arXiv subjects

Soumik Purkayastha

Publications and source records attributed to Soumik Purkayastha.

5 recordsLinked to original sources

arXiv2025

Quantification and cross-fitting inference of asymmetric relations under generative exposure mapping models

Learning directionality between variables is crucial yet challenging, especially for mechanistic relationships without a priori ordering assumptions. We propose a coefficient of asymmetry to quantify directional asymmetry using Shannon's entropy within a generative exposure mapping (GEM) framework. GEMs arise from experiments where a generative function $g$ maps exposure $X$ to outcome $Y$ through $Y = g(X)$, extended to noise-perturbed GEMs as $Y = g(X) + ε$. Our approach considers a rich class of generative functions while providing statistical inference for uncertainty quantification - a gap in existing bivariate causal discovery techniques. We establish large-sample theoretical guarantees through data-splitting and cross-fitting techniques, implementing fast Fourier transformation-based density estimation to avoid parameter tuning. The methodology accommodates contamination in outcome measurements. Extensive simulations demonstrate superior performance compared to competing causal discovery methods. Applied to epigenetic data examining DNA methylation and blood pressure relationships, our method unveils novel pathways for cardiovascular disease genes \emph{FGF5} and \emph{HSD11B2}. This framework serves as a discovery tool for improving scientific research rigor, with GEM-induced asymmetry representing a low-dimensional imprint of underlying causality

stat.ME↗

arXiv2025

A Framework for Covariate-Adjusted Bivariate Causal Discovery

Ascertaining causal direction from observational data is a fundamental challenge in scientific inquiry. Of particular interest is the problem of covariate-adjusted bivariate causal discovery, i.e., determining the causal direction between X and Y in the presence of Z. While unadjusted bivariate causal discovery has seen significant advances (Hoyer et al., 2008; Ni, 2022), there is a lack of methodology dealing with real-world bivariate relationships, which are often modulated by a set of covariate(s), Z. Building on previous work in Purkayastha and Song (2025), we introduce a novel, nonparametric framework for the covariate-adjusted bivariate causal discovery problem and propose a conditional asymmetry coefficient to track said direction of causation. We develop a robust estimation procedure using kernel-based conditional density estimation with cross-fitting and also provide rigorous uncertainty quantification using a nonparametric kernel smoothing technique, addressing a key limitation of many existing algorithms. As a key application, we demonstrate how this framework can be applied to the problem of collider detection, a persistent challenge in causal structure learning. Simulation studies show our method's superior performance in identifying causal structures. We apply our approach to an epigenetic study (Perng et al., 2019), investigating the role of blood pressure in regulating the effects of DNA methylation. In summary, our work offers methodological advancement by providing a robust, inferential toolkit for dissecting complex, moderated bivariate causal relationships in observational data.

stat.ME↗

arXiv2023

Asymmetric predictability in causal discovery: an information theoretic approach

Causal investigations in observational studies pose a great challenge in research where randomized trials or intervention-based studies are not feasible. We develop an information geometric causal discovery and inference framework of "predictive asymmetry". For $(X, Y)$, predictive asymmetry enables assessment of whether $X$ is more likely to cause $Y$ or vice-versa. The asymmetry between cause and effect becomes particularly simple if $X$ and $Y$ are deterministically related. We propose a new metric called the Directed Mutual Information ($DMI$) and establish its key statistical properties. $DMI$ is not only able to detect complex non-linear association patterns in bivariate data, but also is able to detect and infer causal relations. Our proposed methodology relies on scalable non-parametric density estimation using Fourier transform. The resulting estimation method is manyfold faster than the classical bandwidth-based density estimation. We investigate key asymptotic properties of the $DMI$ methodology and a data-splitting technique is utilized to facilitate causal inference using the $DMI$. Through simulation studies and an application, we illustrate the performance of $DMI$.

stat.ME↗

arXiv2023

fastMI: a fast and consistent copula-based estimator of mutual information

As a fundamental concept in information theory, mutual information ($MI$) has been commonly applied to quantify association between random vectors. Most existing nonparametric estimators of $MI$ have unstable statistical performance since they involve parameter tuning. We develop a consistent and powerful estimator, called fastMI, that does not incur any parameter tuning. Based on a copula formulation, fastMI estimates $MI$ by leveraging Fast Fourier transform-based estimation of the underlying density. Extensive simulation studies reveal that fastMI outperforms state-of-the-art estimators with improved estimation accuracy and reduced run time for large data sets. fastMI provides a powerful test for independence that exhibits satisfactory type I error control. Anticipating that it will be a powerful tool in estimating mutual information in a broad range of data, we develop an R package fastMI for broader dissemination.

stat.AP↗

arXiv2020

On minimum Bregman divergence inference

In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed. The popular density power divergence (DPD) class of estimators is a sub-class of Bregman divergences. We propose and study a new sub-class of Bregman divergences called the exponentially weighted divergence (EWD). Like the minimum DPD estimator, the minimum EWD estimator is recognised as an M-estimator. This characterisation is useful while discussing the asymptotic behaviour as well as the robustness properties of this class of estimators. Performances of the two classes are compared -- both through simulations as well as through real life examples. We develop an estimation process not only for independent and homogeneous data, but also for non-homogeneous data. General tests of parametric hypotheses based on the Bregman divergences are also considered. We establish the asymptotic null distribution of our proposed test statistic and explore its behaviour when applied to real data. The inference procedures generated by the new EWD divergence appear to be competitive or better that than the DPD based procedures.

math.ST↗