Identification of State-space Linear Time-varying Systems with Sum-of-norms Regularization
Identification of State-space Linear Time-varying Systems with Sum-of-norms Regularization
复制标题
状态空间线性时变系统的范数和正则化辨识
DOI：
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发表时间：
2018
期刊：
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通讯作者：
V. Preciado
中科院分区：
文献类型：
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作者：
Cassiano O. Becker;V. Preciado
在本文中，我们提出了一种方法估计的线性时变系统的状态空间模型使用范数和正则化。具体而言，假设系统参数遵循具有跨时间样本的马尔可夫依赖性的概率分布。这种先验信息被纳入贝叶斯框架，这导致了一个最大后验准则涉及的总和的范数惩罚项。由此产生的估计问题与广义期望最大化算法，其最大化步骤包括一个“凸的差异”的优化问题，建立了一个单调的过程。使用合成数据进行控制计算实验，以显示该方法的有效性。该算法有望在不同领域，特别是经济学和神经科学领域的动态过程建模中找到实际应用。
In this paper, we propose a method for the estimation of state-space models for linear time-varying systems using sum-of-norms regularization. Specifically, the system parameters are assumed to follow a probability distribution with a Markovian dependency across time samples. This prior information is incorporated in a Bayesian framework, which leads to a maximum-a-posteriori criterion involving a sum-of-norms penalty term. The resulting estimation problem is addressed with a generalized expectation maximization algorithm, whose maximization step consists of a ‘difference of convex’ optimization problem, for which a monotone procedure is established. Controlled computational experiments using synthetic data are performed to show the effectiveness of the approach. The proposed algorithm is expected to find practical application in modeling dynamical processes arising in different domains, particularly in the fields of economics and neuroscience.