A1680
Title: Testing conditional independence via the spectral generalized covariance measure: Beyond Euclidean data
Authors: Ryunosuke Miyazaki - Hitotsubashi University (Japan) [presenting]
Yoshimasa Uematsu - Hitotsubashi University (Japan)
Abstract: A conditional independence (CI) test is proposed based on a new measure, the spectral generalized covariance measure (SGCM). The SGCM is constructed by expressing the squared norm of the conditional cross-covariance operator in spectral coordinates and approximating it in finite dimensions using data-dependent bases obtained from empirical covariance operators. This avoids direct estimation of conditional mean embeddings and reduces nuisance estimation to a finite collection of scalar-valued regressions. On the theoretical side, under a doubly robust product-bias condition, uniform bootstrap validity and uniform asymptotic size control are established, and nontrivial uniform power and uniform consistency over classes of projected separated alternatives are derived. The analysis also clarifies the role of spectral truncation: stronger truncation relaxes nuisance-estimation requirements, whereas weaker truncation retains more of the projected signal. To support applications beyond Euclidean data, characteristic-kernel constructions on general Polish spaces are developed via a pullback principle and non-constant completely monotone transforms of continuous negative-type semimetrics, with closure under finite tensor products. These constructions cover examples such as trajectories in metric spaces. Simulations show near-nominal size in the main settings and competitive power across a range of challenging scenarios.
