关于稀疏多变量ARX模型识别：一种稀疏贝叶斯学习方法
On Identification of Sparse Multivariable ARX Model: A Sparse Bayesian Learning Approach
AI总结：
本文提出一种基于稀疏贝叶斯学习的方法，用于识别稀疏多变量ARX模型的布尔结构和节点间动态，无需先验知识，通过最大后验估计结合复杂性和组稀疏性惩罚。
摘要：
本文首先考虑了由多变量ARX模型描述的稀疏线性时不变网络的识别问题。此类模型具有相对简单的结构，因此被用作基准以促进进一步研究。在保证网络可识别性的情况下，本文提出了一种识别方法，该方法从数据中推断网络的布尔结构和节点间的内部动态。识别直接从数据中进行，而无需任何系统先验知识，包括其阶数。所提出的方法通过最大后验估计（MAP）解决识别问题，但采用分离的惩罚项来处理复杂性，包括元素（非零连接的阶数）和组稀疏性（网络拓扑）。这种方法广泛应用于压缩感知（CS）中，被称为稀疏贝叶斯学习（SBL）。随后，本文提出了一种新的方案，结合稀疏贝叶斯和组稀疏贝叶斯以高效解决问题。所得到的算法形式与标准稀疏组正则化（SGL）相似，当已知噪声方差时，简化为精确的加权SGL。该方法和开发的工具包可应用于从各种领域推断网络，包括系统生物学中的信号和基因调控网络应用。
英文摘要：
This paper begins with considering the identification of sparse linear time-invariant networks described by multivariable ARX models. Such models possess relatively simple structure thus used as a benchmark to promote further research. With identifiability of the network guaranteed, this paper presents an identification method that infers both the Boolean structure of the network and the internal dynamics between nodes. Identification is performed directly from data without any prior knowledge of the system, including its order. The proposed method solves the identification problem using Maximum a posteriori estimation (MAP) but with inseparable penalties for complexity, both in terms of element (order of nonzero connections) and group sparsity (network topology). Such an approach is widely applied in Compressive Sensing (CS) and known as Sparse Bayesian Learning (SBL). We then propose a novel scheme that combines sparse Bayesian and group sparse Bayesian to efficiently solve the problem. The resulted algorithm has a similar form of the standard Sparse Group Lasso (SGL) while with known noise variance, it simplifies to exact re-weighted SGL. The method and the developed toolbox can be applied to infer networks from a wide range of fields, including systems biology applications such as signaling and genetic regulatory networks.
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