Conditional kernel mean embeddings are nonparametric models that encode
conditional expectations in a reproducing kernel Hilbert space. While they
provide a flexible and powerful framework for probabilistic inference, their
performance is highly dependent on the choice of kernel and regularization
hyperparameters. Nevertheless, current hyperparameter tuning methods
predominantly rely on expensive cross validation or heuristics that is not
optimized for the inference task. For conditional kernel mean embeddings with
categorical targets and arbitrary inputs, we propose a hyperparameter learning
framework based on Rademacher complexity bounds to prevent overfitting by
balancing data fit against model complexity. Our approach only requires batch
updates, allowing scalable kernel hyperparameter tuning without invoking kernel
approximations. Experiments demonstrate that our learning framework outperforms
competing methods, and can be further extended to incorporate and learn deep
neural network weights to improve generalization.

本研究提出了一种基于 Rademacher 复杂度界限的超参数学习框架，用于平衡数据拟合与模型复杂度，从而达到无需核逼近的可扩展核超参数调整方法，并证明本方法优于现行竞争者，可进一步扩展以融合有效应用深度神经网络的权重以提高泛化性能。