Cheap and Powerful Tests for Supervised Subspaces: Per-Component Inference for PLS
Partial Least Squares (PLS) regression extracts a few outcome-aligned directions in a high-dimensional X and is widely used across applied science, but inference on the resulting fit is either expensive, biased and discouraged, or absent. We reduce inference to held-out OLS refits of the supervised subspace, a primitive shared by PLS, supervised PCA, and linear probes, and supply two tests using held-out correlations: a Nadeau-Bengio corrected asymptotic t-test as a fast approximation, and a permutation test with comparable power, finite-sample valid under outcome-predictor independence and iid rows. Held-out predictions are unchanged under any orthogonal rebasing of the supervised span, ...
| Authors | Paweł Lenartowicz, Hubert Plisiecki |
|---|---|
| Primary category | cs.LG |
| Published | 28 September 2026 |
| Last updated at source | 28 September 2026 |
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