Network Identifiability from Intrinsic Noise
Network Identifiability from Intrinsic Noise
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DOI：
10.1109/tac.2016.2640219
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发表时间：
2017-08
影响因子：
6.8
通讯作者：
David P. Hayden;Ye Yuan;J. Gonçalves
中科院分区：
文献类型：
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作者：
David P. Hayden;Ye Yuan;J. Gonçalves
本文考虑了由未知的、固有的、噪声输入驱动的动力系统的未知网络的推断问题。同样，我们试图仅通过观察这些变量来确定这些变量之间的直接因果依赖关系。对于最小阶线性时不变系统，我们刻画了该问题在什么条件下是适定的。我们首先证明了如果从输入到显式状态的转移矩阵是最小相位，则无论网络拓扑如何，该问题都有唯一解。这相当于输出频谱密度只有一个有效的频谱因子(直到输入符号的选择)。如果放松位相极小的假设，我们证明了问题的特征是一个由潜态数目决定的单个代数Riccati方程(ARE)。解决方案的数量是网络解决方案数量的上限。我们给出了任意两个动态网络具有相等输出谱密度的充要条件，这些条件可用于构造所有等价网络。广泛的模拟量化了一系列问题规模的解决方案的数量。对于稍微简单一点的情况，我们还给出了一个由输出谱密度构造所有等价网络的算法。
This paper considers the problem of inferring an unknown network of dynamical systems driven by unknown, intrinsic, noise inputs. Equivalently we seek to identify direct causal dependencies among manifest variables only from observations of these variables. For linear, time-invariant systems of minimal order, we characterise under what conditions this problem is well posed. We first show that if the transfer matrix from the inputs to manifest states is minimum phase, this problem has a unique solution irrespective of the network topology. This is equivalent to there being only one valid spectral factor (up to a choice of signs of the inputs) of the output spectral density. If the assumption of phase-minimality is relaxed, we show that the problem is characterised by a single Algebraic Riccati Equation (ARE), of dimension determined by the number of latent states. The number of solutions to this ARE is an upper bound on the number of solutions for the network. We give necessary and sufficient conditions for any two dynamical networks to have equal output spectral density, which can be used to construct all equivalent networks. Extensive simulations quantify the number of solutions for a range of problem sizes. For a slightly simpler case, we also provide an algorithm to construct all equivalent networks from the output spectral density.