Exact Stiefel optimization and noise-subspace estimation yield closed-form updates, finite-sample error bounds matching a minimax rate, and native calibrated uncertainty for probabilistic PLS.
If s⋆ ≤ 0, then ∂ℓi/∂s does not change sign on s > 0 (it is non-negative throughout or non-positive throughout), so the minimum of ℓi on s > 0 is achieved as s→ 0+
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Exact Stiefel Optimization for Probabilistic PLS: Closed-Form Updates, Error Bounds, and Calibrated Uncertainty
Exact Stiefel optimization and noise-subspace estimation yield closed-form updates, finite-sample error bounds matching a minimax rate, and native calibrated uncertainty for probabilistic PLS.