多项式时间内的鲁棒网络重构
Robust Network Reconstruction in Polynomial Time
摘要：
针对存在噪声、估计误差和未建模非线性的线性定常（LTI）系统，提出了一种鲁棒网络重构的有效算法。这里的方法建立在以前的工作，强大的重建提供了一个实用的实现与多项式计算复杂性。遵循相同的实验协议，该算法获得了一组结构相关的候选解决方案，跨越每一个层次的稀疏。我们证明了存在的噪声，如果满足，保证这些结构之一是正确的解决方案的幅度限制。一个特定问题的模型选择过程，然后选择一个单一的解决方案，从这个集合，并提供了一个解决方案的信心措施。大量的模拟量化了不同噪声水平的预期性能，并表明与原始方法相比，可以容忍更多的噪声。
英文摘要：
This paper presents an efficient algorithm for robust network reconstruction of Linear Time-Invariant (LTI) systems in the presence of noise, estimation errors and unmodelled nonlinearities. The method here builds on previous work on robust reconstruction to provide a practical implementation with polynomial computational complexity. Following the same experimental protocol, the algorithm obtains a set of structurally-related candidate solutions spanning every level of sparsity. We prove the existence of a magnitude bound on the noise, which if satisfied, guarantees that one of these structures is the correct solution. A problem-specific model-selection procedure then selects a single solution from this set and provides a measure of confidence in that solution. Extensive simulations quantify the expected performance for different levels of noise and show that significantly more noise can be tolerated in comparison to the original method.
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