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Bayesian and regularization approaches to multivariable linear system identification: The role of rank penalties

机译:多变量线性系统识别的贝叶斯和正规化方法:排名罚款的作用

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摘要

Recent developments in linear system identification have proposed the use ofnon-parameteric methods, relying on regularization strategies, to handle theso-called bias/variance trade-off. This paper introduces an impulse responseestimator which relies on an $ell_2$-type regularization including arank-penalty derived using the log-det heuristic as a smooth approximation tothe rank function. This allows to account for different properties of theestimated impulse response (e.g. smoothness and stability) while alsopenalizing high-complexity models. This also allows to account and enforcecoupling between different input-output channels in MIMO systems. According tothe Bayesian paradigm, the parameters defining the relative weight of the tworegularization terms as well as the structure of the rank penalty are estimatedoptimizing the marginal likelihood. Once these hyperameters have beenestimated, the impulse response estimate is available in closed form.Experiments show that the proposed method is superior to the estimator relyingon the "classic" $ell_2$-regularization alone as well as those based in atomicand nuclear norm.
机译:线性系统辨识的最新发展提出了依靠正则化策略来使用非参数方法来处理所谓的偏差/方差折衷的问题。本文介绍了一种脉冲响应估计器,该估计器依赖于$ ell_2 $型正则化,包括使用对数启发式启发法作为秩函数的平滑近似而得出的惩罚罚分。这允许考虑估计的脉冲响应的不同属性(例如,平滑度和稳定性),同时还对高复杂度模型进行惩罚。这也允许考虑并执行MIMO系统中不同输入输出通道之间的耦合。根据贝叶斯范式,估计用于定义两个正则项的相对权重的参数以及秩罚分的结构,以优化边际可能性。一旦估计了这些超电流,就可以以闭合形式获得脉冲响应估计。实验表明,所提出的方法优于仅依靠“经典” $ ell_2 $-正则化以及基于原子和核规范的正则化的估计器。

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