Work

Signal Processing over Product DAGs: Causal Shifts and Filters

Year: 2026

Type: preprint

Abstract: We develop a signal processing framework for signals indexed by the product of two directed acyclic graphs (DAGs) and described by a linear structural equation model (SEM). Such a setup arises whenever (linear) causal relations act along two domains, as in component versus manufacturing stage or gene versus experimental condition. Disregarding the factorization of the underlying graph and the native two-axis causal structure requires inverting a weighted transitive closure matrix whose size is the product of the two factor sizes for Fourier analysis. Recognizing that standard graph products fail to yield factorizable transitive closures, we introduce a new DAG product under which separability holds. We motivate the new operator in the vertex domain, and show that it also renders the SEM, the Fourier modes, the causal shifts, and the filters on the product DAG separable across its constituent graph factors.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.40275

Authors: Chepuri, Sundeep Prabhakar, Marques, Antonio G., Devmurari, Maulik, Mateos, Gonzalo

Institutions: Indian Institute of Science Bangalore, University of Rochester, Universidad Rey Juan Carlos

Language: English

Topic: Bayesian Modeling and Causal Inference

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Comunidad de Madrid, Agencia Estatal de Investigación, Division of Electrical, Communications and Cyber Systems

Awards: G638709848, G800634236, ASCENT: Using Optical Frequency Comb for Ultrafast Nature-Based Computing for Machine Learning Algorithms, G873222275

OpenAlex ID: W7215103340

Cites: 1

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