SVM direction. Using this geometry, we derive non-asymptotic regret bounds showing that once $B$ exceeds a margin-dependent threshold, the regret becomes independent of $B$ and grows only logarithmically with the inverse margin. Overall, our results show that EW can be both computationally tractable and geometrically adaptive in online classification.

cs.LG↗
arXiv2026

A Nonparametric Bayesian Local-Global Model for Enhanced Adverse Event Signal Detection in Spontaneous Reporting System Data

Spontaneous reporting system databases are key resources for post-marketing surveillance, providing real-world evidence (RWE) on the adverse events (AEs) of regulated drugs or other medical products. Various statistical methods have been proposed for AE signal detection in these databases, flagging drug-specific AEs with disproportionately high observed counts compared to expected counts under independence. However, signal detection remains challenging for rare AEs or newer drugs, which receive small observed and expected counts and thus suffer from reduced statistical power. Principled information sharing on signal strengths across drugs/AEs is crucial in such cases to enhance signal detection. However, existing methods typically ignore complex between-drug associations on AE signal strengths, limiting their ability to detect signals. We propose novel local-global mixture Dirichlet process (DP) prior-based nonparametric Bayesian models to capture these associations, enabling principled information sharing between drugs while balancing flexibility and shrinkage for each drug, thereby enhancing statistical power. We develop efficient Markov chain Monte Carlo algorithms for implementation and employ a false discovery rate (FDR)-controlled, false negative rate (FNR)-optimized hypothesis testing framework for AE signal detection. Extensive simulations demonstrate our methods' superior sensitivity -- often surpassing existing approaches by a twofold or greater margin -- while strictly controlling the FDR. An application to FDA FAERS data on statin drugs further highlights our methods' effectiveness in real-world AE signal detection. Software implementing our methods is provided as supplementary material.

stat.ME↗
arXiv2025

Core@Shell AgBr@CsPbBr3 Nanocrystals as Precursors to Hollow Lead Halide Perovskite Nanocubes

We report the synthesis of colloidal core@shell AgBr@CsPbBr3 nanocubes by a one-pot approach, where the nucleation and growth of AgBr nanocrystals occurs rapidly after the injection of chemical precursors. This is immediately followed by the overgrowth of CsPbBr3, delivering AgBr@CsPbBr3 nanocubes of several tens of nanometers in size, with the volume of the AgBr core being only a small fraction of the overall nanocrystal volume. The formation of a core@shell geometry is facilitated by the epitaxial compatibility between AgBr and CsPbBr3 along multiple crystallographic directions. Exchange with Cl-ions leads to Ag@CsPbCl3 nanocubes, whereas exchange with I-ions leads to hollow CsPbI3 nanocubes, due to selective etching of the AgBr (or Ag) core region by the I-ions diffusing in the nanocubes. These hollow CsPbI3 nanocubes can then be converted into hollow CsPbBr3 and CsPbCl3 nanocubes by halide exchange. The optical emission properties of the hollow CsPbX3 (X=Cl, Br, I) nanocubes are in line with those expected from large, non-hollow halide perovskite nanocrystals, indicating that the small hollow region in the cubes has no major influence on their optical properties.

cond-mat.mtrl-sci↗
arXiv2025

pvEBayes: An R Package for Empirical Bayes Methods in Pharmacovigilance

Monitoring the safety of medical products is a core concern of contemporary pharmacovigilance. To support drug safety assessment, Spontaneous Reporting Systems (SRS) collect reports of suspected adverse events of approved medical products offering a critical resource for identifying potential safety concerns that may not emerge during clinical trials. Modern nonparametric empirical Bayes methods are flexible statistical approaches that can accurately identify and estimate the strength of the association between an adverse event and a drug from SRS data. However, there is currently no comprehensive and easily accessible implementation of these methods. Here, we introduce the R package pvEBayes, which implements a suite of nonparametric empirical Bayes methods for pharmacovigilance, along with post-processing tools and graphical summaries for streamlining the application of these methods. Detailed examples are provided to demonstrate the application of the package through analyses of two real-world SRS datasets curated from the publicly available FDA FAERS database.

stat.AP↗
arXiv2025

Convex Clustering Redefined: Robust Learning with the Median of Means Estimator

Clustering approaches that utilize convex loss functions have recently attracted growing interest in the formation of compact data clusters. Although classical methods like k-means and its wide family of variants are still widely used, all of them require the number of clusters k to be supplied as input, and many are notably sensitive to initialization. Convex clustering provides a more stable alternative by formulating the clustering task as a convex optimization problem, ensuring a unique global solution. However, it faces challenges in handling high-dimensional data, especially in the presence of noise and outliers. Additionally, strong fusion regularization, controlled by the tuning parameter, can hinder effective cluster formation within a convex clustering framework. To overcome these challenges, we introduce a robust approach that integrates convex clustering with the Median of Means (MoM) estimator, thus developing an outlier-resistant and efficient clustering framework that does not necessitate prior knowledge of the number of clusters. By leveraging the robustness of MoM alongside the stability of convex clustering, our method enhances both performance and efficiency, especially on large-scale datasets. Theoretical analysis demonstrates weak consistency under specific conditions, while experiments on synthetic and real-world datasets validate the method's superior performance compared to existing approaches.

stat.ML↗
arXiv2025

A Statistical Analysis of Deep Federated Learning for Intrinsically Low-dimensional Data

Despite significant research on the optimization aspects of federated learning, the exploration of generalization error, especially in the realm of heterogeneous federated learning, remains an area that has been insufficiently investigated, primarily limited to developments in the parametric regime. This paper delves into the generalization properties of deep federated regression within a two-stage sampling model. Our findings reveal that the intrinsic dimension, characterized by the entropic dimension, plays a pivotal role in determining the convergence rates for deep learners when appropriately chosen network sizes are employed. Specifically, when the true relationship between the response and explanatory variables is described by a $β$-Hölder function and one has access to $n$ independent and identically distributed (i.i.d.) samples from $m$ participating clients, for participating clients, the error rate scales at most as $\Tilde{O}((mn)^{-2β/(2β+ \bar{d}_{2β}(λ))})$, whereas for non-participating clients, it scales as $\Tilde{O}(Δ\cdot m^{-2β/(2β+ \bar{d}_{2β}(λ))} + (mn)^{-2β/(2β+ \bar{d}_{2β}(λ))})$. Here $\bar{d}_{2β}(λ)$ denotes the corresponding $2β$-entropic dimension of $λ$, the marginal distribution of the explanatory variables. The dependence between the two stages of the sampling scheme is characterized by $Δ$. Consequently, our findings not only explicitly incorporate the ``heterogeneity" of the clients, but also highlight that the convergence rates of errors of deep federated learners are not contingent on the nominal high dimensionality of the data but rather on its intrinsic dimension.

stat.ML↗
arXiv2025

On the Statistical Properties of Generative Adversarial Models for Low Intrinsic Data Dimension

Despite the remarkable empirical successes of Generative Adversarial Networks (GANs), the theoretical guarantees for their statistical accuracy remain rather pessimistic. In particular, the data distributions on which GANs are applied, such as natural images, are often hypothesized to have an intrinsic low-dimensional structure in a typically high-dimensional feature space, but this is often not reflected in the derived rates in the state-of-the-art analyses. In this paper, we attempt to bridge the gap between the theory and practice of GANs and their bidirectional variant, Bi-directional GANs (BiGANs), by deriving statistical guarantees on the estimated densities in terms of the intrinsic dimension of the data and the latent space. We analytically show that if one has access to $n$ samples from the unknown target distribution and the network architectures are properly chosen, the expected Wasserstein-1 distance of the estimates from the target scales as $O\left( n^{-1/d_μ} \right)$ for GANs and $\tilde{O}\left( n^{-1/(d_μ+\ell)} \right)$ for BiGANs, where $d_μ$ and $\ell$ are the upper Wasserstein-1 dimension of the data-distribution and latent-space dimension, respectively. The theoretical analyses not only suggest that these methods successfully avoid the curse of dimensionality, in the sense that the exponent of $n$ in the error rates does not depend on the data dimension but also serve to bridge the gap between the theoretical analyses of GANs and the known sharp rates from optimal transport literature. Additionally, we demonstrate that GANs can effectively achieve the minimax optimal rate even for non-smooth underlying distributions, with the use of interpolating generator networks.

stat.ML↗
arXiv2025

Harnessing self-sensitized scintillation by supramolecular engineering of CsPbBr3 nanocrystals in dense mesoporous template nanospheres

Perovskite-based nanoscintillators, such as CsPbBr3 nanocrystals (NCs), are emerging as promising candidates for ionizing radiation detection, thanks to their high emission efficiency, rapid response, and facile synthesis. However, their nanoscale dimensions - smaller than the mean free path of secondary carriers - and relatively low emitter density per unit volume, limited by their high molecular weight and reabsorption losses, restrict efficient secondary carrier conversion and hamper their practical deployment. In this work, we introduce a strategy to enhance scintillation performance by organizing NCs into densely packed domains within porous SiO2 mesospheres (MSNs). This engineered architecture achieves up to a 40-fold increase in radioluminescence intensity compared to colloidal NCs, driven by improved retention and conversion of secondary charges, as corroborated by electron release measurements. This approach offers a promising pathway toward developing next-generation nanoscintillators with enhanced performance, with potential applications in high-energy physics, medical imaging, and space technologies.

cond-mat.mtrl-sci↗
arXiv2025

A generalized Bayesian approach for high-dimensional robust regression with serially correlated errors and predictors

This paper introduces a loss-based generalized Bayesian methodology for high-dimensional robust regression with serially correlated errors and predictors. The proposed framework employs a novel scaled pseudo-Huber (SPH) loss function, which smooths the well-known Huber loss, effectively balancing quadratic ($\ell_2$) and absolute linear ($\ell_1$) loss behaviors. This flexibility enables the framework to accommodate both thin-tailed and heavy-tailed data efficiently. The generalized Bayesian approach constructs a working likelihood based on the SPH loss, facilitating efficient and stable estimation while providing rigorous uncertainty quantification for all model parameters. Notably, this approach allows formal statistical inference without requiring ad hoc tuning parameter selection while adaptively addressing a wide range of tail behavior in the errors. By specifying appropriate prior distributions for the regression coefficients--such as ridge priors for small or moderate-dimensional settings and spike-and-slab priors for high-dimensional settings--the framework ensures principled inference. We establish rigorous theoretical guarantees for accurate parameter estimation and correct predictor selection under sparsity assumptions for a wide range of data generating setups. Extensive simulation studies demonstrate the superior performance of our approach compared to traditional Bayesian regression methods based on $\ell_2$ and $\ell_1$-loss functions. The results highlight its flexibility and robustness, particularly in challenging high-dimensional settings characterized by data contamination.

stat.ME↗
arXiv2025

Flexible Empirical Bayesian Approaches to Pharmacovigilance for Simultaneous Signal Detection and Signal Strength Estimation in Spontaneous Reporting Systems Data

Inferring adverse events (AEs) of medical products from Spontaneous Reporting Systems (SRS) databases is a core challenge in contemporary pharmacovigilance. Bayesian methods for pharmacovigilance are attractive for their rigorous ability to simultaneously detect potential AE signals and estimate their strengths/degrees of relevance. However, existing Bayesian and empirical Bayesian methods impose restrictive parametric assumptions and/or demand substantial computational resources, limiting their practical utility. This paper introduces a suite of novel, scalable empirical Bayes methods for pharmacovigilance that utilize flexible non-parametric priors and custom, efficient data-driven estimation techniques to enhance signal detection and signal strength estimation at a low computational cost. Our highly flexible methods accommodate a broader range of data and achieve signal detection performance comparable to or better than existing Bayesian and empirical Bayesian approaches. More importantly, they provide coherent and high-fidelity estimation and uncertainty quantification for potential AE signal strengths, offering deeper insights into the comparative importance and relevance of AEs. Extensive simulation experiments across diverse data-generating scenarios demonstrate the superiority of our methods in terms of accurate signal strength estimation, as measured by replication root mean squared errors. Additionally, our methods maintain or exceed the signal detection performance of state-of-the-art techniques, as evaluated by frequentist false discovery rates and sensitivity metrics. Applications on FDA FAERS data for the statin group of drugs reveal interesting insights through Bayesian posterior probabilities.

stat.ME↗
arXiv2024

A Statistical Analysis for Supervised Deep Learning with Exponential Families for Intrinsically Low-dimensional Data

Recent advances have revealed that the rate of convergence of the expected test error in deep supervised learning decays as a function of the intrinsic dimension and not the dimension $d$ of the input space. Existing literature defines this intrinsic dimension as the Minkowski dimension or the manifold dimension of the support of the underlying probability measures, which often results in sub-optimal rates and unrealistic assumptions. In this paper, we consider supervised deep learning when the response given the explanatory variable is distributed according to an exponential family with a $β$-Hölder smooth mean function. We consider an entropic notion of the intrinsic data-dimension and demonstrate that with $n$ independent and identically distributed samples, the test error scales as $\tilde{\mathcal{O}}\left(n^{-\frac{2β}{2β+ \bar{d}_{2β}(λ)}}\right)$, where $\bar{d}_{2β}(λ)$ is the $2β$-entropic dimension of $λ$, the distribution of the explanatory variables. This improves on the best-known rates. Furthermore, under the assumption of an upper-bounded density of the explanatory variables, we characterize the rate of convergence as $\tilde{\mathcal{O}}\left( d^{\frac{2\lfloorβ\rfloor(β+ d)}{2β+ d}}n^{-\frac{2β}{2β+ d}}\right)$, establishing that the dependence on $d$ is not exponential but at most polynomial. We also demonstrate that when the explanatory variable has a lower bounded density, this rate in terms of the number of data samples, is nearly optimal for learning the dependence structure for exponential families.

stat.ML↗
arXiv2024

Neural-g: A Deep Learning Framework for Mixing Density Estimation

Mixing (or prior) density estimation is an important problem in machine learning and statistics, especially in empirical Bayes $g$-modeling where accurately estimating the prior is necessary for making good posterior inferences. In this paper, we propose neural-$g$, a new neural network-based estimator for $g$-modeling. Neural-$g$ uses a softmax output layer to ensure that the estimated prior is a valid probability density. Under default hyperparameters, we show that neural-$g$ is very flexible and capable of capturing many unknown densities, including those with flat regions, heavy tails, and/or discontinuities. In contrast, existing methods struggle to capture all of these prior shapes. We provide justification for neural-$g$ by establishing a new universal approximation theorem regarding the capability of neural networks to learn arbitrary probability mass functions. To accelerate convergence of our numerical implementation, we utilize a weighted average gradient descent approach to update the network parameters. Finally, we extend neural-$g$ to multivariate prior density estimation. We illustrate the efficacy of our approach through simulations and analyses of real datasets. A software package to implement neural-$g$ is publicly available at https://github.com/shijiew97/neuralG.

stat.ML↗
arXiv2024

A Statistical Analysis of Wasserstein Autoencoders for Intrinsically Low-dimensional Data

Variational Autoencoders (VAEs) have gained significant popularity among researchers as a powerful tool for understanding unknown distributions based on limited samples. This popularity stems partly from their impressive performance and partly from their ability to provide meaningful feature representations in the latent space. Wasserstein Autoencoders (WAEs), a variant of VAEs, aim to not only improve model efficiency but also interpretability. However, there has been limited focus on analyzing their statistical guarantees. The matter is further complicated by the fact that the data distributions to which WAEs are applied - such as natural images - are often presumed to possess an underlying low-dimensional structure within a high-dimensional feature space, which current theory does not adequately account for, rendering known bounds inefficient. To bridge the gap between the theory and practice of WAEs, in this paper, we show that WAEs can learn the data distributions when the network architectures are properly chosen. We show that the convergence rates of the expected excess risk in the number of samples for WAEs are independent of the high feature dimension, instead relying only on the intrinsic dimension of the data distribution.

cs.LG↗