Vyacheslav Kungurtsev

Vyacheslav Kungurtsev, Leonardo Christov Moore, Gustav Sir et al.

Causal Learning has emerged as a major theme of research in statistics and machine learning in recent years, promising specific computational techniques to apply to datasets that reveal the true nature of cause and effect in a number of important domains. In this paper we consider the epistemology of recognizing true cause and effect phenomena. We apply the Ordinary Language method of engaging on the customary use of the word 'cause' to investigate valid semantics of reasoning about cause and effect. We recognize that the grammars of cause and effect are fundamentally distinct in form across scientific domains, yet they maintain a consistent and central function. This function can best be described as the mechanism underlying fundamental forces of influence as considered prominent in the respective scientific domain. We demarcate 1) physics and engineering as domains wherein mathematical models are sufficient to comprehensively describe causality, 2) biology as introducing challenges of emergence while providing opportunities for showing consistent mechanisms across scale, and 3) the social sciences as introducing grander difficulties for establishing models of low prediction error but providing, through Hermeneutics, the potential for findings that are still instrumentally useful to individuals. We posit that definitive causal claims regarding a given phenomenon (writ large) can only come through an agglomeration of consistent evidence across multiple domains. This presents important methodological questions as far as harmonizing between language games and emergence across scales. Given the role of epistemic hubris in the contemporary crisis of credibility in the sciences, exercising greater caution as far as communicating precision as to the real degree of certainty certain evidence provides for rich collections of open problems in optimizing integration of different findings.

Farid Bozorgnia, Vyacheslav Kungurtsev, Shirali Kadyrov et al.

In this work, we introduce novel algorithms for label propagation and self-training using fractional heat kernel dynamics with a source term. We motivate the methodology through the classical correspondence of information theory with the physics of parabolic evolution equations. We integrate the fractional heat kernel into Graph Neural Network architectures such as Graph Convolutional Networks and Graph Attention, enhancing their expressiveness through adaptive, multi-hop diffusion. By applying Chebyshev polynomial approximations, large graphs become computationally feasible. Motivating variational formulations demonstrate that by extending the classical diffusion model to fractional powers of the Laplacian, nonlocal interactions deliver more globally diffusing labels. The particular balance between supervision of known labels and diffusion across the graph is particularly advantageous in the case where only a small number of labeled training examples are present. We demonstrate the effectiveness of this approach on standard datasets.