In this short note, recent results on the predictive power of kernel principal component in a regression setting are extended in two ways: (1) in the model-free setting, we relax a conditional independence model assumption to obtain a stronger result; and (2) the model-free setting is also extended in the infinite-dimensional setting.

中文翻译：

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重访内核主成分的预测能力

在此简短说明中，有关回归设置中内核主成分的预测能力的最新结果以两种方式扩展：（1）在无模型设置中，我们放宽了条件独立模型的假设，以获得更强的结果；（2）无模型的设置在无限维设置中也得到了扩展。