Purnamrita Sarkar

Dynamic social network analysis using latent space models

This paper explores two aspects of social network modeling. First, we generalize a successful static model of relationships into a dynamic model that accounts for friendships drifting over time. Second, we show how to make it tractable to learn such models from data, even as the number of entities n gets large. The generalized model associates each entity with a point in p-dimensional Euclidean latent space. The points can move as time progresses but large moves in latent space are improbable. Observed links between entities are more likely if the entities are close in latent space. We show how to make such a model tractable (sub-quadratic in the number of entities) by the use of appropriate kernel functions for similarity in latent space; the use of low dimensional KD-trees; a new efficient dynamic adaptation of multidimensional scaling for a first pass of approximate projection of entities into latent space; and an efficient conjugate gradient update rule for non-linear local optimization in which amortized time per entity during an update is O(log n). We use both synthetic and real-world data on up to 11,000 entities which indicate near-linear scaling in computation time and improved performance over four alternative approaches. We also illustrate the system operating on twelve years of NIPS co-authorship data.

Fast incremental proximity search in large graphs

In this paper we investigate two aspects of ranking problems on large graphs. First, we augment the deterministic pruning algorithm in Sarkar and Moore (2007) with sampling techniques to compute approximately correct rankings with high probability under random walk based proximity measures at query time. Second, we prove some surprising locality properties of these proximity measures by examining the short term behavior of random walks. The proposed algorithm can answer queries on the fly without caching any information about the entire graph. We present empirical results on a 600, 000 node author-word-citation graph from the Citeseer domain on a single CPU machine where the average query processing time is around 4 seconds. We present quantifiable link prediction tasks. On most of them our techniques outperform Personalized Pagerank, a well-known diffusion based proximity measure.

Crowdsourced enumeration queries

Hybrid human/computer database systems promise to greatly expand the usefulness of query processing by incorporating the crowd for data gathering and other tasks. Such systems raise many implementation questions. Perhaps the most fundamental question is that the closed world assumption underlying relational query semantics does not hold in such systems. As a consequence the meaning of even simple queries can be called into question. Furthermore, query progress monitoring becomes difficult due to non-uniformities in the arrival of crowdsourced data and peculiarities of how people work in crowdsourcing systems. To address these issues, we develop statistical tools that enable users and systems developers to reason about query completeness. These tools can also help drive query execution and crowdsourcing strategies. We evaluate our techniques using experiments on a popular crowdsourcing platform.

Scaling up crowd-sourcing to very large datasets: a case for active learning

Crowd-sourcing has become a popular means of acquiring labeled data for many tasks where humans are more accurate than computers, such as image tagging, entity resolution, and sentiment analysis. However, due to the time and cost of human labor, solutions that rely solely on crowd-sourcing are often limited to small datasets (i.e., a few thousand items). This paper proposes algorithms for integrating machine learning into crowd-sourced databases in order to combine the accuracy of human labeling with the speed and cost-effectiveness of machine learning classifiers. By using active learning as our optimization strategy for labeling tasks in crowd-sourced databases, we can minimize the number of questions asked to the crowd, allowing crowd-sourced applications to scale (i.e., label much larger datasets at lower costs). Designing active learning algorithms for a crowd-sourced database poses many practical challenges: such algorithms need to be generic, scalable, and easy to use, even for practitioners who are not machine learning experts. We draw on the theory of nonparametric bootstrap to design, to the best of our knowledge, the first active learning algorithms that meet all these requirements. Our results, on 3 real-world datasets collected with Amazons Mechanical Turk, and on 15 UCI datasets, show that our methods on average ask 1--2 orders of magnitude fewer questions than the baseline, and 4.5--44× fewer than existing active learning algorithms.

Theoretical justification of popular link prediction heuristics

There are common intuitions about how social graphs are generated (for example, it is common to talk informally about nearby nodes sharing a link). There are also common heuristics for predicting whether two currently unlinked nodes in a graph should be linked (e.g. for suggesting friends in an online social network or movies to customers in a recommendation network). This paper provides what we believe to be the first formal connection between these intuitions and these heuristics. We look at a familiar class of graph generation models in which nodes are associated with locations in a latent metric space and connections are more likely between closer nodes. We also look at popular link-prediction heuristics such as number-of-common-neighbors and its weighted variants [Adamic and Adar, 2003] which have proved successful in predicting missing links, but are not direct derivatives of latent space graph models. We provide theoretical justifications for the success of some measures as compared to others, as reported in previous empirical studies. In particular we present a sequence of formal results that show bounds related to the role that a nodes degree plays in its usefulness for link prediction, the relative importance of short paths versus long paths, and the effects of increasing non-determinism in the link generation process on link prediction quality. Our results can be generalized to any model as long as the latent space assumption holds.

Role of normalization in spectral clustering for stochastic blockmodels

Spectral clustering is a technique that clusters elements using the top few eigenvectors of their (possibly normalized) similarity matrix. The quality of spectral clustering is closely tied to the convergence properties of these principal eigenvectors. This rate of convergence has been shown to be identical for both the normalized and unnormalized variants in recent random matrix theory literature. However, normalization for spectral clustering is commonly believed to be beneficial [Stat. Comput. 17 (2007) 395-416]. Indeed, our experiments show that normalization improves prediction accuracy. In this paper, for the popular stochastic blockmodel, we theoretically show that normalization shrinks the spread of points in a class by a constant fraction under a broad parameter regime. As a byproduct of our work, we also obtain sharp deviation bounds of empirical principal eigenvalues of graphs generated from a stochastic blockmodel.

Fast dynamic reranking in large graphs

In this paper we consider the problem of re-ranking search results by incorporating user feedback. We present a graph theoretic measure for discriminating irrelevant results from relevant results using a few labeled examples provided by the user. The key intuition is that nodes relatively closer (in graph topology) to the relevant nodes than the irrelevant nodes are more likely to be relevant. We present a simple sampling algorithm to evaluate this measure at specific nodes of interest, and an efficient branch and bound algorithm to compute the top k nodes from the entire graph under this measure. On quantifiable prediction tasks the introduced measure outperforms other diffusion-based proximity measures which take only the positive relevance feedback into account. On the Entity-Relation graph built from the authors and papers of the entire DBLP citation corpus (1.4 million nodes and 2.2 million edges) our branch and bound algorithm takes about 1.5 seconds to retrieve the top 10 nodes w.r.t. this measure with 10 labeled nodes.

Random Walks in Social Networks and their Applications: A Survey

A wide variety of interesting real world applications, e.g. friend suggestion in social networks, keyword search in databases, web-spam detection etc. can be framed as ranking entities in a graph. In order to obtain ranking we need a graph-theoretic measure of similarity. Ideally this should capture the information hidden in the graph structure. For example, two entities are similar, if there are lots of short paths between them. Random walks have proven to be a simple, yet powerful mathematical tool for extracting information from the ensemble of paths between entities in a graph. Since real world graphs are enormous and complex, ranking using random walks is still an active area of research. The research in this area spans from new applications to novel algorithms and mathematical analysis, bringing together ideas from different branches of statistics, mathematics and computer science. In this book chapter, we describe different random walk based proximity measures, their applications, and existing algorithms for computing them.

Trade-offs between Agility and Reliability of Predictions in Dynamic Social Networks Used to Model Risk of Microbial Contamination of Food

This paper evaluates trade-offs between agility and reliability of predictions arising due to sparseness of data modeled with dynamic social networks. We use real field data from food safety domain to illustrate the discussion. We model food production facilities as one type of entities in a social network evolving in time. Another type of entities denotes various specific strains of Salmonella. Two entities are linked in the graph if a microbial test of food sample conducted at the specific food facility over specific period of time turns out positive for the particular pathogen. We use a computationally efficient latent space model to predict future occurrences of pathogens in individual facilities. Empirical results indicate predictive utility of the proposed representation. However, sparseness of data limits the attainable agility of predictions. We identify exploiting recency of data and using the known patterns in it, such as seasonality, as plausible means of battling the challenge of sparseness.

Answering enumeration queries with the crowd

Hybrid human/computer database systems promise to greatly expand the usefulness of query processing by incorporating the crowd. Such systems raise many implementation questions. Perhaps the most fundamental issue is that the closed-world assumption underlying relational query semantics does not hold in such systems. As a consequence the meaning of even simple queries can be called into question. Furthermore, query progress monitoring becomes difficult due to nonuniformities in the arrival of crowdsourced data and peculiarities of how people work in crowdsourcing systems. To address these issues, we develop statistical tools that enable users and systems developers to reason about query completeness. These tools can also help drive query execution and crowdsourcing strategies. We evaluate our techniques using experiments on a popular crowdsourcing platform.