{"ID":2876475,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.00472","arxiv_id":"2509.00472","title":"Partially Functional Dynamic Backdoor Diffusion-based Causal Model","abstract":"Causal inference in spatio-temporal settings is critically hindered by unmeasured confounders with complex spatio-temporal dynamics and the prevalence of multi-resolution data. While diffusion models present a promising avenue for estimating structural causal models, existing approaches are limited by assumptions of causal sufficiency or static confounding, failing to capture the region-specific, temporally dependent nature of real-world latent variables or to directly handle functional variables. We bridge this gap by introducing the Partially Functional Dynamic Backdoor Diffusion-based Causal Model (PFD-BDCM), a unified generative framework designed to simultaneously tackle causal inference with dynamic confounding and functional data. Our approach formalizes a novel structural causal model that captures spatio-temporal dependencies in latent confounders through conditional autoregressive processes, represents functional variables via basis expansion coefficients treated as standard graph nodes, and integrates valid backdoor adjustment into a diffusion-based generative process. We provide theoretical guarantees on the preservation of causal effects under basis expansion and derive error bounds for counterfactual estimates. Experiments on synthetic data and a real-world air pollution case study demonstrate that PFD-BDCM outperforms existing methods across observational, interventional, and counterfactual queries. This work provides a rigorous and practical tool for robust causal inference in complex spatio-temporal systems characterized by non-stationarity and multi-resolution data.","short_abstract":"Causal inference in spatio-temporal settings is critically hindered by unmeasured confounders with complex spatio-temporal dynamics and the prevalence of multi-resolution data. While diffusion models present a promising avenue for estimating structural causal models, existing approaches are limited by assumptions of ca...","url_abs":"https://arxiv.org/abs/2509.00472","url_pdf":"https://arxiv.org/pdf/2509.00472v3","authors":"[\"Xinwen Liu\",\"Lei Qian\",\"Song Xi Chen\",\"Niansheng Tang\"]","published":"2025-08-30T12:11:23Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"math.ST\"]","methods":"[\"Diffusion Model\"]","has_code":false}