平稳Phi-混合和Beta-混合过程的稳定性界
Stability Bound for Stationary Phi-mixing and Beta-mixing Processes
摘要：
学习理论中的大多数泛化边界都是基于所使用的假设类的复杂性的某种度量，而与任何算法无关。相比之下，算法稳定性的概念可以用于通过利用特定的学习算法的特定属性来推导出针对特定学习算法的严格泛化边界。然而，在许多学习理论中，现有的稳定性分析和界限仅适用于样本独立且同分布的情况。然而，在许多机器学习应用中，这个假设并不成立。由学习算法接收的观测通常具有一些固有的时间依赖性。本文研究的情况下，观察是从一个固定的φ-混合或β-混合序列，广泛采用的假设在非独立同分布的研究。这意味着观测之间的依赖性随着时间的推移而减弱。我们证明了新的和不同的稳定性为基础的推广范围固定的φ混合和β混合序列。这些界限严格推广了独立同分布中给出的界限。的情况下，并适用于所有稳定的学习算法，从而扩展使用的稳定性界限，非独立同分布。场景我们还说明了我们的φ混合泛化界的一般类的学习算法，包括支持向量回归，核岭回归，和支持向量机，以及许多其他内核正则化和相对熵为基础的正则化算法的应用。这些新的界限，因此可以被视为第一个理论基础，这些算法在非独立同分布使用。场景
英文摘要：
Most generalization bounds in learning theory are based on some measure of the complexity of the hypothesis class used, independently of any algorithm. In contrast, the notion of algorithmic stability can be used to derive tight generalization bounds that are tailored to specific learning algorithms by exploiting their particular properties. However, as in much of learning theory, existing stability analyses and bounds apply only in the scenario where the samples are independently and identically distributed. In many machine learning applications, however, this assumption does not hold. The observations received by the learning algorithm often have some inherent temporal dependence. This paper studies the scenario where the observations are drawn from a stationary phi-mixing or beta-mixing sequence, a widely adopted assumption in the study of non-i.i.d. processes that implies a dependence between observations weakening over time. We prove novel and distinct stability-based generalization bounds for stationary phi-mixing and beta-mixing sequences. These bounds strictly generalize the bounds given in the i.i.d. case and apply to all stable learning algorithms, thereby extending the use of stability-bounds to non-i.i.d. scenarios. We also illustrate the application of our phi-mixing generalization bounds to general classes of learning algorithms, including Support Vector Regression, Kernel Ridge Regression, and Support Vector Machines, and many other kernel regularization-based and relative entropy-based regularization algorithms. These novel bounds can thus be viewed as the first theoretical basis for the use of these algorithms in non-i.i.d. scenarios.
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