Kernel-based independence tests for causal structure learning on functional data
File(s)
Published version
Author(s)
Laumann, Felix
von Kuegelgen, Julius
Park, Junhyung
Scholkopf, Bernhard
Barahona, Mauricio
Type
Journal Article
Abstract
Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering. Such measurements can be viewed as realisations of an underlying smooth process sampled over the continuum. However, traditional methods for independence testing and causal learning are not directly applicable to such data, as they do not take into account the dependence along the functional dimension. By using specifically designed kernels, we introduce statistical tests for bivariate, joint, and conditional independence for functional variables. Our method not only extends the applicability to functional data of the Hilbert–Schmidt independence criterion (hsic) and its d-variate version (d-hsic), but also allows us to introduce a test for conditional independence by defining a novel statistic for the conditional permutation test (cpt) based on the Hilbert–Schmidt conditional independence criterion (hscic), with optimised regularisation strength estimated through an evaluation rejection rate. Our empirical results of the size and power of these tests on synthetic functional data show good performance, and we then exemplify their application to several constraint- and regression-based causal structure learning problems, including both synthetic examples and real socioeconomic data.
Date Issued
2023-11-28
Date Acceptance
2023-11-15
Citation
Entropy: international and interdisciplinary journal of entropy and information studies, 2023, 25 (12)
ISSN
1099-4300
Publisher
MDPI AG
Journal / Book Title
Entropy: international and interdisciplinary journal of entropy and information studies
Volume
25
Issue
12
Copyright Statement
© 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
License URL
Publication Status
Published
Article Number
ARTN 1597