跟踪网络推理的复杂性

B. Abrahao, Flavio Chierichetti, Robert D. Kleinberg, A. Panconesi
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引用次数: 85

摘要

网络推理问题包括重建一个网络的边缘集,该网络给出了代表传染病在网络中传播的时间顺序的迹线。这个问题是机器学习中预测任务的典型代表,它需要从观察到的网络活动模式中推断潜在结构,这通常需要不切实际的大量资源(例如,可用数据量或计算时间)。一个基本的问题是了解我们可以利用现有资源以合理的精度预测哪些属性,哪些属性不能。我们将迹复杂度定义为在重建未观察网络的拓扑或更一般地说,其某些属性时实现高保真度所需的不同迹的数量。我们给出了与现有网络推理方法竞争的算法,同时比现有网络推理方法更简单、更有效。此外,我们证明了我们的算法几乎是最优的,通过证明了在一般情况下执行该任务所需的最优推理算法的跟踪数的信息理论下界。给定这些强下界,我们将注意力转向特殊情况,例如树和有界度图,以及属性恢复任务,例如在不推断网络的情况下重建度分布。我们表明,这些问题需要更少(和更现实)的跟踪数量,使它们在实践中有可能解决。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Trace complexity of network inference
The network inference problem consists of reconstructing the edge set of a network given traces representing the chronology of infection times as epidemics spread through the network. This problem is a paradigmatic representative of prediction tasks in machine learning that require deducing a latent structure from observed patterns of activity in a network, which often require an unrealistically large number of resources (e.g., amount of available data, or computational time). A fundamental question is to understand which properties we can predict with a reasonable degree of accuracy with the available resources, and which we cannot. We define the trace complexity as the number of distinct traces required to achieve high fidelity in reconstructing the topology of the unobserved network or, more generally, some of its properties. We give algorithms that are competitive with, while being simpler and more efficient than, existing network inference approaches. Moreover, we prove that our algorithms are nearly optimal, by proving an information-theoretic lower bound on the number of traces that an optimal inference algorithm requires for performing this task in the general case. Given these strong lower bounds, we turn our attention to special cases, such as trees and bounded-degree graphs, and to property recovery tasks, such as reconstructing the degree distribution without inferring the network. We show that these problems require a much smaller (and more realistic) number of traces, making them potentially solvable in practice.
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