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What is Learnable in Valiant's Theory of the Learnable? 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A Goodness-of-Fit Test for Independent Component Models in High Dimensions
Mingshuo Liu, Siyao Wang, Miles E. Lopes · 2026-05-20 · via math.ST updates on arXiv.org

Independent component (IC) models are a standard tool for representing multivariate data in statistics, signal processing, and machine learning. Despite the extensive use of IC models, much less attention has been given to goodness-of-fit tests for assessing their compatibility with data. We develop the first goodness-of-fit test for IC models that is supported by a theoretical validity guarantee when the data dimension and sample size diverge proportionally. This is made possible by the fact that the test does not rely on a pre-whitening step, which often limits the applicability of other goodness-of-fit tests in high dimensions. Our theoretical analysis is complemented with numerical experiments that demonstrate the test's size control and power under a range of conditions. In addition, we provide examples involving gene-expression data to illustrate that the test has potential for effective diagnostic use in practice.

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