arXiv subjects

Sayantan Banerjee

Publications and source records attributed to Sayantan Banerjee.

At least 19 recordsLinked to original sources

arXiv2026

Multiple testing with the horseshoe

We study multiple testing under continuous global--local shrinkage priors, with a focus on the horseshoe prior in high-dimensional sparse settings. While such priors provide adaptive shrinkage and computational scalability, they do not induce exact zeros and hence do not directly yield posterior inclusion probabilities, making principled false discovery control nontrivial. We propose posterior--based decision rules for signal detection that are applicable across a broad class of continuous shrinkage priors and are calibrated to control the false discovery rate (FDR) while retaining high power. In the sparse normal means model, we show that the proposed procedures attain the optimal detection boundary and achieve frequentist asymptotic control of both FDR and false negative rate (FNR). The method is readily implementable via standard posterior sampling, and empirical studies indicate that the realised FDR and FNR closely track their theoretical targets. Applications to high-dimensional regression and Gaussian graphical models further illustrate the scope and practical effectiveness of the approach.

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arXiv2026

Projection Diagnostics for Directional Asymmetry and Tail-Ratio Departure in Multivariate Data

We study projection-based diagnostics for distinguishing directional asymmetry from tail-ratio departure in multivariate data. The procedure reduces the problem to one-dimensional projections and computes two quantile-based summaries: a directional skewness measure evaluated over several quantile levels, and an interquantile tail-ratio evaluated relative to a chosen benchmark. The two summaries lead to a four-regime classification: symmetric benchmark-tail, symmetric tail-departed, skewed benchmark-tail, and skewed tail-departed. The quantile formulation avoids relying on third and fourth moments, which can be unstable in heavy-tailed settings. We establish population properties under central symmetry and ellipticity, uniform finite-sample bounds over the searched directions, and consistency of the threshold classifier under separated regimes. A sparse rank-one calculation is also used to show why coordinate directions can complement random directions in high dimensions. The resulting diagnostic is meant to guide subsequent modelling choices, for example whether a symmetric, skewed, tail-departed, or combined multivariate model is appropriate.

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arXiv2026

A Leakage Bound for Confidence Sets after Black-Box Selection

In many analyses the object reported at the end is not fixed in advance, but is chosen after a preliminary search over variables, subgroups, transformations, models or contrasts. Classical selective-inference methods are most effective when this search can be written as an explicit selection event. This note treats the less structured case in which the selection rule is a black box and inference is required for the target indexed by the selected object. We show that, for any fixed-target confidence procedure, selected-target noncoverage is bounded by the nominal fixed-target noncoverage plus the average total variation distance between the marginal law of the inferential data and its conditional law given the selected object. A mutual-information bound follows immediately. The result recovers sample splitting as the zero-leakage case and gives explicit guarantees for noisy screening through a Gaussian information bound. Thus the inferential cost of black-box selection is quantified by the information that the selected object carries about the inferential sample.

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arXiv2026

BayPrAnoMeta: Bayesian Proto-MAML for Few-Shot Industrial Image Anomaly Detection

Industrial image anomaly detection is a challenging problem owing to extreme class imbalance and the scarcity of labeled defective samples, particularly in few-shot settings. We propose BayPrAnoMeta, a Bayesian generalization of Proto-MAML for few-shot industrial image anomaly detection. Unlike existing Proto-MAML approaches that rely on deterministic class prototypes and distance-based adaptation, BayPrAnoMeta replaces prototypes with task-specific probabilistic normality models and performs inner-loop adaptation via a Bayesian posterior predictive likelihood. We model normal support embeddings with a Normal-Inverse-Wishart (NIW) prior, producing a Student-$t$ predictive distribution that enables uncertainty-aware, heavy-tailed anomaly scoring and is essential for robustness in extreme few-shot settings. We further extend BayPrAnoMeta to a federated meta-learning framework with supervised contrastive regularization for heterogeneous industrial clients and prove convergence to stationary points of the resulting nonconvex objective. Experiments on the MVTec AD benchmark demonstrate consistent and significant AUROC improvements over MAML, Proto-MAML, and PatchCore-based methods in few-shot anomaly detection settings.

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arXiv2026

FSL-BDP: Federated Survival Learning with Bayesian Differential Privacy for Credit Risk Modeling

Credit risk models are a critical decision-support tool for financial institutions, yet tightening data-protection rules (e.g., GDPR, CCPA) increasingly prohibit cross-border sharing of borrower data, even as these models benefit from cross-institution learning. Traditional default prediction suffers from two limitations: binary classification ignores default timing, treating early defaulters (high loss) equivalently to late defaulters (low loss), and centralized training violates emerging regulatory constraints. We propose a Federated Survival Learning framework with Bayesian Differential Privacy (FSL-BDP) that models time-to-default trajectories without centralizing sensitive data. The framework provides Bayesian (data-dependent) differential privacy (DP) guarantees while enabling institutions to jointly learn risk dynamics. Experiments on three real-world credit datasets (LendingClub, SBA, Bondora) show that federation fundamentally alters the relative effectiveness of privacy mechanisms. While classical DP performs better than Bayesian DP in centralized settings, the latter benefits substantially more from federation (+7.0\% vs +1.4\%), achieving near parity of non-private performance and outperforming classical DP in the majority of participating clients. This ranking reversal yields a key decision-support insight: privacy mechanism selection should be evaluated in the target deployment architecture, rather than centralized benchmarks. These findings provide actionable guidance for practitioners designing privacy-preserving decision support systems in regulated, multi-institutional environments.

cs.LG↗

arXiv2026

DP-FedSOFIM: Differentially Private Federated Stochastic Optimization using Regularized Fisher Information Matrix

Differentially private federated learning (DP-FL) often suffers from slow convergence under tight privacy budgets because the noise required for privacy preservation degrades gradient quality. Although second-order optimization can accelerate training, existing approaches for DP-FL face significant scalability limitations: Newton-type methods require clients to compute Hessians, while feature covariance methods scale poorly with model dimension. We propose DP-FedSOFIM, a simple and scalable Hessian approximation-based second-order optimization method for DP-FL. The method constructs a regularized proxy for the Fisher information matrix at the server using only privatized aggregated gradients, capturing useful curvature information without requiring full Hessian computations or feature covariance estimation. Efficient rank-one updates based on the Sherman-Morrison formula enable communication costs proportional to the model size and require only O(d) client-side memory. Because all curvature and preconditioning operations are performed at the server on already privatized gradients, DP-FedSOFIM introduces no additional privacy cost beyond the underlying privatized gradient release mechanism. Experiments on CIFAR-10 and PathMNIST demonstrate that DP-FedSOFIM converges faster and consistently achieves higher accuracy than several competitive differentially private federated learning baselines across a wide range of privacy budgets.

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arXiv2026

Censored Graphical Horseshoe: Bayesian sparse precision matrix estimation with censored and missing data

Gaussian graphical models provide a powerful framework for studying conditional dependencies in multivariate data, with widespread applications spanning biomedical, environmental sciences, and other data-rich scientific domains. While the Graphical Horseshoe (GHS) method has emerged as a state-of-the-art Bayesian method for sparse precision matrix estimation, existing approaches assume fully observed data and thus fail in the presence of censoring or missingness, which are pervasive in real-world studies. In this paper, we develop the Censored Graphical Horseshoe (CGHS), a novel Bayesian framework that extends the GHS to censored and arbitrarily missing Gaussian data. By introducing a latent-variable representation, CGHS accommodates incomplete observations while retaining the adaptive global-local shrinkage properties of the Horseshoe prior. We derive efficient Gibbs samplers for posterior computation and establish new theoretical results on posterior behavior under censoring and missingness, filling a gap not addressed by frequentist Lasso-based methods. Through extensive simulations, we demonstrate that CGHS consistently improves estimation accuracy compared to penalized likelihood approaches. Our methods are implemented in the package GHScenmis available on Github: https://github.com/tienmt/ghscenmis .

stat.ME↗

arXiv2025

Bayesian Effective Dimension from Information Growth

Nominal dimension can greatly overstate how much a Bayesian model actually learns from data. We quantify this gap through a prior-dependent effective dimension based on parameter--data mutual information, normalized so that regular parametric information growth provides the benchmark scale. The main theoretical result shows that, in infinite-dimensional Gaussian experiments, information growth is determined by the spectral counting function: regularly varying spectra yield a sharp asymptotic law with an explicit constant, while exponential spectral decay produces a distinct polylogarithmic regime. In Gaussian regression the same information scale has a spectral representation and is linked exactly to ridge degrees of freedom. For scalar Gaussian scale-mixture priors, we separate information about latent scales from conditional Gaussian information and show that the full marginal information remains finite under polynomially heavy-tailed mixing.

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arXiv2025

PDx -- Adaptive Credit Risk Forecasting Model in Digital Lending using Machine Learning Operations

This paper presents PDx, an adaptive, machine learning operations (MLOps) driven decision system for forecasting credit risk using probability of default (PD) modeling in digital lending. While conventional PD models prioritize predictive accuracy during model development with complex machine learning algorithms, they often overlook continuous adaptation to changing borrower behaviour, resulting in static models that degrade over time in production and generate inaccurate default predictions. Many financial institutes also find it difficult transitioning ML models from development environment to production and maintaining their health. With PDx we aimed to addresses these limitations using a dynamic, end-to-end model lifecycle management approach that integrates continuous model monitoring, retraining, and validation through a robust MLOps pipeline. We introduced a dynamic champion-challenger framework for PDx to regularly update baseline models to recalibrate independent parameters with the latest data and select the best-performing model through out-of-time validation, ensuring resilience against data drift and changing credit risk patterns. Our empirical analysis shows that decision tree-based ensemble models consistently outperform others in classifying defaulters but require frequent updates to sustain performance. Linear models (e.g., logistic regression) and neural networks exhibit greater performance degradation. The study demonstrate with PDx we can mitigates value erosion for digital lenders, particularly in short-term, small-ticket loans, where borrower behavior shifts rapidly. We have validated the effectiveness of PDx using datasets from peer-to-peer lending, business loans, and auto loans, demonstrating its scalability and adaptability for modern credit risk forecasting.

cs.LG↗

arXiv2025

A self-supervised learning approach for denoising autoregressive models with additive noise: finite and infinite variance cases

The autoregressive time series model is a popular second-order stationary process, modeling a wide range of real phenomena. However, in applications, autoregressive signals are often corrupted by additive noise. Further, the autoregressive process and the corruptive noise may be highly impulsive, stemming from an infinite-variance distribution. The model estimation techniques that account for additional noise tend to show reduced efficacy when there is very strong noise present in the data, especially when the noise is heavy-tailed. In this paper, we propose a novel self-supervised learning method to denoise the additive noise-corrupted autoregressive model. Our approach is motivated by recent work in computer vision and does not require full knowledge of the noise distribution. We use the proposed method to recover exemplary finite- and infinite-variance autoregressive signals, namely, Gaussian and alpha-stable distributed signals, respectively, from their noise-corrupted versions. The simulation study conducted on both synthetic and semi-synthetic data demonstrates strong denoising performance of our method compared to several baseline methods, particularly when the corruption is significant and impulsive in nature. Finally, we apply the presented methodology to forecast the pure autoregressive signal from the noise-corrupted data.

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arXiv2023

Maximum a Posteriori Estimation in Graphical Models Using Local Linear Approximation

Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among variables. However, maximum a posteriori (MAP) estimation is challenging under hierarchical prior models, and traditional numerical optimization routines or expectation--maximization algorithms are difficult to implement. To this end, our contribution is a novel local linear approximation scheme that circumvents this issue using a very simple computational algorithm. Most importantly, the condition under which our algorithm is guaranteed to converge to the MAP estimate is explicitly stated and is shown to cover a broad class of completely monotone priors, including the graphical horseshoe. Further, the resulting MAP estimate is shown to be sparse and consistent in the $\ell_2$-norm. Numerical results validate the speed, scalability, and statistical performance of the proposed method.

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arXiv2023

Nonparametric Bayes multiresolution testing for high-dimensional rare events

In a variety of application areas, there is interest in assessing evidence of differences in the intensity of event realizations between groups. For example, in cancer genomic studies collecting data on rare variants, the focus is on assessing whether and how the variant profile changes with the disease subtype. Motivated by this application, we develop multiresolution nonparametric Bayes tests for differential mutation rates across groups. The multiresolution approach yields fast and accurate detection of spatial clusters of rare variants, and our nonparametric Bayes framework provides great flexibility for modeling the intensities of rare variants. Some theoretical properties are also assessed, including weak consistency of our Dirichlet Process-Poisson-Gamma mixture over multiple resolutions. Simulation studies illustrate excellent small sample properties relative to competitors, and we apply the method to detect rare variants related to common variable immunodeficiency from whole exome sequencing data on 215 patients and over 60,027 control subjects.

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arXiv2022

A New Spatio-Temporal Model Exploiting Hamiltonian Equations

The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations, incorporating appropriate stochasticity via Gaussian processes. The resultant spatio-temporal process, continuously varying with time, turns out to be nonparametric, non-stationary, non-separable, and non-Gaussian. Additionally, the lagged correlations converge to zero as the spatio-temporal lag goes to infinity. We investigate the theoretical properties of the new spatio-temporal process, including its continuity and smoothness properties. We derive methods for complete Bayesian inference using MCMC techniques in the Bayesian paradigm. The performance of our method has been compared with that of a non-stationary Gaussian process (GP) using two simulation studies, where our method shows a significant improvement over the non-stationary GP. Further, applying our new model to two real data sets revealed encouraging performance.

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arXiv2022

Evidence Estimation in Gaussian Graphical Models Using a Telescoping Block Decomposition of the Precision Matrix

Marginal likelihood, also known as model evidence, is a fundamental quantity in Bayesian statistics. It is used for model selection using Bayes factors or for empirical Bayes tuning of prior hyper-parameters. Yet, the calculation of evidence has remained a longstanding open problem in Gaussian graphical models. Currently, the only feasible solutions that exist are for special cases such as the Wishart or G-Wishart, in moderate dimensions. We develop an approach based on a novel telescoping block decomposition of the precision matrix that allows the estimation of evidence by application of Chib's technique under a very broad class of priors under mild requirements. Specifically, the requirements are: (a) the priors on the diagonal terms on the precision matrix can be written as gamma or scale mixtures of gamma random variables and (b) those on the off-diagonal terms can be represented as normal or scale mixtures of normal. This includes structured priors such as the Wishart or G-Wishart, and more recently introduced element-wise priors, such as the Bayesian graphical lasso and the graphical horseshoe. Among these, the true marginal is known in an analytically closed form for Wishart, providing a useful validation of our approach. For the general setting of the other three, and several more priors satisfying conditions (a) and (b) above, the calculation of evidence has remained an open question that this article resolves under a unifying framework.

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arXiv2022

Precision Matrix Estimation under the Horseshoe-like Prior-Penalty Dual

Precision matrix estimation in a multivariate Gaussian model is fundamental to network estimation. Although there exist both Bayesian and frequentist approaches to this, it is difficult to obtain good Bayesian and frequentist properties under the same prior--penalty dual. To bridge this gap, our contribution is a novel prior--penalty dual that closely approximates the graphical horseshoe prior and penalty, and performs well in both Bayesian and frequentist senses. A chief difficulty with the horseshoe prior is a lack of closed form expression of the density function, which we overcome in this article. In terms of theory, we establish posterior convergence rate of the precision matrix that matches the oracle rate, in addition to the frequentist consistency of the MAP estimator. In addition, our results also provide theoretical justifications for previously developed approaches that have been unexplored so far, e.g. for the graphical horseshoe prior. Computationally efficient EM and MCMC algorithms are developed respectively for the penalized likelihood and fully Bayesian estimation problems. In numerical experiments, the horseshoe-based approaches echo their superior theoretical properties by comprehensively outperforming the competing methods. A protein--protein interaction network estimation in B-cell lymphoma is considered to validate the proposed methodology.

math.ST↗

arXiv2021

High-dimensional Portfolio Optimization using Joint Shrinkage

We consider the problem of optimizing a portfolio of financial assets, where the number of assets can be much larger than the number of observations. The optimal portfolio weights require estimating the inverse covariance matrix of excess asset returns, classical solutions of which behave badly in high-dimensional scenarios. We propose to use a regression-based joint shrinkage method for estimating the partial correlation among the assets. Extensive simulation studies illustrate the superior performance of the proposed method with respect to variance, weight, and risk estimation errors compared with competing methods for both the global minimum variance portfolios and Markowitz mean-variance portfolios. We also demonstrate the excellent empirical performances of our method on daily and monthly returns of the components of the S&P 500 index.

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arXiv2021

ReCo1: A Fault resilient technique of Correlation Sensitive Stochastic Designs

In stochastic circuits, major sources of error are correlation errors, soft errors and random fluctuation errors that affect the accuracy and reliability of the circuit. The soft error has the effect of changing the correlation status and in turn changes the probability of numbers leading to the erroneous output. This has serious impact on security and medical systems where highly accurate systems are required. We tackle this problem by introducing the fault-tolerant technique of correlation-sensitive stochastic logic circuits. We develop a framework of Remodelling Correlation(ReCo) for Stochastic Logic Elements; AND, XOR and OR for reliable operation. We present two variants of ReCo models in combinational circuits with contradictory requirements by stating two interesting case studies. The proposed technique selects logic elements and places correction blocks based on a priority-based rule that helps to converge to the desired MSE quickly requiring less hardware area. It is shown that this technique does not alter the reliability of the overall circuit. To demonstrate the practical effectiveness of the proposed framework, contrast stretch operation on a standard image in a noisy environment is studied. A high structural similarity index measure of 92.80 is observed for the output image with the proposed approach compared to the image (with error) 66.43.

cs.ET↗

arXiv2021

Horseshoe shrinkage methods for Bayesian fusion estimation

We consider the problem of estimation and structure learning of high dimensional signals via a normal sequence model, where the underlying parameter vector is piecewise constant, or has a block structure. We develop a Bayesian fusion estimation method by using the Horseshoe prior to induce a strong shrinkage effect on successive differences in the mean parameters, simultaneously imposing sufficient prior concentration for non-zero values of the same. The proposed method thus facilitates consistent estimation and structure recovery of the signal pieces. We provide theoretical justifications of our approach by deriving posterior convergence rates and establishing selection consistency under suitable assumptions. We also extend our proposed method to signal de-noising over arbitrary graphs and develop efficient computational methods along with providing theoretical guarantees. We demonstrate the superior performance of the Horseshoe based Bayesian fusion estimation method through extensive simulations and two real-life examples on signal de-noising in biological and geophysical applications. We also demonstrate the estimation performance of our method on a real-world large network for the graph signal de-noising problem.

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