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Regularized System Identification: A Hierarchical Bayesian Approach ?

机译：正规系统识别：分层贝叶斯方法 ？

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In this paper, the hierarchical Bayesian method for regularized system identification is introduced. To this end, a hyperprior distribution is considered for the regularization matrix and then, the impulse response and the regularization matrix are jointly estimated based on a maximum a posteriori (MAP) approach. Toward introducing a suitable hyperprior, we decompose the regularization matrix using Cholesky decomposition and reduce the estimation problem to the cone of upper triangular matrices with positive diagonal entries. Following this, the hyperprior is introduced on a designed sub-cone of this set. The method differs from the current trend in regularized system identification from various aspect, e.g., the estimation is performed by solving a single stage problem. The MAP estimation problem reduces to a multi-convex optimization problem and a sequential convex programming algorithm is introduced for solving this problem. Consequently, the proposed method is a computationally efficient strategy specially when the regularization matrix has a large size. The method is numerically verified on benchmark examples. Owing to the employed full Bayesian approach, the estimation method shows a satisfactory bias-variance trade-off.
机译：本文介绍了介绍了用于正则化系统识别的分层贝叶斯方法。为此，考虑正则化矩阵的高度分布，然后，基于最大后验（MAP）方法共同估计脉冲响应和正则化矩阵。朝向引入合适的高度，我们使用Cholesky分解来分解正则化矩阵，并将估计问题降低到具有正对角线条目的上三角矩阵的锥体。在此之后，高度高于本集的设计子锥引入。该方法与来自各个方面的正则化系统识别的当前趋势不同，例如，通过解决单个阶段问题来执行估计。地图估计问题减少到多凸优化问题，并引入了顺序凸编程算法来解决这个问题。因此，当正则化矩阵具有大尺寸时，所提出的方法是一种特殊的计算有效策略。该方法在基准示例上进行了数值验证。由于采用了全面的贝叶斯方法，估计方法显示了令人满意的偏差差异。

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