Abstract In this paper, we first establish the generalization bounds of Lagrangian Support Vector Machines (LSVM) based on uniformly ergodic Markov chain (u.e.M.c.) samples. As an application, we also obtain the generalization bounds of LSVM based on strongly mixing sequence, independent and identically distributed (i.i.d.) samples, respectively. The fast learning rates of LSVM for u.e.M.c., strongly mixing sequence and i.i.d. samples are established. We also propose a new LSVM algorithm based on Markov sampling (LSVM MS) and show the learning performance of LSVM MS for UCI datasets. The experimental results show that the LSVM MS can improve obviously the learning performance of the classical LSVM algorithm. If the sampling and training total time is a main concern, the LSVM MS algorithm is the preferred method compared the known SVM algorithm based on Markov sampling.

中文翻译：

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基于马尔可夫采样的拉格朗日支持向量机的泛化性能

摘要 在本文中，我们首先建立了基于均匀遍历马尔可夫链（ueMc）样本的拉格朗日支持向量机（LSVM）的泛化界。作为应用，我们还分别基于强混合序列、独立和同分布 (iid) 样本获得了 LSVM 的泛化边界。建立了 ueMc、强混合序列和 iid 样本的 LSVM 的快速学习率。我们还提出了一种基于马尔可夫采样 (LSVM MS) 的新 LSVM 算法，并展示了 LSVM MS 对 UCI 数据集的学习性能。实验结果表明，LSVM MS 可以明显提高经典 LSVM 算法的学习性能。如果采样和训练总时间是主要问题，