Probabilistic partial least squares (PPLS) is a central likelihood-based model for two-view learning when one needs both interpretable latent factors and calibrated uncertainty. Building on the identifiable parameterization of Bouhaddani et al.\ (2018), existing fitting pipelines still face two practical bottlenecks: noise--signal coupling under joint EM/ECM updates and nontrivial handling of orthogonality constraints. Following the fixed-noise scalar-likelihood protocol, we develop an end-to-end framework that combines noise pre-estimation, constrained likelihood optimization, and prediction calibration in one pipeline. We estimate the observation noise from the low-eigenvalue noise subspace and enforce orthogonality through exact Stiefel-manifold optimization. The noise-subspace estimator attains a signal-strength-independent leading finite-sample rate and matches a minimax lower bound, whereas a full-spectrum noise estimator carries a deterministic bias under the same model. We further extend the framework to sub-Gaussian settings via optional Gaussianization and provide closed-form standard errors through a block-structured Fisher analysis. Across synthetic high-noise settings and two multi-omics benchmarks (TCGA-BRCA and PBMC CITE-seq), the method achieves near-nominal coverage without post-hoc recalibration, reaches Ridge-level point accuracy on TCGA-BRCA at rank $r=3$, matches or exceeds PO2PLS on cross-view prediction while providing native calibrated uncertainty, and improves stability of parameter recovery.

翻译：概率性偏最小二乘（PPLS）是一种基于似然的双视角学习核心模型，既能提供可解释的潜在因子，又能给出校准后的不确定性估计。基于Bouhaddani等人(2018)的可辨识参数化方案，现有拟合流程仍面临两个实际瓶颈：联合EM/ECM更新下的噪声-信号耦合，以及正交约束的非平凡处理。遵循固定噪声标量似然框架，我们开发了一个端到端方案，将噪声预估计、约束似然优化和预测校校准整合于同一管道中。我们从低特征值噪声子空间中估计观测噪声，并通过精确的Stiefel流形优化强制执行正交性。噪声子空间估计器在有限样本下达到了与信号强度无关的前导速率，并匹配极小极大下界，而全谱噪声估计器在同一模型下存在确定性偏差。我们进一步通过可选的高斯化方法将框架扩展到次高斯场景，并利用分块结构Fisher分析提供闭式标准误。在合成高噪声设置和两个多组学基准（TCGA-BRCA和PBMC CITE-seq）上，该方法无需事后重校准即可实现接近名义覆盖率的校准不确定性，在秩$r=3$的TCGA-BRCA上达到Ridge级点精度，在跨视角预测上匹配或超越PO2PLS同时提供原生校准不确定性，并提升了参数恢复的稳定性。