[2509.00472] Partially Functional Dynamic Backdoor Diffusion-based Causal Model

Statistics > Machine Learning arXiv:2509.00472 (stat) [Submitted on 30 Aug 2025 (v1), last revised 4 Apr 2026 (this version, v3)] Title:Partially Functional Dynamic Backdoor Diffusion-based Causal Model Authors:Xinwen Liu, Lei Qian, Song Xi Chen, Niansheng Tang View a PDF of the paper titled Partially Functional Dynamic Backdoor Diffusion-based Causal Model, by Xinwen Liu and 3 other authors View PDF HTML (experimental) 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 dif...