发表机构
Eindhoven University of Technology（埃因霍温理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出残差相关性诊断指标D_logdet，用于预测多输出高斯过程协同区域化在联合不确定性量化中的增益，并据此提出Residual-ICM模型，在16个基准上验证了其有效性。
AI 中文摘要
在多目标回归中，相关目标通常通过具有内在协同区域化模型（GP-ICM）的多输出高斯过程进行耦合，假设共享统计强度能够提升整体性能。然而在实践中，这种收益并不一致。在所研究的各种设置中，我们发现协同区域化的主要益处在于联合不确定性量化，而非点预测。原始目标相关性并不能预测耦合何时有帮助；在本研究中的可分离GP-ICM设置下，残差相关性（即独立逐目标预测器未解释的跨目标依赖性）是联合不确定性增益的最强预测因子。我们引入了一种轻量级诊断指标 $D_{\rm logdet}=-\frac{1}{2}\log\det R_{\rm res}$，它表示相对于对角残差协方差，建模完整残差协方差所带来的理想化联合负对数似然（NLL）增益，且仅需独立高斯过程即可计算。在受控合成研究、16个多目标基准以及用于关键点回归的冻结Transformer和卷积神经网络表示中，点预测基本保持不变（$\Delta R^2\approx 0$）。相比之下，$D_{\rm logdet}$ 强有力地预测了观测到的ICM NLL改进（$\rho_s=-0.83$，$p<0.001$），优于诸如特征与样本比率之类的启发式方法。我们还提出了Residual-ICM，它在保留独立边际方差的同时，向联合协方差中添加残差相关结构。在比较的方法中，Residual-ICM取得了最佳的平均联合NLL，而诊断指标则指示了协方差耦合何时可能有用。该诊断指标专门针对全局高斯残差依赖性，即可分离协同区域化所捕获的结构。
英文摘要
In multi-target regression, correlated targets are often coupled through multi-output Gaussian processes with an intrinsic model of coregionalisation (GP-ICM), assuming that sharing statistical strength improves overall performance. In practice, the benefits are inconsistent. Across the settings studied, we find that the main benefit of coregionalisation is joint uncertainty quantification rather than point prediction. Raw target correlation does not predict when coupling helps; in the separable GP-ICM settings studied here, residual correlation, the cross-target dependence left unexplained by independent per-target predictors, is the strongest predictor of joint-uncertainty gains. We introduce a lightweight diagnostic, $D_{\rm logdet}=-\frac{1}{2}\log\det R_{\rm res}$, which represents the idealised joint negative log-likelihood (NLL) gain from modelling a full rather than diagonal residual covariance and is computable from independent GPs alone. Across a controlled synthetic study, 16 multi-target benchmarks, and frozen transformer and convolutional neural network representations for keypoint regression, point prediction remains largely unchanged ($ΔR^2\approx 0$). In contrast, $D_{\rm logdet}$ strongly predicts observed ICM NLL improvements ($ρ_s=-0.83$, $p<0.001$), outperforming heuristics such as the feature-to-sample ratio. We also propose Residual-ICM, which preserves independent marginal variances while adding residual-correlation structure to the joint covariance. Residual-ICM achieves the best average joint NLL among the compared methods, while the diagnostic indicates when covariance coupling is likely to be useful. The diagnostic is specific to global Gaussian residual dependence, the structure captured by separable coregionalisation.
CommentsAccepted at ACML 2026
