In this paper, we derive upper bounds on generalization errors for deep neural networks with Markov datasets. These bounds are developed based on Koltchinskii and Panchenko's approach for bounding the generalization error of combined classifiers with i.i.d. datasets. The development of new symmetrization inequalities in high-dimensional probability for Markov chains is a key element in our extension, where the spectral gap of the infinitesimal generator of the Markov chain plays a key parameter in these inequalities. We also propose a simple method to convert these bounds and other similar ones in traditional deep learning and machine learning to Bayesian counterparts for both i.i.d. and Markov datasets. Extensions to $m$-order homogeneous Markov chains such as AR and ARMA models and mixtures of several Markov data services are given.
翻译:在本文中,我们用Markov数据集对深神经网络的概括误差进行上限。 这些误差是根据Koltchinskii和Panchenko将混合分类器与i.i.d.数据集的统合误差捆绑起来的方法开发的。 开发Markov链的高维概率中新的平衡误差是我们扩展范围的一个关键要素, 在那里, Markov链的无限微量生成器的光谱差在这些不平等中扮演了关键参数。 我们还提出了一个简单的方法, 将这些误差和传统深层学习和机器学习中的其他类似误差转换为Bayesian对应方的i. id. 和 Markov 数据集。 提供了等AR和ARMA模型和若干Markov数据服务的混合物等按百万元排序的同质马尔科夫链的扩展。