The Importance of Being Correlated: Implications of Dependence in Joint Spectral Inference across Multiple Networks.
The Importance of Being Correlated: Implications of Dependence in Joint Spectral Inference across Multiple Networks.
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发表时间：
2022
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通讯作者：
Lyzinski V
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作者：
Pantazis K;Athreya A;Arroyo J;Frost WN;Hill ES;Lyzinski V
多网络上的谱推断是图统计学的一个快速发展的分支。最近的工作表明，多个独立网络的联合或同时频谱嵌入可以提供比这些相同网络的单独频谱分解更准确的估计。这种推理过程通常严重依赖于跨多个网络实现的独立性假设，即使在这种情况下，也很少关注可能是这种联合嵌入的结果的诱导网络相关性。在本文中，我们提出了一个广义的综合嵌入方法，我们提供了一个详细的分析，这种嵌入在独立和相关的网络，后者显着扩展了这种程序的范围，我们描述了这种综合嵌入本身可以诱导相关性。这使我们区分内在的相关性，即多样本网络数据中自然产生的相关性和诱导相关性，这是联合嵌入方法的一种技巧。我们证明了广义综合嵌入过程是灵活和强大的，我们证明了嵌入点的一致性和中心极限定理。我们研究了诱导和固有相关性如何影响网络时间序列数据的推断，并提供了经典问题的网络模拟，例如更普遍相关数据的有效样本大小。此外，我们展示了如何适当校准的广义综合嵌入可以检测到以前的嵌入程序无法辨别的真实的生物网络中的变化，证实了固有和诱导相关性的影响可以是微妙的和变革性的。通过允许和解构这两种形式的相关性，我们的方法拓宽了网络推理的频谱技术的范围，在理论和实践中具有重要意义。
Spectral inference on multiple networks is a rapidly-developing subfield of graph statistics. Recent work has demonstrated that joint, or simultaneous, spectral embedding of multiple independent networks can deliver more accurate estimation than individual spectral decompositions of those same networks. Such inference procedures typically rely heavily on independence assumptions across the multiple network realizations, and even in this case, little attention has been paid to the induced network correlation that can be a consequence of such joint embeddings. In this paper, we present a generalized omnibus embedding methodology and we provide a detailed analysis of this embedding across both independent and correlated networks, the latter of which significantly extends the reach of such procedures, and we describe how this omnibus embedding can itself induce correlation. This leads us to distinguish between inherent correlation—that is, the correlation that arises naturally in multisample network data—and induced correlation, which is an artifice of the joint embedding methodology. We show that the generalized omnibus embedding procedure is flexible and robust, and we prove both consistency and a central limit theorem for the embedded points. We examine how induced and inherent correlation can impact inference for network time series data, and we provide network analogues of classical questions such as the effective sample size for more generally correlated data. Further, we show how an appropriately calibrated generalized omnibus embedding can detect changes in real biological networks that previous embedding procedures could not discern, confirming that the effect of inherent and induced correlation can be subtle and transformative. By allowing for and deconstructing both forms of correlation, our methodology widens the scope of spectral techniques for network inference, with import in theory and practice.