Statistical Network Analysis: Model Selection, Differential Privacy, and Dynamic Structures

在这项提案中，我们解决了统计网络分析的以下三个方面的一些具有挑战性的问题。选择网络模型的抖动重采样统计建模的第一步，也是可以说是最重要的一步，是为给定的数据集选择合适的模型。虽然统计学中普遍存在许多数据驱动的模型选择方法，包括基于数据重用的方法(即引导重采样、交叉验证)，但它们在网络数据中的应用是有问题的。因此，主观地选择网络模型仍然很常见。网络数据重用的主要困难是模拟底层的概率机制。一些现有的尝试包括在某些特定设置下的交叉验证。我们提出了一种新的“引导抖动”或“抖动重采样”方法来选择合适的网络模型。该方法不强加任何特定的形式/条件，因此为网络模型的选择提供了通用工具。网络数据的边缘差分保密网络数据个体通常由节点来表示，其相互关系由边来表示。因此，网络数据通常包含敏感的个人/个人信息。另一方面，应保存数据中感兴趣的信息。因此，对数据隐私的主要关注是双重的：(A)仅发布原始网络数据的净化版本以保护隐私，以及(B)净化后的数据应保留感兴趣的信息，以便基于净化后的数据的分析仍然有意义。这是一个充满活力的研究领域，因为在这个信息时代，随着可用的大量数字格式的个人信息，数据隐私变得越来越敏感和重要，尽管统计数据的贡献仍处于初步阶段。我们将采用所谓的双向随机回应方法。虽然这样的方案是差别保密的，但基于已公布数据的推断在很大程度上是未知的。我们的初步研究揭示了这种方法的一些吸引人的特征，表明比基于其他数据发布机制的统计推断更有效。我们将进一步发展这一计划，以处理具有额外节点特征/属性的网络(例如，具有关于年龄、性别、爱好、职业等额外信息的社交网络)。动态网络的建模和预测大多数现有的网络统计推断方法仅限于静态网络数据，尽管相当大一部分真实网络本质上是动态的。了解并能够预测随时间的变化对于例如监控互联网交通网络中的异常、预测电力供应网络中的需求和设定价格、管理传感器网络中的环境读数中的自然资源以及了解新闻和观点如何在在线社交网络中传播具有极其重要的意义。不幸的是，动态网络基础的发展仍处于初级阶段，可用的建模和推理工具很少。对于处理网络的动态变化，现有的大多数技术都是基于快照网络随时间的演化分析，而没有真正对变化进行动态建模。虽然这反映了大多数网络随时间缓慢变化的事实，但它不能提供任何关于变化背后的动态的洞察，并且对于未来的预测几乎是无能为力的，因此必须建立适当的随机模型来明确地捕捉动态依赖和动态变化。将张量分解和因子驱动降维的最新进展与指数平滑和卡尔曼滤波等有效的时间序列工具相结合，我们将接受这一挑战，建立一些新的动态模型。

In this proposal we tackle some challenging problems in the following three aspects of statistical network analysis.1. Jittered resampling for selecting network modelsThe first and arguably the most important step in statistical modelling is to choose an appropriate model for a given data set. While there exist many data-driven model-selection methods in statistics in general, including those based on data reuse (i.e., bootstrap resampling, cross-validation), their application to network data is problematic. Therefore it remains common to choose a network model subjectively. The major difficulty in the reuse of network data is to mimic the underlying probability mechanisms. A few existing attempts include cross-validation under some specific settings. We propose a new `bootstrap jittering' or `jittered resampling' method for selecting an appropriate network model. The method does not impose any specific forms/conditions, therefore providing a generic tool for network model selection.2. Edge differential privacy for network dataIn network data individuals are typically represented by nodes and their inter-relationships are represented by edges. Therefore network data often contain sensitive individual/personal information. On the other hand the information of interest in the data should be perserved. Hence the primary concern for data privacy is two-folded: (a) to release only a sanitized version of the original network data to protect privacy, and (b) the sanitized data should preserves the information of interest such that the analysis based on the sanitized data is still meaningful. This is a vibrant research area now as data privacy becomes ever increasingly sensitive and important with available abundant personal information in digital format in this information age, though the contribution from statistics is still at a preliminary stage. We will adopt the so-called dyadwise randomized response approach. While such a scheme is differentially private, the inference based on the released data is largely unknown. Our initial investigation reveals some attractive features of this approach, suggesting more efficient statistical inference than those based on other data release mechanism. We will further develop this scheme to handle networks with additional node features/attributes (e.g., social networks with additional information on age, gender, hobby, occupation etc).3. Modelling and forecasting dynamic networksMost existing statistical inference methods for networks are confined to static network data, though a substantial proportion of real networks are dynamic in nature. Understanding and being able to forecast the changes over time are of immense importance for, e.g., monitoring anomalies in internet traffic networks, predicting demand and setting pricing in electricity supply networks, managing natural resources in environmental readings in sensor networks, and understanding how news and opinion propagates in online social networks. Unfortunately the development of the foundation for dynamic networks is still in its infancy, and the available modelling and inference tools are sparse. As for dealing with dynamic changes of networks, most available techniques are based on the evolution analysis of snapshot networks over time without really modelling the changes dynamically. Although this reflects the fact that most networks change slowly over time, it does not provides any insight on the dynamics underlying the changes and is almost powerless for future prediction for which it is essential to build appropriate stochastic models to capture dynamic dependence and dynamic changes explicitly. Combining recent developments on tensor decomposition and factor-driven dimension reduction with the efficient time series tools such as exponential smoothing and Kalman filters, we will take on this challenge to build some new dynamic models.