Primary Submission Category: Causal Discovery
Causal Discovery for High-Dimensional Functional Data with Latent Confounders
Authors: Filippo Fiocchi, Samuel Wang,
Presenting Author: Filippo Fiocchi*
Constraint-based causal discovery methods such as the PC algorithm are widely used to infer causal structure from observational data, but their application to high-dimensional functional data has only recently been explored. Moreover, existing approaches assume that all variables of interest are observed, excluding the presence of latent confounders. In this work, we develop a framework for causal discovery in multivariate functional data that extends the PC algorithm to settings with unobserved confounding. Our approach estimates conditional independence relations of the underlying unconfounded processes via low-rank–plus–signal decompositions of covariance operators, enabling separation of latent confounding effects from intrinsic dependencies. Under partial separability and more general covariance structures, we show that conditional independences between functional variables can be characterized through partial correlations of projected scores, leading to a modified PC procedure that remains valid in high-dimensional regimes. We establish consistency guarantees for skeleton recovery and CPDAG estimation, and demonstrate through simulations that the proposed method reliably recovers causal structure even when classical functional PC methods fail in the presence of hidden confounders.