aiqbench analysis
This paper introduces a semi-analytical inference framework for Structural Causal Models (SCMs) that utilizes message passing and spline projections to perform probabilistic reasoning without explicit distribution construction. By combining numerical quadrature with linear algebra, the method offers a unified approach for forward and backward propagation in causal graphs, validated against Monte Carlo benchmarks on continuous SCMs.
A Semi-Analytical Inference Framework for Structural Causal Models
arXiv:2610.28103v1 Announce Type: new Abstract: Structural Causal Models (SCMs) provide a principled framework for observational, interventional, and counterfactual reasoning, all of which rely on probabilistic inference. Existing frameworks either transform SCMs into alternative tractable representations or rely on approximate inference with expressive generative models. We instead perform inference using a message passing scheme directly on the SCM by representing structural mechanisms and probability densities in a common finite-dimensional function space. Forward propagation combines a numerical realization of the Law of the Unconscious Statistician, while propagated densities are recovered by spline projection from LOTUS moments. The same representation naturally yields backward message passing for conditioning, providing a unified framework for causal inference. Using tensor-product B-spline bases, the resulting algorithm expresses inference through numerical quadrature and linear algebra without explicitly constructing conditional distributions. Experiments on randomly generated continuous SCMs demonstrate accurate approximation of Monte Carlo reference solutions and systematic improvement with increasing basis resolution.
Abstract:Structural Causal Models (SCMs) provide a principled framework for observational, interventional, and counterfactual reasoning, all of which rely on probabilistic inference. Existing frameworks either transform SCMs into alternative tractable representations or rely on approximate inference with expressive generative models. We instead perform inference using a message passing scheme directly on the SCM by representing structural mechanisms and probability densities in a common finite-dimensional function space. Forward propagation combines a numerical realization of the Law of the Unconscious Statistician, while propagated densities are recovered by spline projection from LOTUS moments. The same representation naturally yields backward message passing for conditioning, providing a unified framework for causal inference. Using tensor-product B-spline bases, the resulting algorithm expresses inference through numerical quadrature and linear algebra without explicitly constructing conditional distributions. Experiments on randomly generated continuous SCMs demonstrate accurate approximation of Monte Carlo reference solutions and systematic improvement with increasing basis resolution.
Artificial Intelligence (cs.AI)
arXiv:2610.28103 [cs.AI]
(or arXiv:2610.28103v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2610.28103 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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