arXiv subjects

Soham Sarkar

Publications and source records attributed to Soham Sarkar.

15 recordsLinked to original sources

arXiv2026

Polaris : Multi Agentic System for Conversational Enterprise Analytics

In today's fast-paced environment, the ability to swiftly access, understand, and act on data is no longer optional; it is essential. Yet most organizations remain data-rich but insight-poor, constrained by the complexity of querying, interpreting, and explaining enterprise-scale information. We present Polaris, a supervisor-led multi-agent framework for conversational enterprise analytics that bridges this gap. Polaris introduces Dynamic Task Coordination (DTC), a decision-theoretic orchestration layer that models agent-task assignment as adaptive bipartite matching, enabling real-time coordination, recovery, and optimization across specialized agents for querying, visualization, and reasoning. By coupling DTC with reason-first, ReAct-style agents, Polaris transforms natural-language queries into coherent analytical workflows that not only retrieve and visualize data but also explain the underlying "why." Evaluation on structured enterprise datasets demonstrates high semantic fidelity and answer relevancy, underscoring the potential of multi-agent orchestration to deliver trustworthy, end-to-end business intelligence at scale.

cs.AI↗

arXiv2026

A scalable version of MADD for big-data classification

Distance-based classifiers are very popular, and the Euclidean distance is one of the most commonly used metrics in distance-based classifiers. However, classifiers based on the Euclidean distance often suffer in high-dimensional setups due to issues such as distance concentration, violation of neighborhood structures, and the presence of hubs. In high-dimension, low-sample-size (HDLSS) situations, a data-driven semi-metric called the Mean Absolute Difference of Distances (MADD) is known to circumvent these issues. But one major problem with MADD is that its computational complexity increases quadratically with the training sample size. As a result, the application of MADD becomes computationally challenging for big datasets that have both a high dimension as well as a large number of observations. In this paper, we propose a scalable version of MADD that significantly reduces its computational complexity while retaining its advantages. This speed-up is achieved by selecting a representative set during the computation of MADD. Further speed-ups are achieved by using the idea of Random Fourier Features, particularly when the sample size is very large. We establish that our proposed methods achieve performances similar to MADD but only at a fraction of its computing time, both theoretically as well as numerically. Our approach broadens the scope of MADD, allowing its use to big-data with a very large number of observations.

stat.ME↗

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.

cs.LG↗

arXiv2026

Deep learning estimation of the spectral density of functional time series on large domains

We derive an estimator of the spectral density of a functional time series that is the output of a multilayer perceptron neural network. The estimator is motivated by difficulties with the computation of existing spectral density estimators for time series of functions defined on very large grids that arise, for example, in climate compute models and medical scans. Existing estimators use autocovariance kernels represented as large $G \times G$ matrices, where $G$ is the number of grid points on which the functions are evaluated. In many recent applications, functions are defined on 2D and 3D domains, and $G$ can be of the order $G \sim 10^5$, making the evaluation of the autocovariance kernels computationally intensive or even impossible. We use the theory of spectral functional principal components to derive our deep learning estimator and prove that it is a universal approximator to the spectral density under general assumptions. Our estimator can be trained without computing the autocovariance kernels and it can be parallelized to provide the estimates much faster than existing approaches. We validate its performance by simulations and an application to fMRI images.

stat.ME↗

arXiv2025

A Review of Statistical and Machine Learning Approaches for Coral Bleaching Assessment

Coral bleaching is a major concern for marine ecosystems; more than half of the world's coral reefs have either bleached or died over the past three decades. Increasing sea surface temperatures, along with various spatiotemporal environmental factors, are considered the primary reasons behind coral bleaching. The statistical and machine learning communities have focused on multiple aspects of the environment in detail. However, the literature on various stochastic modeling approaches for assessing coral bleaching is extremely scarce. Data-driven strategies are crucial for effective reef management, and this review article provides an overview of existing statistical and machine learning methods for assessing coral bleaching. Statistical frameworks, including simple regression models, generalized linear models, generalized additive models, Bayesian regression models, spatiotemporal models, and resilience indicators, such as Fisher's Information and Variance Index, are commonly used to explore how different environmental stressors influence coral bleaching. On the other hand, machine learning methods, including random forests, decision trees, support vector machines, and spatial operators, are more popular for detecting nonlinear relationships, analyzing high-dimensional data, and allowing integration of heterogeneous data from diverse sources. In addition to summarizing these models, we also discuss potential data-driven future research directions, with a focus on constructing statistical and machine learning models in specific contexts related to coral bleaching.

stat.AP↗

arXiv2024

Classification Using Global and Local Mahalanobis Distances

We propose a novel semiparametric classifier based on Mahalanobis distances of an observation from the competing classes. Our tool is a generalized additive model with the logistic link function that uses these distances as features to estimate the posterior probabilities of different classes. While popular parametric classifiers like linear and quadratic discriminant analyses are mainly motivated by the normality of the underlying distributions, the proposed classifier is more flexible and free from such parametric modeling assumptions. Since the densities of elliptic distributions are functions of Mahalanobis distances, this classifier works well when the competing classes are (nearly) elliptic. In such cases, it often outperforms popular nonparametric classifiers, especially when the sample size is small compared to the dimension of the data. To cope with non-elliptic and possibly multimodal distributions, we propose a local version of the Mahalanobis distance. Subsequently, we propose another classifier based on a generalized additive model that uses the local Mahalanobis distances as features. This nonparametric classifier usually performs like the Mahalanobis distance based semiparametric classifier when the underlying distributions are elliptic, but outperforms it for several non-elliptic and multimodal distributions. We also investigate the behaviour of these two classifiers in high dimension, low sample size situations. A thorough numerical study involving several simulated and real datasets demonstrate the usefulness of the proposed classifiers in comparison to many state-of-the-art methods.

stat.ME↗

arXiv2023

Nearest Neighbor Classification based on Imbalanced Data: A Statistical Approach

When the competing classes in a classification problem are not of comparable size, many popular classifiers exhibit a bias towards larger classes, and the nearest neighbor classifier is no exception. To take care of this problem, we develop a statistical method for nearest neighbor classification based on such imbalanced data sets. First, we construct a classifier for the binary classification problem and then extend it for classification problems involving more than two classes. Unlike the existing oversampling or undersampling methods, our proposed classifiers do not need to generate any pseudo observations or remove any existing observations, hence the results are exactly reproducible. We establish the Bayes risk consistency of these classifiers under appropriate regularity conditions. Their superior performance over the existing methods is amply demonstrated by analyzing several benchmark data sets.

stat.ME↗

arXiv2023

On Exact Feature Screening in Ultrahigh-dimensional Binary Classification

We propose a new model-free feature screening method based on energy distances for ultrahigh-dimensional binary classification problems. With a high probability, the proposed method retains only relevant features after discarding all the noise variables. The proposed screening method is also extended to identify pairs of variables that are marginally undetectable but have differences in their joint distributions. Finally, we build a classifier that maintains coherence between the proposed feature selection criteria and discrimination method and also establish its risk consistency. An extensive numerical study with simulated and real benchmark data sets shows clear and convincing advantages of our proposed method over the state-of-the-art methods.

stat.ME↗

arXiv2022

On Generalizations of Some Distance Based Classifiers for HDLSS Data

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get masked by scale differences. To rectify this problem, several modifications of these classifiers have been proposed in the literature. However, existing methods are confined to location and scale differences only, and often fail to discriminate among populations differing outside of the first two moments. In this article, we propose some simple transformations of these classifiers resulting into improved performance even when the underlying populations have the same location and scale. We further propose a generalization of these classifiers based on the idea of grouping of variables. The high-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated examples as well as an extensive analysis of real data sets exhibit advantages of the proposed methods.

stat.ME↗

arXiv2022

Separable Expansions for Covariance Estimation

The non-parametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are typically alleviated by assuming separability. However, separability is often questionable, sometimes even demonstrably inadequate. We propose a framework for the analysis of covariance operators of random surfaces that generalises separability, while retaining its major advantages. Our approach is based on the expansion of the covariance into a series of separable terms. The expansion is valid for any covariance over a two-dimensional domain. Leveraging the key notion of the partial inner product, we extend the power iteration method to general Hilbert spaces and show how the aforementioned expansion can be efficiently constructed in practice. Truncation of the expansion and retention of the leading terms automatically induces a non-parametric estimator of the covariance, whose parsimony is dictated by the truncation level. The resulting estimator can be calculated, stored and manipulated with little computational overhead relative to separability. Consistency and rates of convergence are derived under mild regularity assumptions, illustrating the trade-off between bias and variance regulated by the truncation level. The merits and practical performance of the proposed methodology are demonstrated in a comprehensive simulation study and on classification of EEG signals.

math.ST↗

arXiv2021

CovNet: Covariance Networks for Functional Data on Multidimensional Domains

Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively inapplicable. To address this problem, we introduce "Covariance Networks" (CovNet) as a modeling and estimation tool. The CovNet model is "universal" - it can be used to approximate any covariance up to desired precision. Moreover, the model can be fitted efficiently to the data and its neural network architecture allows us to employ modern computational tools in the implementation. The CovNet model also admits a closed-form eigendecomposition, which can be computed efficiently, without constructing the covariance itself. This facilitates easy storage and subsequent manipulation of a covariance in the context of the CovNet. We establish consistency of the proposed estimator and derive its rate of convergence. The usefulness of the proposed method is demonstrated by means of an extensive simulation study and an application to resting state fMRI data.

stat.ME↗

arXiv2020

On a Generalization of the Average Distance Classifier

In high dimension, low sample size (HDLSS)settings, the simple average distance classifier based on the Euclidean distance performs poorly if differences between the locations get masked by the scale differences. To rectify this issue, modifications to the average distance classifier was proposed by Chan and Hall (2009). However, the existing classifiers cannot discriminate when the populations differ in other aspects than locations and scales. In this article, we propose some simple transformations of the average distance classifier to tackle this issue. The resulting classifiers perform quite well even when the underlying populations have the same location and scale. The high-dimensional behaviour of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated as well as real data sets exhibit the usefulness of the proposed methodology.

stat.ME↗

arXiv2019

Choline chloride as a nano-crowder protects HP-36 from urea-induced denaturation: Insights from Solvent Dynamics and Protein-Solvent interaction

Urea at sufficiently high concentration unfolds the secondary structure of proteins leading to denaturation. In contrast, Choline Chloride (ChCl) and urea, in 1:2 molar ratio form a deep eutectic mixture, a liquid at room temperature and protect proteins from denaturation. In order to get a microscopic picture of this phenomenon, we perform extensive all-atom molecular dynamics simulations on a model protein HP-36. Based on our calculation of Kirkwood-Buff integrals, we analyze the relative accumulation of these osmolytes around the protein. Additional insights are drawn from the analyses of the translational and rotational dynamics of solvent molecules and also from the hydrogen bond auto-correlation functions. In the presence of urea, water shows slow subdiffusive dynamics around the protein backbone as a consequence of stronger interaction of water molecules with the backbone atoms. Urea also shows subdiffusive motion. Addition of choline further slows down the dynamics of urea restricting its inclusion around the protein backbone. Adding to this, choline molecules in the first solvation shell of the protein shows the strongest subdiffusive behavior. In other words, ChCl behaves as a nano-crowder by excluding urea from the protein backbone and thereby slowing down the dynamics of the water layer around the protein. This prevents the protein from denaturation and makes it structurally rigid which in turn is supported by the smaller radius of gyration and root mean square deviation values of HP-36 when ChCl is present in the system.

cond-mat.soft↗

arXiv2018

On high-dimensional modifications of some graph-based two-sample tests

Testing for the equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been proposed in the literature, which can be used for data of arbitrary dimensions. Most of these test statistics are computed using pairwise Euclidean distances among the observations. But, due to concentration of pairwise Euclidean distances, these tests have poor performance in many high-dimensional problems. Some of them can have powers even below the nominal level when the scale-difference between two distributions dominates the location-difference. To overcome these limitations, we introduce a new class of dissimilarity indices and use it to modify some popular graph-based tests. These modified tests use the distance concentration phenomenon to their advantage, and as a result, they outperform the corresponding tests based on the Euclidean distance in a wide variety of examples. We establish the high-dimensional consistency of these modified tests under fairly general conditions. Analyzing several simulated as well as real data sets, we demonstrate their usefulness in high dimension, low sample size situations.

stat.ME↗

arXiv2017

On perfect clustering of high dimension, low sample size data

Popular clustering algorithms based on usual distance functions (e.g., Euclidean distance) often suffer in high dimension, low sample size (HDLSS) situations, where concentration of pairwise distances has adverse effects on their performance. In this article, we use a dissimilarity measure based on the data cloud, called MADD, which takes care of this problem. MADD uses the distance concentration phenomenon to its advantage, and as a result, clustering algorithms based on MADD usually perform better for high dimensional data. Using theoretical and numerical results, we amply demonstrate it in this article. We also address the problem of estimating the number of clusters. This is a very challenging problem in cluster analysis, and several algorithms have been proposed for it. We show that many of these existing algorithms have superior performance in high dimensions when MADD is used instead of the Euclidean distance. We also construct a new estimator based on penalized Dunn index and prove its consistency in the HDLSS asymptotic regime, where the sample size remains fixed and the dimension grows to infinity. Several simulated and real data sets are analyzed to demonstrate the importance of MADD for cluster analysis of high dimensional data.

stat.ME↗