Kernel-Based Independence Tests for Causal Structure Learning on Functional Data

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 contin...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2023-11, Vol.25 (12), p.1597
Main Authors: Laumann, Felix, von Kügelgen, Julius, Park, Junhyung, Schölkopf, Bernhard, Barahona, Mauricio
Format: Article
Language:English
Subjects:
Algorithms
Bivariate analysis
causal discovery
Causality
Continuity (mathematics)
Corruption
Criteria
Data analysis
functional data analysis
Hypotheses
Income inequality
independence tests
kernel methods
Kernels
Learning
Mathematical analysis
Permutations
Random variables
Regularization
Rejection rate
Statistical analysis
Statistical tests
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Summary: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 ( -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.
ISSN:1099-4300
1099-4300
DOI:10.3390/e25121597