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

Area of Science:

• Statistics
• Machine Learning
• Causal Inference

Background:

• Measurements along continuous dimensions (time, space) are common across scientific fields.
• Traditional independence tests and causal learning methods struggle with the inherent dependence in functional data.
• Existing methods do not account for the smooth, continuous nature of functional data.

Purpose of the Study:

• To develop statistical tests for bivariate, joint, and conditional independence specifically for functional data.
• To extend the Hilbert-Schmidt independence criterion (hsic) and its d-variate version (d-hsic) to functional variables.
• To introduce a novel conditional permutation test (cpt) statistic based on the Hilbert-Schmidt conditional independence criterion (hscic) for functional data.

Main Methods:

• Utilized specifically designed kernels to create independence tests for functional variables.
• Extended the Hilbert-Schmidt independence criterion (hsic) and its d-variate version (d-hsic).
• Developed a new statistic for the conditional permutation test (cpt) using the Hilbert-Schmidt conditional independence criterion (hscic), with optimized regularization.

Main Results:

• Empirical results demonstrate good performance in terms of size and power for the proposed tests on synthetic functional data.
• The methods successfully extend applicability of hsic and d-hsic to functional data.
• The novel cpt statistic shows effectiveness in conditional independence testing for functional data.

Conclusions:

• The developed statistical tests provide effective tools for analyzing independence in functional data.
• These methods facilitate causal structure learning from continuous, time- or space-dependent measurements.
• The approach is validated on both synthetic and real-world socioeconomic datasets.