半监督核岭Fréchet回归
Semi-Supervised Kernel Ridge Fréchet Regression
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中文总结 AI 辅助
本文提出半监督核岭Fréchet回归（SS-KRFR），利用未标记协变量学习核谱特征，在标记样本稀缺时估计条件Fréchet函数，并给出误差界、收敛速率及混合方法，模拟和EEG应用验证了其有效性。
中文摘要 AI 辅助
Fréchet回归通过最小化条件期望平方距离，为预测随机对象值响应提供了一个框架。我们提出半监督核岭Fréchet回归（SS-KRFR），以在标记样本稀缺时利用未标记协变量。该方法从标记和未标记协变量中学习核谱特征，然后使用标记响应通过岭回归估计条件Fréchet函数。我们推导了预测误差界，区分了标记和未标记样本的作用，并在适当条件下建立了多项式收敛速率。在额外的核假设下，更精细的分析放宽了学习特征所需的样本量要求。我们还开发了混合方法，结合来自有无未标记协变量拟合模型的特征、预测或两者，并在Hadamard空间中在常见调谐下对混合权重均匀地建立混合稳定性，同时为预测混合提供单独的速率保证。模拟和一项EEG应用表明，在若干设置中，半监督增益以及对竞争性Fréchet回归方法的改进。
英文摘要
Fréchet regression provides a framework for predicting random object-valued responses by minimizing the conditional expected squared distances. We propose semi-supervised kernel ridge Fréchet regression (SS-KRFR) to exploit unlabeled covariates when labeled samples are scarce. The method learns kernel spectral features from both labeled and unlabeled covariates, then utilizes labeled responses to estimate the conditional Fréchet function by kernel ridge regression. We derive prediction error bounds that distinguish the roles of labeled and unlabeled samples, and establish polynomial convergence rates under suitable conditions. Under additional kernel assumptions, a sharper analysis relaxes the sample size requirements for learning the features. We also develop hybrids that combine features, predictions, or both from models fitted with and without unlabeled covariates, establishing uniform stability over mixing weights in Hadamard spaces at common tuning and a separate rate guarantee for prediction mixing. Simulations and a real-data application show semi-supervised gains and improvements over competing Fréchet regression methods in several settings.
发表机构
- Seoul National University（首尔国立大学）
- Korea University（高丽大学）
机构由 AI 辅助整理，请以论文原文为准。
