Searcharxiv⌕ Search

arXiv subjects

Abhik Ghosh

Publications and source records attributed to Abhik Ghosh.

At least 19 recordsLinked to original sources
arXiv2026

A Composite Divergence Approach to Robust Multivariate Estimation under Cellwise and Casewise Contamination

Composite likelihood (CL) methods provide a computationally efficient alternative to full likelihood inference for complex multivariate models by replacing the joint likelihood with a product of lower-dimensional marginal or conditional components. Like the MLE, however, the maximum CL estimator (MCLE) is highly sensitive to data contamination. On the other hand, robust divergence-based procedures such as the minimum density power divergence (DPD) estimator require the full joint density and so scale poorly to complex multivariate models. We introduce the composite DPD (CDPD), a genuine statistical divergence built entirely from the low-dimensional component densities defining a CL, combining the computational scalability of CL with the robustness of the DPD. The resulting minimum CDPD estimator (MCDPDE) robustifies the MCLE without requiring integration over the full multivariate sample space. We establish consistency, asymptotic normality, and the influence function of the MCDPDE under regularity conditions on the component models alone, without requiring correct specification of the full joint distribution. We show that it is qualitatively robust for every positive value of its tuning parameter, unlike the MCLE recovered as the limit. Because its components can be chosen at the pairwise or cell level, the framework guards simultaneously against casewise and cellwise contamination. Operating directly on component densities rather than elliptical distance structures, it extends robust inference beyond the elliptical models to which most existing cellwise-robust procedures are confined. We develop computational algorithms implemented in the accompanying R package mvdpd. Simulation studies and real-data applications show that the MCDPDE achieves substantial robustness gains over the MCLE while retaining competitive efficiency under the assumed model.

math.ST↗
arXiv2026

No Unique Minimizer, No Problem: On the Consistency of Robust Neural Classifiers

Neural network classifiers trained by cross-entropy minimization are highly sensitive to label noise and adversarial contamination. While robust alternatives offer bounded influence and resistance to corruption, their statistical foundations in the deep learning setting are insufficient due to a fundamental difficulty: neural parameterizations are non-identifiable, so the population loss minimizer is an equivalence class of parameters, not a unique point. We develop a consistency theory for robust neural classifiers based on the S-divergence family that requires no identifiability assumption. Casting training as stochastic optimization over a non-identifiable parameter space, we prove that empirical S-divergence minimizers converge to the population-optimal equivalence class under mild regularity conditions, and verify these conditions for three architecture choices. We further establish that limit points of the robust training algorithm are stationary points of the empirical objective. Experiments on vision and language benchmark datasets confirm that S-divergence training maintains clean-data accuracy while exhibiting performance competitive with existing robust methods.

cs.LG↗
arXiv2026

Universally Optimal Robustness-Efficiency Tradeoffs for a General Class of Minimum Divergence Estimators

Balancing the efficiency of an estimator under ideal conditions against its robustness under contamination remains a central challenge in robust statistics. While minimum divergence methods offer a flexible alternative to traditional M-estimation, choosing the appropriate discrepancy measure has historically relied on heuristic or empirical justifications. This manuscript introduces a rigorous optimality criterion for this selection process. By investigating the comprehensive Generalized Alpha-Beta Divergence (GABD) family, we explicitly characterize the Pareto frontier dictating the lowest possible asymptotic variance for any strictly enforced asymptotic breakdown point. Our main theoretical results establish that the estimator achieving this mathematical optimum invariably falls within the extended $(\phi, \gamma)$-divergence class. Crucially, the derived optimal tuning parameter, $\phi^*$, given other parameters, depends solely on the desired breakdown threshold and is entirely invariant to both the assumed parametric model and the exact nature of the data contamination. Supported by comprehensive derivations of asymptotic normality, influence functions, and breakdown thresholds for both continuous and discrete settings, this work offers a unified, theoretical resolution to the long-standing problem of optimal divergence selection in robust inference.

math.ST↗
arXiv2026

Robust and Scalable Sure Screening of Fixed effects in Ultrahigh-dimensional Linear Mixed Models

In modern applications of linear mixed models, the number of candidate fixed-effects covariates can grow exponentially with the sample size, while dependence induced by random effects and possible data contamination pose substantial challenges for existing variable screening methods. We propose a robust and computationally efficient sure screening procedure for identifying relevant fixed-effects covariates in ultrahigh-dimensional linear mixed models with known random effects. The proposed method leverages a proxy-based transformation to decouple dependence induced by random effects, enabling screening via marginal analysis in a transformed regression model. Robustness is achieved by constructing marginal utilities based on minimum density power divergence, yielding stability under data contamination and model misspecification without sacrificing scalability. The resulting procedure, termed DPD-SISP, is shown to retain all relevant covariates (sure screening property) with exponentially high probability under general conditions, allowing for non-Gaussian errors and nonpolynomial growth of dimensionality. In addition, DPD-SISP exhibits strong robustness properties supported by influence function and breakdown point analyses. The framework is further extended to incorporate prior information through conditional screening, mitigate correlation-induced masking via iterative refinement, and enable robust post-screening estimation of fixed effects. Extensive simulation studies demonstrate competitive performance of DPD-SISP under ideal settings and substantial gains in stability under data contamination. Its practical utility is illustrated through an application to high-dimensional longitudinal data from the ADNI2 study. The proposed framework thus provides a unified, robust, and scalable approach for variable screening in ultrahigh-dimensional linear mixed models.

stat.ME↗
arXiv2026

Methodological Frontiers in 21-cm Intensity Mapping: the Treatment of Systematics and Foreground Contamination

The distribution of neutral hydrogen (HI) in the post-reionization universe traces the cosmic large-scale structure and therefore serves as a powerful cosmological probe. An efficient way to measure its distribution over wide sky areas and redshift ranges is through single-dish intensity mapping, which exploits the autocorrelation signal of each dish in a telescope array while scanning the same sky patch. Thanks to its broad frequency coverage and technical capabilities, SKA-Mid will enable measurements of the integrated 21 cm emission from HI up to redshift $z\sim3$, making single-dish intensity mapping a key observable for probing dark matter and dark energy. Isolating the faint 21 cm cosmological signal without introducing biases is, however, challenging. The 21 cm signal is several orders of magnitude weaker than the astrophysical foregrounds, and its analysis is further affected by instrumental systematics. Overcoming these difficulties requires detailed modelling together with continuous improvements and innovations in data-analysis techniques. Over the past decade, the international community has developed and tested new methods to address current observational challenges and prepare for forthcoming SKA-Mid observations. This chapter reviews recent advances in map-making and component-separation techniques, with particular emphasis on telescope-specific systematics such as beam response and correlated noise. We focus on results obtained in controlled simulation environments, providing a valuable framework for assessing the strengths and limitations of different approaches. Developing robust algorithms capable of accurately handling instrumental effects and sky-model uncertainties is a crucial step toward fully exploiting the cosmological potential of HI intensity-mapping surveys in the SKA Observatory era.

astro-ph.CO↗
arXiv2026

Faraday Complexity and Depolarisation in a High-Rotation-Measure Radio Galaxy from the Spectra and Polarisation In Cutouts of Extragalactic Sources (SPICE-RACS) DR2

We present a broadband spectro-polarimetric analysis of the extragalactic radio source \texttt{RACS\_0900-28\_7036} using SPICE-RACS DR2 observations with the Australian Square Kilometre Array Pathfinder (ASKAP). The source was selected for its large rotation measure (${\rm RM}=345.7\pm0.2~{\rm rad~m^{-2}}$), substantial excess relative to the local foreground ($\Delta {\rm RM}\approx171~{\rm rad~m^{-2}}$), and strong evidence of Faraday complexity ($\sigma_{\rm add}/\delta\sigma_{\rm add}\approx8.6$). Observations span 803--1083~MHz in 36 spectral channels, enabling detailed characterization of Faraday rotation and wavelength-dependent depolarization. One-dimensional QU-fitting and Bayesian model selection identify a multi-component model comprising one Burn-slab component and two external Faraday dispersion components (1 Slab + 2 EFD) as the preferred description. The dominant astrophysical component exhibits ${\rm RM}\approx345.5~{\rm rad~m^{-2}}$ with modest Faraday dispersion ($\sigma_{\rm RM}\approx3~{\rm rad~m^{-2}}$), consistent with the Galactic foreground rotation measure at the source position (${\rm RM}_{\rm Gal}=331.9\pm33.1~{\rm rad~m^{-2}}$). A secondary broader component at ${\rm RM}\approx131.5~{\rm rad~m^{-2}}$ shows strong depolarization ($\sigma_{\rm RM}\approx19.5~{\rm rad~m^{-2}}$), indicating an additional turbulent Faraday-active medium along the line of sight. The fractional polarization spectrum and $q$--$u$ plane evolution further confirm multiple Faraday-active regions along the line of sight. These results demonstrate that ASKAP broadband spectropolarimetry can resolve complex Faraday structures and probe turbulent magnetized environments, providing a framework for systematic depolarization studies across the full SPICE-RACS catalog and enabling statistical investigations of Faraday complexity in diverse extragalactic radio sources.

astro-ph.CO↗
arXiv2026

Faraday Complexity and Depolarization in LOFAR Two-metre Sky Survey (LoTSS-DR2) Polarized Radio Sources

We present a broadband spectro-polarimetric analysis of 1,565 polarized radio sources from the LOFAR Two-Metre Sky Survey Data Release 2 (LoTSS-DR2) RM Grid catalogue. This study uses frequency-dependent Stokes Q and U spectra across the 120-168 MHz LOFAR HBA band to investigate their polarization properties. The polarization behaviour of each source is modelled with multi-component Faraday depolarization models to investigate the magneto-ionic environments responsible for low-frequency depolarization. Significant Faraday complexity is observed throughout the sample, with 43.2% of sources requiring two or three Faraday components. External Faraday dispersion dominates the depolarization behaviour, with 54.1% of sources classified as external-screen dominated and approximately 60% showing statistically significant evidence for turbulent external Faraday-active media, while only 10.3% are consistent with pure internal differential Faraday rotation. The intrinsic polarization angle and RM separations between fitted components are generally small, suggesting that many RM components trace physically related emission regions embedded within common magneto-ionic environments. A weak but statistically significant anti-correlation is detected between the polarization spectral index, $\beta$, and weighted Faraday dispersion, $\sigma_{\rm RM,wtd}$, for two-component systems, whereas one- and three-component populations show no significant trend. The rest-frame Faraday dispersion, $\sigma_{\rm RM,rest}$, exhibits significant positive correlations with redshift for the external-screen dominated and mixed depolarization populations, even after controlling for radio luminosity, indicating increasingly turbulent or strongly magnetized environments surrounding radio AGN at earlier cosmic epochs.

astro-ph.CO↗
arXiv2026

rSDNet: Unified Robust Neural Learning against Label Noise and Adversarial Attacks

Neural networks are central to modern artificial intelligence, yet their training remains highly sensitive to data contamination. Standard neural classifiers are trained by minimizing the categorical cross-entropy loss, corresponding to maximum likelihood estimation under a multinomial model. While statistically efficient under ideal conditions, this approach is highly vulnerable to contaminated observations including label noises corrupting supervision in the output space, and adversarial perturbations inducing worst-case deviations in the input space. In this paper, we propose a unified and statistically grounded framework for robust neural classification that addresses both forms of contamination within a single learning objective. We formulate neural network training as a minimum-divergence estimation problem and introduce rSDNet, a robust learning algorithm based on the general class of $S$-divergences. The resulting training objective inherits robustness properties from classical statistical estimation, automatically down-weighting aberrant observations through model probabilities. We establish essential population-level properties of rSDNet, including Fisher consistency, classification calibration implying Bayes optimality, and robustness guarantees under uniform label noise and infinitesimal feature contamination. Experiments on three benchmark image classification datasets show that rSDNet improves robustness to label corruption and adversarial attacks while maintaining competitive accuracy on clean data, Our results highlight minimum-divergence learning as a principled and effective framework for robust neural classification under heterogeneous data contamination.

stat.ML↗
arXiv2026

Provably robust learning of regression neural networks using $β$-divergences

Regression neural networks (NNs) are most commonly trained by minimizing the mean squared prediction error, which is highly sensitive to outliers and data contamination. Existing robust training methods for regression NNs are often limited in scope and rely primarily on empirical validation, with only a few offering partial theoretical guarantees. In this paper, we propose a new robust learning framework for regression NNs based on the $β$-divergence (also known as the density power divergence) which we call `rRNet'. It applies to a broad class of regression NNs, including models with non-smooth activation functions and error densities, and recovers the classical maximum likelihood learning as a special case. The rRNet is implemented via an alternating optimization scheme, for which we establish convergence guarantees to stationary points under mild, verifiable conditions. The (local) robustness of rRNet is theoretically characterized through the influence functions of both the parameter estimates and the resulting rRNet predictor, which are shown to be bounded for suitable choices of the tuning parameter $β$, depending on the error density. We further prove that rRNet attains the optimal 50\% asymptotic breakdown point at the assumed model for all $β\in(0, 1]$, providing a strong global robustness guarantee that is largely absent for existing NN learning methods. Our theoretical results are complemented by simulation experiments and real-data analyses, illustrating practical advantages of rRNet over existing approaches in both function approximation problems and prediction tasks with noisy observations.

stat.ML↗
arXiv2026

Faraday Depolarization Study of a Radio Galaxy Using LOFAR Two-metre Sky Survey: Data Release 2

We present a detailed depolarization analysis of the radio galaxy \texttt{ILTJ012215.21+254334.8} using polarimetric data from the \textit{LOFAR Two-metre Sky Survey} (LoTSS) Data Release 2 (DR2) catalogue. This source, with \textit{RM} $\sim$ 47 rad m$^{-2}$ and projected linear size $\sim$ 335 kpc at $z \approx 0.05$, serves as a pilot for systematic QU-fitting of unresolved LoTSS sources, building on prior single-target studies that established the need for multi-component Faraday models in complex magneto-ionic media. Fitting five depolarization models to the LoTSS HBA (120-168 MHz) fractional polarization spectra reveals a decisively preferred three-component model (one Faraday-thin instrumental leakage, plus two external Faraday dispersions), demonstrating that LoTSS data alone can constrain moderate Faraday complexity in typical DR2 galaxies. Our results highlight turbulence and inhomogeneity in the foreground magneto-ionic medium and outline a path for population studies of LoTSS FR-I sources.

astro-ph.CO↗
arXiv2026

Robust Inference for Non-Linear Regression Models with Applications in Enzyme Kinetics

Despite linear regression being the most popular statistical modelling technique, in real-life we often need to deal with situations where the true relationship between the response and the covariates is nonlinear in parameters. In such cases one needs to adopt appropriate non-linear regression (NLR) analysis, having wider applications in biochemical and medical studies among many others. In this paper we propose a new improved robust estimation and testing methodologies for general NLR models based on the minimum density power divergence approach and apply our proposal to analyze the widely popular Michaelis-Menten (MM) model in enzyme kinetics. We establish the asymptotic properties of our proposed estimator and tests, along with their theoretical robustness characteristics through influence function analysis. For the particular MM model, we have further empirically justified the robustness and the efficiency of our proposed estimator and the testing procedure through extensive simulation studies and several interesting real data examples of enzyme-catalyzed (biochemical) reactions.

stat.ME↗
arXiv2025

Robust Estimation for Dependent Binary Network Data

We consider the problem of learning the interaction strength between the nodes of a network based on dependent binary observations residing on these nodes, generated from a Markov Random Field (MRF). Since these observations can possibly be corrupted/noisy in larger networks in practice, it is important to robustly estimate the parameters of the underlying true MRF to account for such inherent contamination in observed data. However, it is well-known that classical likelihood and pseudolikelihood based approaches are highly sensitive to even a small amount of data contamination. So, in this paper, we propose a density power divergence (DPD) based robust generalization of the computationally efficient maximum pseudolikelihood (MPL) estimator of the interaction strength parameter, and derive its rate of consistency under the pure model. Along the way, we establish consistency and asymptotics for a class of general $Z$-estimators, covering our proposed DPD based estimators, under flexible assumptions that hold for a substantial class of standard models. To the best of our knowledge, these are the first central limit theorems for the class of general $Z$-estimators in such settings. Moreover, we show that the gross error sensitivities of the proposed DPD based estimators are significantly smaller than that of the MPL estimator, thereby theoretically justifying the greater (local) robustness of the former under contaminated settings. Finally, we demonstrate the superior (finite sample) performance of the DPD based variants over the traditional MPL estimator in a number of synthetically generated contaminated network datasets, and apply them to learn the network interaction strength in several real datasets from diverse domains of social science, neurobiology and genomics.

stat.ME↗
arXiv2025

A Componentwise Estimation Procedure for Multivariate Location and Scatter: Robustness, Efficiency and Scalability

Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model misspecification and the presence of outliers in the data; on the other hand robust estimators with reasonably high efficiency are often computationally challenging for modern large and complex datasets. In this work, we propose a new, simple, robust and highly efficient method for estimation of the location vector and the scatter matrix for elliptically symmetric distributions. The proposed estimation procedure is designed in the spirit of the minimum density power divergence (DPD) estimation approach with appropriate modifications which makes our proposal (sequential minimum DPD estimation) computationally very economical and scalable to large as well as higher dimensional datasets. Consistency and asymptotic normality of the proposed sequential estimators of the multivariate location and scatter are established along with asymptotic positive definiteness of the estimated scatter matrix. Robustness of our estimators are studied by means of influence functions. All theoretical results are illustrated further under multivariate normality. A large-scale simulation study is presented to assess finite sample performances and scalability of our method in comparison to the usual maximum likelihood estimator (MLE), the ordinary minimum DPD estimator (MDPDE) and other popular non-parametric methods. The applicability of our method is further illustrated with a real dataset on credit card transactions.

stat.ME↗
arXiv2025

Robust Rank Estimation for Noisy Matrices

Estimating the true rank of a noisy data matrix is a fundamental problem underlying techniques such as principal component analysis, matrix completion, etc. Existing rank estimation criteria, including information-based and cross-validation methods, are either highly sensitive to outliers or computationally demanding when combined with robust estimators. This paper proposes a new criterion, the Divergence Information Criterion for Matrix Rank (DICMR), that achieves both robustness and computational simplicity. Derived from the density power divergence framework, DICMR inherits the robustness properties while being computationally very simple. We provide asymptotic bounds on its overestimation and underestimation probabilities, and demonstrate first-order B-robustness of the criteria. Extensive simulations show that DICMR delivers accuracy comparable to the robustified cross-validation methods, but with far lower computational cost. We also showcase a real-data application to microarray imputation to further demonstrate its practical utility, outperforming several state-of-the-art algorithms.

stat.ME↗
arXiv2025

On Generalized Likelihood Estimation Based on the Logarithmic Norm Relative Entropy

Traditional likelihood based methods for parameter estimation get highly affected when the given data is contaminated by outliers even in a small proportion. In this paper, we consider a robust parameter estimation method, namely the minimum logarithmic norm relative entropy (LNRE) estimation procedure, and study different (generalized) sufficiency principles associated with it. We introduce a new two-parameter power-law family of distributions (namely, $\mathcal{M}^{(α,β)}$-family), which is shown to have a fixed number of sufficient statistics, independent of the sample size, with respect to the generalized likelihood function associated with the LNRE. Then, we obtain the generalized minimal sufficient statistic for this family and derive the generalized Rao-Blackwell theorem and the generalized Cramér-Rao lower bound for the minimum LNRE estimation. We also study the minimum LNRE estimators (MLNREEs) for the family of Student's distributions particularly in detail. Our general results reduces to the classical likelihood based results under the exponential family of distributions at specific choices of the tuning parameter $α$ and $β$. Finally, we present simulation studies followed by a real data analysis, which highlight the practical utility of the MLNREEs for data contaminated by possible outliers. Along the way we also correct a mistake found in a recent paper on related theory of generalized likelihoods.

math.ST↗
arXiv2025

Asymptotic breakdown point analysis of the minimum density power divergence estimator under independent non-homogeneous setups

The minimum density power divergence estimator (MDPDE) has gained significant attention in the literature of robust inference due to its strong robustness properties and high asymptotic efficiency; it is relatively easy to compute and can be interpreted as a generalization of the classical maximum likelihood estimator. It has been successfully applied in various setups, including the case of independent and non-homogeneous (INH) observations that cover both classification and regression-type problems with a fixed design. While the local robustness of this estimator has been theoretically validated through the bounded influence function, no general result is known about the global reliability or the breakdown behavior of this estimator under the INH setup, except for the specific case of location-type models. In this paper, we extend the notion of asymptotic breakdown point from the case of independent and identically distributed data to the INH setup and derive a theoretical lower bound for the asymptotic breakdown point of the MDPDE, under some easily verifiable assumptions. These results are further illustrated with applications to some fixed design regression models and corroborated through extensive simulation studies.

math.ST↗
arXiv2025

A demonstration of the effect of fringe-rate filtering in the Hydrogen Epoch of Reionization Array delay power spectrum pipeline

Radio interferometers targeting the 21cm brightness temperature fluctuations at high redshift are subject to systematic effects that operate over a range of different timescales. These can be isolated by designing appropriate Fourier filters that operate in fringe-rate (FR) space, the Fourier pair of local sidereal time (LST). Applications of FR filtering include separating effects that are correlated with the rotating sky vs. those relative to the ground, down-weighting emission in the primary beam sidelobes, and suppressing noise. FR filtering causes the noise contributions to the visibility data to become correlated in time however, making interpretation of subsequent averaging and error estimation steps more subtle. In this paper, we describe fringe rate filters that are implemented using discrete prolate spheroidal sequences, and designed for two different purposes -- beam sidelobe/horizon suppression (the `mainlobe' filter), and ground-locked systematics removal (the `notch' filter). We apply these to simulated data, and study how their properties affect visibilities and power spectra generated from the simulations. Included is an introduction to fringe-rate filtering and a demonstration of fringe-rate filters applied to simple situations to aid understanding.

astro-ph.CO↗
arXiv2025

Characterization of Generalized Alpha-Beta Divergence and Associated Entropy Measures

Minimum divergence estimators provide a natural framework for robust (parametric) statistical inference. Useful properties of several such divergence measures, including, the Hellinger distance, the power divergence, the density power divergence, the logarithmic density power divergence, etc., have been established in the literature; many of them lead to estimators with high statistical efficiency, sometimes even full asymptotic efficiency. The notable success of these divergences as tools of parametric inference motivates us to explore possible extensions of the alpha-beta divergence family, leading to a superfamily of divergence measures called the ``generalized alpha-beta (GAB) divergences''. This family contains all the aforementioned popular divergence measures as special cases, and additionally provides opportunities to discover new and novel classes of divergences that generate estimators having strong robustness properties without allowing a significant drop in statistical efficiency in various applications. In this paper, we provide the necessary and sufficient conditions for the validity of these generalized divergence measures that enable us to employ them for improved statistical inference. We also show various characterizing properties like duality, inversion, semi-continuity, etc., for the general class of GAB divergences. A discussion on the entropy measure derived from this general family and its properties are also presented along with the associated maximum entropy principle. The class of GAB divergences provide a delicate balance between local and global robustness, and this is illustrated by two examples of robust parameter estimation under the Geometric and the normal scale models.

math.ST↗