Signal Processing over Product DAGs: Causal Shifts and Filters
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.
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BibTeX
@misc{chepuri2026signal,
title = {{Signal Processing over Product DAGs: Causal Shifts and Filters}},
author = {Sundeep Prabhakar Chepuri and Antonio G. Marques and Maulik Devmurari and Gonzalo Mateos},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40275},
eprint = {2609.40275},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40275},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Signal Processing over Product DAGs: Causal Shifts and Filters
AU - Sundeep Prabhakar Chepuri
AU - Antonio G. Marques
AU - Maulik Devmurari
AU - Gonzalo Mateos
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40275
UR - https://arxiv.org/abs/2609.40275
AB - 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.
ER -