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Ruibo Tu: Optimal transport for causal discovery

Time: Tue 2022-04-05 10.15

Location: KTH, 3721, Lindstedtsvägen 25, and Zoom

Video link: Meeting ID: 659 3743 5667

Participating: Ruibo Tu (KTH)

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Causal discovery aims at finding causal relationships purely from observational data. Traditional methods, such as the PC algorithm, recover an equivalence class of the underlying causal structures under the causal Markov condition, the faithfulness assumption, etc. To further identify the unique causal structure, the functional causal model-based methods are proposed; however, the model assumptions are restrictive, and their performance is sensitive to the model assumptions, which makes it difficult to use in practice.

In the talk, functional causal models (FCMs) based methods will be introduced. And a new dynamical system view of FCMs will be introduced by leveraging the connection between FCMs and optimal transport. It provides a new dimension for describing static causal discovery tasks while enjoying more freedom for modeling the quantitative causal influences. Hopefully, in the future, the assumptions of FCMs can be further relaxed.

For simplicity and clarity, we will focus on the FCMs in the bivariate case. With the light of the new view, we find that additive noise models correspond to volume-preserving pressureless flows. Consequently, based on their velocity field divergence, we introduce a criterion to determine the causal relationship in the bivariate case. With this criterion, an optimal transport-based algorithm is proposed, which is robust to the model assumptions.