arXiv subjects

Somnath Mondal

Publications and source records attributed to Somnath Mondal.

6 recordsLinked to original sources

arXiv2026

Estimating order scale parameters of two scale mixture of exponential distributions

The scale mixture of the exponential distribution provides a flexible framework for modelling lifetime and reliability data. This model is widely used in survival analysis, biomedical studies, statistical finance, and other related disciplines. In this work, we investigate the estimation of the ordered scale parameter of two scale mixture of exponential distributions under Stein loss and symmetric loss functions. Under certain conditions, we prove the inadmissibility of the affine equivariant estimator and exhibit several improved estimators. Consequently, we propose a class of estimators that uniformly dominate the best affine equivariant estimators (BAEE). Furthermore, we have proved that the boundary estimator of this class is a generalized Bayes estimator. As an application, we have proposed improved estimators for the ordered scale parameters of the multivariate Lomax and exponential inverse Gaussian distributions. For each case, we have conducted a simulation study to compare the risk performance of the improved estimators. Finally, we have given two real-life data analysis for implementation purposes.

math.ST↗

arXiv2026

Improved estimation of positive powers of scale parameters of exponential distributions under a prior information

Estimating unknown parameters subject to prior constraints is important in statistical inference, particularly in fields such as reliability analysis, survival studies, and engineering, where prior structural information about the parameters is often available. Incorporating such prior information makes the analysis more realistic and usually yields better estimates than methods that ignore such information. In this article, we consider the problem of estimating the positive power of the scale parameter of a two-shifted exponential population under a prior ordering constraint on scale parameters. We derive sufficient conditions under which equivariant estimators are shown to dominate others under scale-invariant strictly convex loss functions. In addition, we derived various estimators that dominate the best affine equivariant estimators (BAEE). Moreover, we derive a smooth estimator which dominates the BAEE using an integrated approach, and we further show that it is a generalized Bayes estimator under a non-informative prior. We also provide an improved estimator based on the Pitman closeness criterion. An extensive simulation study has been done for computational purposes. Finally, we provided real examples to implement the results.

math.ST↗

arXiv2026

What on Earth is AlphaEarth? Hierarchical structure and functional interpretability for global land cover

Geospatial foundation models generate high-dimensional embeddings that achieve strong predictive performance, yet their internal organization remains obscure, limiting their scientific use. Recent interpretability studies relate Google AlphaEarth Foundations (GAEF) embeddings to continuous environmental variables, but it is still unclear whether the embedding space exhibits a functional or hierarchical organization, in which some dimensions act as specialized representations while others encode shared or broader geospatial structure. In this work, we propose a functional interpretability framework that reverse-engineers the role of embedding dimensions by characterizing their contribution to land cover structure from observed classification behavior. The approach combines large-scale experimentation with a structural analysis of embedding-class relationships based on feature importance patterns and progressive ablation. Our results show that embedding dimensions exhibit consistent and non-uniform functional behavior, allowing them to be categorized along a hierarchical functional spectrum: specialist dimensions associated with specific land cover classes, low- and mid-generalist dimensions capturing shared characteristics between classes, and highgeneralist dimensions reflecting broader environmental gradients. Critically, we find that accurate land cover classification (98% of baseline performance) can be achieved using as few as 2 to 12 of the 64 available dimensions, depending on the class. This demonstrates substantial redundancy in the embedding space and offers a pathway toward significant reductions in computational cost. Together, these findings reveal that AlphaEarth embeddings are not only physically informative, but also functionally organized into a hierarchical structure, providing practical guidance for dimension selection in operational classification tasks.

cs.LG↗

arXiv2025

DeepPNI: Language- and graph-based model for mutation-driven protein-nucleic acid energetics

The interaction between proteins and nucleic acids is crucial for processes that sustain cellular function, including DNA maintenance and the regulation of gene expression and translation. Amino acid mutations in protein-nucleic acid complexes often lead to vital diseases. Experimental techniques have their own specific limitations in predicting mutational effects in protein-nucleic acid complexes. In this study, we compiled a large dataset of 1951 mutations including both protein-DNA and protein-RNA complexes and integrated structural and sequential features to build a deep learning-based regression model named DeepPNI. This model estimates mutation-induced binding free energy changes in protein-nucleic acid complexes. The structural features are encoded via edge-aware RGCN and the sequential features are extracted using protein language model ESM-2. We have achieved a high average Pearson correlation coefficient (PCC) of 0.76 in the large dataset via five-fold cross-validation. Consistent performance across individual dataset of protein-DNA, protein-RNA complexes, and different experimental temperature split dataset make the model generalizable. Our model showed good performance in complex-based five-fold cross-validation, which proved its robustness. In addition, DeepPNI outperformed in external dataset validation, and comparison with existing tools

q-bio.BM↗

arXiv2025

Improved estimation of the positive powers ordered restricted standard deviation of two normal populations

The present manuscript is concerned with component-wise estimation of the positive power of ordered restricted standard deviation of two normal populations with certain restrictions on the means. We propose several improved estimators under a general scale invariant bowl-shaped loss function. Also, we proposed a class of improved estimators. It has been shown that the boundary estimator of this class is a generalized Bayes. As an application, the improved estimators are obtained with respect to quadratic loss, entropy loss, and a symmetric loss function. We have conducted extensive Monte Carlo simulations to study and compare the risk performance of the proposed estimators. Finally, a real life data analysis is given to illustrate our findings.

math.ST↗

arXiv2024

Analysis of a special type of soliton on Kenmotsu manifolds

In this paper, we aim to investigate the properties of an almost $*$-Ricci-Bourguignon soliton (almost $*-$R-B-S for short) on a Kenmotsu manifold (K-M). We start by proving that if a Kenmotsu manifold (K-M) obeys an almost $*-$R-B-S, then the manifold is $η$-Einstein. Furthermore, we establish that if a $(κ, -2)'$-nullity distribution, where $κ<-1$, has an almost $*$-Ricci-Bourguignon soliton (almost $*-$R-B-S), then the manifold is Ricci flat. Moreover, we establish that if a K-M has almost $*$-Ricci-Bourguignon soliton gradient and the vector field $ξ$ preserves the scalar curvature $r$, then the manifold is an Einstein manifold with a constant scalar curvature given by $r=-n(2n-1)$. Finaly, we have given en example of a almost $*-$R-B-S gradient on the Kenmotsu manifold.

physics.gen-ph↗