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arXiv 1209.6409cs.LG
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一种在线凸混合专家算法的确定性分析

A Deterministic Analysis of an Online Convex Mixture of Expert Algorithms

Koc University(科克大学)

Mehmet A. Donmez, Sait Tunc, Suleyman S. Kozat

摘要:

我们分析了一个在线学习算法,该算法自适应地结合了并行运行的两个组成算法(或专家)的输出来模拟未知的期望信号。这种在线学习算法实现(并在某些情况下优于)的最佳成分算法的均方误差(MSE)性能的混合物中的稳定状态。然而,在文献中,该算法的MSE分析使用近似,并依赖于底层信号和系统的统计模型。因此,这样的分析可能是没有用的或有效的各种现实生活中的系统,显示出高度的非平稳性,极限环,在许多情况下,甚至是混乱的信号。在本文中,我们产生的结果,在一个单独的序列方式。特别是,我们涉及的时间累积平方估计误差的在线算法在任何时间在任何时间间隔的时间累积平方估计误差的最佳凸混合的组成算法直接调整到基本信号在确定性的意义上,没有任何统计假设。从这个意义上说,我们的分析提供了瞬态,稳态和跟踪行为的算法在一个很强的意义上没有任何近似的基础信号的推导或统计假设,这样我们的结果是保证举行。我们通过例子来说明所介绍的结果。

英文摘要:

We analyze an online learning algorithm that adaptively combines outputs of two constituent algorithms (or the experts) running in parallel to model an unknown desired signal. This online learning algorithm is shown to achieve (and in some cases outperform) the mean-square error (MSE) performance of the best constituent algorithm in the mixture in the steady-state. However, the MSE analysis of this algorithm in the literature uses approximations and relies on statistical models on the underlying signals and systems. Hence, such an analysis may not be useful or valid for signals generated by various real life systems that show high degrees of nonstationarity, limit cycles and, in many cases, that are even chaotic. In this paper, we produce results in an individual sequence manner. In particular, we relate the time-accumulated squared estimation error of this online algorithm at any time over any interval to the time accumulated squared estimation error of the optimal convex mixture of the constituent algorithms directly tuned to the underlying signal in a deterministic sense without any statistical assumptions. In this sense, our analysis provides the transient, steady-state and tracking behavior of this algorithm in a strong sense without any approximations in the derivations or statistical assumptions on the underlying signals such that our results are guaranteed to hold. We illustrate the introduced results through examples.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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