Searcharxiv⌕ Search

arXiv subjects

Aaron Clauset

Publications and source records attributed to Aaron Clauset.

At least 55 records · Page 3Linked to original sources
arXiv2014

Efficiently inferring community structure in bipartite networks

Bipartite networks are a common type of network data in which there are two types of vertices, and only vertices of different types can be connected. While bipartite networks exhibit community structure like their unipartite counterparts, existing approaches to bipartite community detection have drawbacks, including implicit parameter choices, loss of information through one-mode projections, and lack of interpretability. Here we solve the community detection problem for bipartite networks by formulating a bipartite stochastic block model, which explicitly includes vertex type information and may be trivially extended to $k$-partite networks. This bipartite stochastic block model yields a projection-free and statistically principled method for community detection that makes clear assumptions and parameter choices and yields interpretable results. We demonstrate this model's ability to efficiently and accurately find community structure in synthetic bipartite networks with known structure and in real-world bipartite networks with unknown structure, and we characterize its performance in practical contexts.

cs.SI↗
arXiv2014

Learning Latent Block Structure in Weighted Networks

Community detection is an important task in network analysis, in which we aim to learn a network partition that groups together vertices with similar community-level connectivity patterns. By finding such groups of vertices with similar structural roles, we extract a compact representation of the network's large-scale structure, which can facilitate its scientific interpretation and the prediction of unknown or future interactions. Popular approaches, including the stochastic block model, assume edges are unweighted, which limits their utility by throwing away potentially useful information. We introduce the `weighted stochastic block model' (WSBM), which generalizes the stochastic block model to networks with edge weights drawn from any exponential family distribution. This model learns from both the presence and weight of edges, allowing it to discover structure that would otherwise be hidden when weights are discarded or thresholded. We describe a Bayesian variational algorithm for efficiently approximating this model's posterior distribution over latent block structures. We then evaluate the WSBM's performance on both edge-existence and edge-weight prediction tasks for a set of real-world weighted networks. In all cases, the WSBM performs as well or better than the best alternatives on these tasks.

stat.ML↗
arXiv2014

Power-law distributions in binned empirical data

Many man-made and natural phenomena, including the intensity of earthquakes, population of cities and size of international wars, are believed to follow power-law distributions. The accurate identification of power-law patterns has significant consequences for correctly understanding and modeling complex systems. However, statistical evidence for or against the power-law hypothesis is complicated by large fluctuations in the empirical distribution's tail, and these are worsened when information is lost from binning the data. We adapt the statistically principled framework for testing the power-law hypothesis, developed by Clauset, Shalizi and Newman, to the case of binned data. This approach includes maximum-likelihood fitting, a hypothesis test based on the Kolmogorov--Smirnov goodness-of-fit statistic and likelihood ratio tests for comparing against alternative explanations. We evaluate the effectiveness of these methods on synthetic binned data with known structure, quantify the loss of statistical power due to binning, and apply the methods to twelve real-world binned data sets with heavy-tailed patterns.

physics.data-an↗
arXiv2014

Scoring dynamics across professional team sports: tempo, balance and predictability

Despite growing interest in quantifying and modeling the scoring dynamics within professional sports games, relative little is known about what patterns or principles, if any, cut across different sports. Using a comprehensive data set of scoring events in nearly a dozen consecutive seasons of college and professional (American) football, professional hockey, and professional basketball, we identify several common patterns in scoring dynamics. Across these sports, scoring tempo---when scoring events occur---closely follows a common Poisson process, with a sport-specific rate. Similarly, scoring balance---how often a team wins an event---follows a common Bernoulli process, with a parameter that effectively varies with the size of the lead. Combining these processes within a generative model of gameplay, we find they both reproduce the observed dynamics in all four sports and accurately predict game outcomes. These results demonstrate common dynamical patterns underlying within-game scoring dynamics across professional team sports, and suggest specific mechanisms for driving them. We close with a brief discussion of the implications of our results for several popular hypotheses about sports dynamics.

stat.AP↗
arXiv2014

Estimating the historical and future probabilities of large terrorist events

Quantities with right-skewed distributions are ubiquitous in complex social systems, including political conflict, economics and social networks, and these systems sometimes produce extremely large events. For instance, the 9/11 terrorist events produced nearly 3000 fatalities, nearly six times more than the next largest event. But, was this enormous loss of life statistically unlikely given modern terrorism's historical record? Accurately estimating the probability of such an event is complicated by the large fluctuations in the empirical distribution's upper tail. We present a generic statistical algorithm for making such estimates, which combines semi-parametric models of tail behavior and a nonparametric bootstrap. Applied to a global database of terrorist events, we estimate the worldwide historical probability of observing at least one 9/11-sized or larger event since 1968 to be 11-35%. These results are robust to conditioning on global variations in economic development, domestic versus international events, the type of weapon used and a truncated history that stops at 1998. We then use this procedure to make a data-driven statistical forecast of at least one similar event over the next decade.

physics.data-an↗
arXiv2013

A network approach to analyzing highly recombinant malaria parasite genes

The var genes of the human malaria parasite Plasmodium falciparum present a challenge to population geneticists due to their extreme diversity, which is generated by high rates of recombination. These genes encode a primary antigen protein called PfEMP1, which is expressed on the surface of infected red blood cells and elicits protective immune responses. Var gene sequences are characterized by pronounced mosaicism, precluding the use of traditional phylogenetic tools that require bifurcating tree-like evolutionary relationships. We present a new method that identifies highly variable regions (HVRs), and then maps each HVR to a complex network in which each sequence is a node and two nodes are linked if they share an exact match of significant length. Here, networks of var genes that recombine freely are expected to have a uniformly random structure, but constraints on recombination will produce network communities that we identify using a stochastic block model. We validate this method on synthetic data, showing that it correctly recovers populations of constrained recombination, before applying it to the Duffy Binding Like-α (DBLα) domain of var genes. We find nine HVRs whose network communities map in distinctive ways to known DBLα classifications and clinical phenotypes. We show that the recombinational constraints of some HVRs are correlated, while others are independent. These findings suggest that this micromodular structuring facilitates independent evolutionary trajectories of neighboring mosaic regions, allowing the parasite to retain protein function while generating enormous sequence diversity. Our approach therefore offers a rigorous method for analyzing evolutionary constraints in var genes, and is also flexible enough to be easily applied more generally to any highly recombinant sequences.

q-bio.GN↗
arXiv2013

Social Network Dynamics in a Massive Online Game: Network Turnover, Non-densification, and Team Engagement in Halo Reach

Online multiplayer games are a popular form of social interaction, used by hundreds of millions of individuals. However, little is known about the social networks within these online games, or how they evolve over time. Understanding human social dynamics within massive online games can shed new light on social interactions in general and inform the development of more engaging systems. Here, we study a novel, large friendship network, inferred from nearly 18 billion social interactions over 44 weeks between 17 million individuals in the popular online game Halo: Reach. This network is one of the largest, most detailed temporal interaction networks studied to date, and provides a novel perspective on the dynamics of online friendship networks, as opposed to mere interaction graphs. Initially, this network exhibits strong structural turnover and decays rapidly from a peak size. In the following period, however, both network size and turnover stabilize, producing a dynamic structural equilibrium. In contrast to other studies, we find that the Halo friendship network is non-densifying: both the mean degree and the average pairwise distance are stable, suggesting that densification cannot occur when maintaining friendships is costly. Finally, players with greater long-term engagement exhibit stronger local clustering, suggesting a group-level social engagement process. These results demonstrate the utility of online games for studying social networks, shed new light on empirical temporal graph patterns, and clarify the claims of universality of network densification.

cs.SI↗
arXiv2013

Adapting the Stochastic Block Model to Edge-Weighted Networks

We generalize the stochastic block model to the important case in which edges are annotated with weights drawn from an exponential family distribution. This generalization introduces several technical difficulties for model estimation, which we solve using a Bayesian approach. We introduce a variational algorithm that efficiently approximates the model's posterior distribution for dense graphs. In specific numerical experiments on edge-weighted networks, this weighted stochastic block model outperforms the common approach of first applying a single threshold to all weights and then applying the classic stochastic block model, which can obscure latent block structure in networks. This model will enable the recovery of latent structure in a broader range of network data than was previously possible.

stat.ML↗
arXiv2013

Environmental structure and competitive scoring advantages in team competitions

In most professional sports, the structure of the environment is kept neutral so that scoring imbalances may be attributed to differences in team skill. It thus remains unknown what impact structural heterogeneities can have on scoring dynamics and producing competitive advantages. Applying a generative model of scoring dynamics to roughly 10 million team competitions drawn from an online game, we quantify the relationship between a competition's structure and its scoring dynamics. Despite wide structural variations, we find the same three-phase pattern in the tempo of events observed in many sports. Tempo and balance are highly predictable from a competition's structural features alone and teams exploit environmental heterogeneities for sustained competitive advantage. The most balanced competitions are associated with specific environmental heterogeneities, not from equally skilled teams. These results shed new light on the principles of balanced competition, and illustrate the potential of online game data for investigating social dynamics and competition.

physics.soc-ph↗
arXiv2013

Detecting Friendship Within Dynamic Online Interaction Networks

In many complex social systems, the timing and frequency of interactions between individuals are observable but friendship ties are hidden. Recovering these hidden ties, particularly for casual users who are relatively less active, would enable a wide variety of friendship-aware applications in domains where labeled data are often unavailable, including online advertising and national security. Here, we investigate the accuracy of multiple statistical features, based either purely on temporal interaction patterns or on the cooperative nature of the interactions, for automatically extracting latent social ties. Using self-reported friendship and non-friendship labels derived from an anonymous online survey, we learn highly accurate predictors for recovering hidden friendships within a massive online data set encompassing 18 billion interactions among 17 million individuals of the popular online game Halo: Reach. We find that the accuracy of many features improves as more data accumulates, and cooperative features are generally reliable. However, periodicities in interaction time series are sufficient to correctly classify 95% of ties, even for casual users. These results clarify the nature of friendship in online social environments and suggest new opportunities and new privacy concerns for friendship-aware applications that do not require the disclosure of private friendship information.

cs.SI↗
arXiv2013

Friends FTW! Friendship, Collaboration and Competition in Halo: Reach

How important are friendships in determining success by individuals and teams in complex collaborative environments? By combining a novel data set containing the dynamics of millions of ad hoc teams from the popular multiplayer online first person shooter Halo: Reach with survey data on player demographics, play style, psychometrics and friendships derived from an anonymous online survey, we investigate the impact of friendship on collaborative and competitive performance. In addition to finding significant differences in player behavior across these variables, we find that friendships exert a strong influence, leading to both improved individual and team performance--even after controlling for the overall expertise of the team--and increased pro-social behaviors. Players also structure their in-game activities around social opportunities, and as a result hidden friendship ties can be accurately inferred directly from behavioral time series. Virtual environments that enable such friendship effects will thus likely see improved collaboration and competition.

cs.SI↗
arXiv2013

How large should whales be?

The evolution and distribution of species body sizes for terrestrial mammals is well-explained by a macroevolutionary tradeoff between short-term selective advantages and long-term extinction risks from increased species body size, unfolding above the 2g minimum size induced by thermoregulation in air. Here, we consider whether this same tradeoff, formalized as a constrained convection-reaction-diffusion system, can also explain the sizes of fully aquatic mammals, which have not previously been considered. By replacing the terrestrial minimum with a pelagic one, at roughly 7000g, the terrestrial mammal tradeoff model accurately predicts, with no tunable parameters, the observed body masses of all extant cetacean species, including the 175,000,000g Blue Whale. This strong agreement between theory and data suggests that a universal macroevolutionary tradeoff governs body size evolution for all mammals, regardless of their habitat. The dramatic sizes of cetaceans can thus be attributed mainly to the increased convective heat loss is water, which shifts the species size distribution upward and pushes its right tail into ranges inaccessible to terrestrial mammals. Under this macroevolutionary tradeoff, the largest expected species occurs where the rate at which smaller-bodied species move up into large-bodied niches approximately equals the rate at which extinction removes them.

q-bio.PE↗
arXiv2012

Persistence and periodicity in a dynamic proximity network

The topology of social networks can be understood as being inherently dynamic, with edges having a distinct position in time. Most characterizations of dynamic networks discretize time by converting temporal information into a sequence of network "snapshots" for further analysis. Here we study a highly resolved data set of a dynamic proximity network of 66 individuals. We show that the topology of this network evolves over a very broad distribution of time scales, that its behavior is characterized by strong periodicities driven by external calendar cycles, and that the conversion of inherently continuous-time data into a sequence of snapshots can produce highly biased estimates of network structure. We suggest that dynamic social networks exhibit a natural time scale Δ_{nat}, and that the best conversion of such dynamic data to a discrete sequence of networks is done at this natural rate.

physics.data-an↗
arXiv2012

The developmental dynamics of terrorist organizations

We identify robust statistical patterns in the frequency and severity of violent attacks by terrorist organizations as they grow and age. Using group-level static and dynamic analyses of terrorist events worldwide from 1968-2008 and a simulation model of organizational dynamics, we show that the production of violent events tends to accelerate with increasing size and experience. This coupling of frequency, experience and size arises from a fundamental positive feedback loop in which attacks lead to growth which leads to increased production of new attacks. In contrast, event severity is independent of both size and experience. Thus larger, more experienced organizations are more deadly because they attack more frequently, not because their attacks are more deadly, and large events are equally likely to come from large and small organizations. These results hold across political ideologies and time, suggesting that the frequency and severity of terrorism may be constrained by fundamental processes.

physics.soc-ph↗
arXiv2011

Adapting to Non-stationarity with Growing Expert Ensembles

When dealing with time series with complex non-stationarities, low retrospective regret on individual realizations is a more appropriate goal than low prospective risk in expectation. Online learning algorithms provide powerful guarantees of this form, and have often been proposed for use with non-stationary processes because of their ability to switch between different forecasters or ``experts''. However, existing methods assume that the set of experts whose forecasts are to be combined are all given at the start, which is not plausible when dealing with a genuinely historical or evolutionary system. We show how to modify the ``fixed shares'' algorithm for tracking the best expert to cope with a steadily growing set of experts, obtained by fitting new models to new data as it becomes available, and obtain regret bounds for the growing ensemble.

stat.ML↗
arXiv2010

The performance of modularity maximization in practical contexts

Although widely used in practice, the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts. Here, we present a broad characterization of its performance in such situations. First, we revisit and clarify the resolution limit phenomenon for modularity maximization. Second, we show that the modularity function Q exhibits extreme degeneracies: it typically admits an exponential number of distinct high-scoring solutions and typically lacks a clear global maximum. Third, we derive the limiting behavior of the maximum modularity Q_max for one model of infinitely modular networks, showing that it depends strongly both on the size of the network and on the number of modules it contains. Finally, using three real-world metabolic networks as examples, we show that the degenerate solutions can fundamentally disagree on many, but not all, partition properties such as the composition of the largest modules and the distribution of module sizes. These results imply that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts. They also explain why many heuristics are often successful at finding high-scoring partitions in practice and why different heuristics can disagree on the modular structure of the same network. We conclude by discussing avenues for mitigating some of these behaviors, such as combining information from many degenerate solutions or using generative models.

physics.data-an↗
arXiv2010

A generalized aggregation-disintegration model for the frequency of severe terrorist attacks

We present and analyze a model of the frequency of severe terrorist attacks, which generalizes the recently proposed model of Johnson et al. This model, which is based on the notion of self-organized criticality and which describes how terrorist cells might aggregate and disintegrate over time, predicts that the distribution of attack severities should follow a power-law form with an exponent of alpha=5/2. This prediction is in good agreement with current empirical estimates for terrorist attacks worldwide, which give alpha=2.4 \pm 0.2, and which we show is independent of certain details of the model. We close by discussing the utility of this model for understanding terrorism and the behavior of terrorist organizations, and mention several productive ways it could be extended mathematically or tested empirically.

physics.soc-ph↗