Causal Modeling with Stationary Diffusions

Lars Lorch, Andreas Krause, Bernhard Schölkopf
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:1927-1935, 2024.

Abstract

We develop a novel approach towards causal inference. Rather than structural equations over a causal graph, we learn stochastic differential equations (SDEs) whose stationary densities model a system’s behavior under interventions. These stationary diffusion models do not require the formalism of causal graphs, let alone the common assumption of acyclicity. We show that in several cases, they generalize to unseen interventions on their variables, often better than classical approaches. Our inference method is based on a new theoretical result that expresses a stationarity condition on the diffusion’s generator in a reproducing kernel Hilbert space. The resulting kernel deviation from stationarity (KDS) is an objective function of independent interest.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-lorch24a, title = {Causal Modeling with Stationary Diffusions}, author = {Lorch, Lars and Krause, Andreas and Sch\"{o}lkopf, Bernhard}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {1927--1935}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/lorch24a/lorch24a.pdf}, url = {https://proceedings.mlr.press/v238/lorch24a.html}, abstract = {We develop a novel approach towards causal inference. Rather than structural equations over a causal graph, we learn stochastic differential equations (SDEs) whose stationary densities model a system’s behavior under interventions. These stationary diffusion models do not require the formalism of causal graphs, let alone the common assumption of acyclicity. We show that in several cases, they generalize to unseen interventions on their variables, often better than classical approaches. Our inference method is based on a new theoretical result that expresses a stationarity condition on the diffusion’s generator in a reproducing kernel Hilbert space. The resulting kernel deviation from stationarity (KDS) is an objective function of independent interest.} }
Endnote
%0 Conference Paper %T Causal Modeling with Stationary Diffusions %A Lars Lorch %A Andreas Krause %A Bernhard Schölkopf %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-lorch24a %I PMLR %P 1927--1935 %U https://proceedings.mlr.press/v238/lorch24a.html %V 238 %X We develop a novel approach towards causal inference. Rather than structural equations over a causal graph, we learn stochastic differential equations (SDEs) whose stationary densities model a system’s behavior under interventions. These stationary diffusion models do not require the formalism of causal graphs, let alone the common assumption of acyclicity. We show that in several cases, they generalize to unseen interventions on their variables, often better than classical approaches. Our inference method is based on a new theoretical result that expresses a stationarity condition on the diffusion’s generator in a reproducing kernel Hilbert space. The resulting kernel deviation from stationarity (KDS) is an objective function of independent interest.
APA
Lorch, L., Krause, A. & Schölkopf, B.. (2024). Causal Modeling with Stationary Diffusions. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:1927-1935 Available from https://proceedings.mlr.press/v238/lorch24a.html.

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