fix: bootstrap ratios from raw saliences, not S-scaled loadings

[eilidhmacnicol]

Summary

Bootstrap ratios were being formed from S-scaled loadings (U·S, S·Vᵀ) instead of the raw saliences (U, Vᵀ). The canonical PLSC bootstrap ratio (McIntosh & Lobaugh 2004; Krishnan et al. 2011; the pyls reference implementation) is salience / bootstrap SE, with singular values playing no part.

Because S was re-estimated in every resample, its sampling variability leaked into the bootstrap SE, deflating the ratios — most on weaker / non-dominant latent variables. The dominant LV is largely unaffected (its singular value is stable, so S nearly cancels); the error therefore caused under-reporting (false negatives) on secondary effects, never false positives.

Changes

• plsdo/core.py
  • fit(): u_loadings/vt_loadings are now the raw saliences u/vt (no * s).
  • bootstrap(): the bootstrap distribution collects the Procrustes-aligned raw singular vectors, so u_se/vt_se are salience SEs and BSR = salience / SE. Removed the now-unused boot_s.
  • BSR = loadings / SE line and all of pipeline.py are unchanged: the meanings of u_loadings/u_se/u_bootstrap_ratios shift together and stay internally consistent (loading plots, error bars, filter_lvs).
  • Fixes both correlational and discriminatory pipelines (shared SVD engine).
• tests/test_core.py
  • test_loadings_are_scaled_vectors → test_loadings_are_raw_saliences.
  • Dropped the u_loadings[:, -1] ≈ 0 assertion in the inert-LV test (only true under S-scaling; the LV's harmlessness is still guarded by the significance / filter_lvs assertions).
• tests/data/regression/: regenerated the 8 affected loadings/BSR snapshots (both methods). Singular values, p-values, subject scores and CV snapshots re-matched on regeneration, confirming nothing else moved.

Verification

• pytest tests/ → 208 passed.
• ruff check / ruff format --check clean.

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[eilidhmacnicol]

Code review

Found 1 issue (blocker):

1. Y-side bootstrap ratios collapse to ~5e11 (effectively infinite) whenever the Y block has no more features than the X block (n_y <= n_x) — the typical correlational case. Q is solved by orthogonal_procrustes(boot_vt.T, self.vt.T), and when n_components == n_y, boot_vt is a square orthogonal matrix, so the Procrustes solution maps it exactly onto the reference: Q.T @ boot_vt == self.vt for every resample. The bootstrap distribution of aligned_vt therefore has zero spread, vt_se ~ 1e-16 breaches the eps = 1e-12 floor, and vt_bootstrap_ratios = vt_loadings / eps ~ 5e11 for every feature. This silently bypasses the Y-side reliability gate in filter_lvs (y_reliable becomes vacuously true). The old S-scaling masked this because S does not commute with Q, so it kept genuine variance in the distribution; removing it exposes the latent flaw.

Reproduced on tests/data/brain.csv/behaviour.csv (n_x=5, n_y=4): vt_se all ~1e-16, vt_bootstrap_ratios all ~5e11, while u_se is healthy (~0.27). The regenerated snapshots committed in this PR baked in these degenerate values, so test_regression.py compares broken-against-broken under the LOOSE tolerance and passes — the guard does not catch it.

The mathematical motivation (raw-salience BSR, no S) is correct; the alignment step needs reworking so both sides retain genuine resampling variance (e.g. derive the rotation from a non-degenerate quantity rather than the square Vt block, following the pyls/McIntosh convention). Do not merge or release until the Y-side SE is non-degenerate.

plsdo/plsdo/core.py

Lines 146 to 151 in 16d1a0c

	# Procrustes: rotate bootstrap Vt to align with reference
	Q, _ = orthogonal_procrustes(boot_vt.T, self.vt.T)
	aligned_u = boot_u @ Q
	aligned_vt = Q.T @ boot_vt

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[eilidhmacnicol]

This was spearheaded by an LLM hallucination. On further investigation, s-scaled loadings are preferred, so won't fix.