Partially Functional Dynamic Backdoor Diffusion-based Causal Model
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arXiv
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| Format: | Preprint |
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2025
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| author | Liu, Xinwen Qian, Lei Chen, Song Xi Tang, Niansheng |
| author_facet | Liu, Xinwen Qian, Lei Chen, Song Xi Tang, Niansheng |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_00472 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partially Functional Dynamic Backdoor Diffusion-based Causal Model Liu, Xinwen Qian, Lei Chen, Song Xi Tang, Niansheng Machine Learning Statistics Theory G.3; J.2 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. |
| title | Partially Functional Dynamic Backdoor Diffusion-based Causal Model |
| topic | Machine Learning Statistics Theory G.3; J.2 |
| url | https://arxiv.org/abs/2509.00472 |