BLISS: 全局盲识别线性系统与稀疏输入
BLISS: Global Blind Identification of Linear Systems with Sparse Inputs
AI总结：
本文提出BLISS方法，通过将稀疏输入假设下的盲系统识别与完整字典学习联系起来，建立全局可辨识性理论，实现单轨迹全局恢复真实系统。
摘要：
线性系统识别和稀疏字典学习均可视为结构化矩阵分解问题。然而，这两个问题历史上由系统理论和机器学习社区各自研究。尽管线性系统识别在已知输入时有成熟的理论，但盲线性系统识别在非受限设置下仍不明确。相比之下，完整的稀疏字典学习最近受益于强全局可辨识性结果和可扩展的非凸算法。在本文中，我们通过证明在稀疏输入假设下，完全观测的盲系统识别成为完整字典学习的推广，将这两个领域连接起来。这种联系使我们能够利用完整字典学习文献中的技术，为盲系统识别开发全局可辨识性保证。我们进一步证明，通过有原则地应用交替方向乘子法，可以在足够样本和输入稀疏性的情况下，从单条轨迹全局恢复真实系统。
英文摘要：
Linear system identification and sparse dictionary learning can both be seen as structured matrix factorization problems. However, these two problems have historically been studied in isolation by the systems theory and machine learning communities. Although linear system identification enjoys a mature theory when inputs are known, blind linear system identification remains poorly understood beyond restrictive settings. In contrast, complete sparse dictionary learning has recently benefited from strong global identifiability results and scalable nonconvex algorithms. In this work, we bridge these two areas by showing that under a sparse input assumption, fully observed blind system identification becomes a generalization of complete dictionary learning. This connection allows us to develop global identifiability guarantees for blind system identification, by leveraging techniques from the complete dictionary learning literature. We further show empirically that a principled application of the alternating direction method of multipliers can globally recover the ground-truth system from a single trajectory, provided sufficient samples and input sparsity.
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。
