Vishal Routh | Searcharxiv

arXiv2026

Heavy Tailed Homogeneous Structural Causal Models

We consider causal discovery in structural causal models driven by heavy-tailed noise, where extremes carry important information about causal direction. We introduce the Heavy-Tailed Homogeneous Structural Causal Model (HT-HSCM), a unified framework that generalizes heavy-tailed linear and max-linear models. We demonstrate that causal tail coefficients identify the complete ancestral partial order of the underlying directed acyclic graph. We also formulate a recursive algorithm for recovering quantities associated with the model called ancestral impulse-responses from the causal tail coefficients. Our results provide a general and theoretically justified framework for causal discovery in heavy-tailed systems.

math.ST↗

arXiv2026

Conditional Independence under Infinite Measures and Poisson Point Processes

We study conditional independence under infinite measures on punctured product spaces, a notion recently introduced for graphical modeling in multivariate extremes and Lévy processes. In contrast to classical probabilistic conditional independence, this concept is formulated through normalized restrictions of an infinite measure that reflects the non-product structure of the punctured space. We show that this non-standard notion admits a natural probabilistic characterization: it is equivalent to classical conditional independence between coordinate projections of a Poisson point process defined on the punctured space with the given infinite measure as its mean measure. In addition, we provide a functional characterization of the conditional independence concept at the level of the enumerated points of the Poisson point process. We further extend the framework from punctured Euclidean product spaces to a more general abstract setting, thereby broadening its scope of potential applications.

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