相关的重要性:多个网络联合频谱推断中的依赖性影响。

IF 4.3 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS
Journal of Machine Learning Research Pub Date : 2022-01-01
Konstantinos Pantazis, Avanti Athreya, Jesús Arroyo, William N Frost, Evan S Hill, Vince Lyzinski
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引用次数: 0

摘要

多个网络的光谱推断是图统计中发展迅速的一个子领域。最近的研究表明,对多个独立网络进行联合或同步频谱嵌入,比对相同网络进行单独频谱分解能提供更精确的估计。此类推断程序通常严重依赖于多个网络实现的独立性假设,即使在这种情况下,人们也很少关注此类联合嵌入可能导致的网络相关性。在本文中,我们提出了一种通用的总括嵌入方法,并详细分析了这种嵌入在独立和相关网络中的应用,后者大大扩展了此类程序的应用范围,我们还描述了这种总括嵌入本身是如何诱发相关性的。这使我们区分了固有相关性(即多样本网络数据中自然产生的相关性)和诱导相关性(联合嵌入方法的一种伪装)。我们证明了广义总括嵌入程序的灵活性和稳健性,并证明了嵌入点的一致性和中心极限定理。我们研究了诱导相关性和内在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类比,如更一般相关数据的有效样本大小。此外,我们还展示了经过适当校准的广义总括嵌入是如何在真实的生物网络中发现以前的嵌入程序无法辨别的变化的,从而证实了固有相关性和诱导相关性的影响是微妙的,也是可以改变的。通过允许和解构这两种形式的相关性,我们的方法拓宽了用于网络推断的光谱技术的范围,在理论和实践上都具有重要意义。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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.

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.

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.

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来源期刊
Journal of Machine Learning Research
Journal of Machine Learning Research 工程技术-计算机:人工智能
CiteScore
18.80
自引率
0.00%
发文量
2
审稿时长
3 months
期刊介绍: The Journal of Machine Learning Research (JMLR) provides an international forum for the electronic and paper publication of high-quality scholarly articles in all areas of machine learning. All published papers are freely available online. JMLR has a commitment to rigorous yet rapid reviewing. JMLR seeks previously unpublished papers on machine learning that contain: new principled algorithms with sound empirical validation, and with justification of theoretical, psychological, or biological nature; experimental and/or theoretical studies yielding new insight into the design and behavior of learning in intelligent systems; accounts of applications of existing techniques that shed light on the strengths and weaknesses of the methods; formalization of new learning tasks (e.g., in the context of new applications) and of methods for assessing performance on those tasks; development of new analytical frameworks that advance theoretical studies of practical learning methods; computational models of data from natural learning systems at the behavioral or neural level; or extremely well-written surveys of existing work.
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