Matrix completion with structure

Often, data organized in matrix form contains missing entries. Further, such data has been observed to exhibit effective low-rank, and has led to interest in the particular problem of low-rank matrix-completion: Given a partially-observed matrix, estimate the missing entries such that the output completion is low-rank. The goal of this thesis is to improve matrix-completion algorithms by explicitly analyzing two sources of information in the observed entries: their locations and their values. First, we provide a categorization of a new approach to matrix-completion, which we call structural. Structural methods quantify the possibility of completion using tests applied only to the locations of known entries. By framing each test as the class of partially-observed matrices that pass the test, we provide the first organizing framework for analyzing the relationship among structural completion methods. Building on the structural approach, we then develop a new algorithm for active matrix-completion that is combinatorial in nature. The algorithm uses just the locations of known entries to suggest a small number of queries to be made on the missing entries that allow it to produce a full and accurate completion. If a budget is placed on the number of queries, the algorithm outputs a partial completion, indicating which entries it can and cannot accurately estimate given the observations at hand. Finally, we propose a local approach to matrix-completion that analyzes the values of the observed entries to discover a structure that is more fine-grained than the traditional low-rank assumption. Motivated by the Singular Value Decomposition, we develop an algorithm that finds low-rank submatrices using only the first few singular vectors of a matrix. By completing low-rank submatrices separately from the rest of the matrix, the local approach to matrix-completion produces more accurate reconstructions than traditional algorithms

Targeted matrix completion

Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume that the input partially-observed matrix is low rank. The success of these methods depends on the number of observed entries and the rank of the matrix; the larger the rank, the more entries need to be observed in order to accurately complete the matrix. In this paper, we deal with matrices that are not necessarily low rank themselves, but rather they contain low-rank submatrices. We propose Targeted, which is a general framework for completing such matrices. In this framework, we first extract the low-rank submatrices and then apply a matrix-completion algorithm to these low-rank submatrices as well as the remainder matrix separately. Although for the completion itself we use state-of-the-art completion methods, our results demonstrate that Targeted achieves significantly smaller reconstruction errors than other classical matrix-completion methods. One of the key technical contributions of the paper lies in the identification of the low-rank submatrices from the input partially-observed matrices.Comment: Proceedings of the 2017 SIAM International Conference on Data Mining (SDM

CSI: A Hybrid Deep Model for Fake News Detection

The topic of fake news has drawn attention both from the public and the academic communities. Such misinformation has the potential of affecting public opinion, providing an opportunity for malicious parties to manipulate the outcomes of public events such as elections. Because such high stakes are at play, automatically detecting fake news is an important, yet challenging problem that is not yet well understood. Nevertheless, there are three generally agreed upon characteristics of fake news: the text of an article, the user response it receives, and the source users promoting it. Existing work has largely focused on tailoring solutions to one particular characteristic which has limited their success and generality. In this work, we propose a model that combines all three characteristics for a more accurate and automated prediction. Specifically, we incorporate the behavior of both parties, users and articles, and the group behavior of users who propagate fake news. Motivated by the three characteristics, we propose a model called CSI which is composed of three modules: Capture, Score, and Integrate. The first module is based on the response and text; it uses a Recurrent Neural Network to capture the temporal pattern of user activity on a given article. The second module learns the source characteristic based on the behavior of users, and the two are integrated with the third module to classify an article as fake or not. Experimental analysis on real-world data demonstrates that CSI achieves higher accuracy than existing models, and extracts meaningful latent representations of both users and articles.Comment: In Proceedings of the 26th ACM International Conference on Information and Knowledge Management (CIKM) 201

Matrix completion with queries

In many applications, e.g., recommender systems and traffic monitoring, the data comes in the form of a matrix that is only partially observed and low rank. A fundamental data-analysis task for these datasets is matrix completion, where the goal is to accurately infer the entries missing from the matrix. Even when the data satisfies the low-rank assumption, classical matrix-completion methods may output completions with significant error -- in that the reconstructed matrix differs significantly from the true underlying matrix. Often, this is due to the fact that the information contained in the observed entries is insufficient. In this work, we address this problem by proposing an active version of matrix completion, where queries can be made to the true underlying matrix. Subsequently, we design Order&Extend, which is the first algorithm to unify a matrix-completion approach and a querying strategy into a single algorithm. Order&Extend is able identify and alleviate insufficient information by judiciously querying a small number of additional entries. In an extensive experimental evaluation on real-world datasets, we demonstrate that our algorithm is efficient and is able to accurately reconstruct the true matrix while asking only a small number of queries.Comment: Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Minin

A Kernel of Truth: Determining Rumor Veracity on Twitter by Diffusion Pattern Alone

Recent work in the domain of misinformation detection has leveraged rich signals in the text and user identities associated with content on social media. But text can be strategically manipulated and accounts reopened under different aliases, suggesting that these approaches are inherently brittle. In this work, we investigate an alternative modality that is naturally robust: the pattern in which information propagates. Can the veracity of an unverified rumor spreading online be discerned solely on the basis of its pattern of diffusion through the social network? Using graph kernels to extract complex topological information from Twitter cascade structures, we train accurate predictive models that are blind to language, user identities, and time, demonstrating for the first time that such "sanitized" diffusion patterns are highly informative of veracity. Our results indicate that, with proper aggregation, the collective sharing pattern of the crowd may reveal powerful signals of rumor truth or falsehood, even in the early stages of propagation.Comment: Published at The Web Conference (WWW) 202

Inferring Visibility: Who’s (Not) Talking to Whom?

Consider this simple question: how can a network operator identify the set of routes that pass through its network? Answering this question is surprisingly hard: BGP only informs an operator about a limited set of routes. By observing traffic, an operator can only conclude that a particular route passes through its network – but not that a route does not pass through its network. We approach this problem as one of statistical inference, bringing varying levels of additional information to bear: (1) the existence of traffic, and (2) the limited set of publicly available routing tables. We show that the difficulty depends critically on the position of the network in the overall Internet topology, and that the operators with the greatest incentive to solve this problem are those for which the problem is hardest. Nonetheless, we show that suitable application of nonparametric inference techniques can solve this problem quite accurately. For certain networks, traffic existence information yields good accuracy, while for other networks an accurate approach uses the ‘distance ’ between prefixes, according to a new network distance metric that we define. We then show how solving this problem leads to improved solutions for a particular application: traffic matrix completion