Recent research on instant runoff voting (IRV) shows that it exhibits a striking property over unimodal one-dimensional preferences: there is an exclusion zone around the median voter such that the winner must come from the exclusion zone, unless no such candidate exists. Thus, IRV cannot elect an extreme candidate in this setting as long as a sufficiently moderate candidate runs. In this work, we examine the mathematical structure of exclusion zones as a broad phenomenon in more general preference spaces. We prove that with voters uniformly distributed over any d-dimensional hyperrectangle (for d > 1), IRV has no such exclusion zone. However, we also show that IRV exclusion zones are not solely a one-dimensional phenomenon. For irregular higher-dimensional preference spaces with fewer symmetries than hyperrectangles, IRV can have nontrivial exclusion zones. As a further exploration, we study IRV exclusion zones with graph-based preferences, where nodes represent voters who prefer candidates closer to them in the graph. Here, we show that IRV exclusion zones present a surprising computational challenge: even checking whether a given set of positions is an IRV exclusion zone is NP-hard. We develop an efficient randomized approximation algorithm for checking and finding exclusion zones in graphs. Finally, we report on computational experiments with exclusion zones: (i) performing an exhaustive computer search of small graphs and trees, we find nontrivial IRV exclusion zones in most small graphs; and (ii) applying our approximation algorithm to a collection of larger real-world school friendship networks, we find that about 60% of these networks have probable nontrivial IRV exclusion zones. While our focus is on IRV, the properties of exclusion zones we establish provide new methods for analyzing voting systems in metric spaces more generally.

A core tension in the study of plurality elections is the clash between the classic Hotelling-Downs model, which predicts that two office-seeking candidates should cater to the median voter, and the empirical observation that democracies often have two major parties with divergent policies. Motivated in part by this tension, we introduce a dynamic model of candidate positioning based on a simple bounded rationality heuristic: candidates imitate the policy of previous winners. The resulting model is closely connected to evolutionary replicator dynamics. For uniformly-distributed voters, we prove in our model that with k = 2, 3, or 4 candidates per election, any symmetric candidate distribution converges over time to the center. With k ≥ 5 candidates per election, however, we prove that the candidate distribution does not converge to the center and provide an even stronger non-convergence result in a special case with no extreme candidates. Our conclusions are qualitatively unchanged if a small fraction of candidates are not winner-copiers and are instead positioned uniformly at random in each election. Beyond our theoretical analysis, we illustrate our results in extensive simulations; for five or more candidates, we find a tendency towards the emergence of two clusters, a mechanism suggestive of Duverger's Law, the empirical finding that plurality leads to two-party systems. Our simulations also explore several variations of the model, where we find the same general pattern: convergence to the center with four or fewer candidates, but not with five or more. Finally, we discuss the relationship between our replicator dynamics model and prior work on strategic equilibria of candidate positioning games.

A wide range of graph embedding objectives decompose into two components: one that enforces similarity, attracting the embeddings of nodes that are perceived as similar, and another that enforces dissimilarity, repelling the embeddings of nodes that are perceived as dissimilar. Without repulsion, the embeddings would collapse into trivial solutions. Skip-Gram Negative Sampling (SGNS) is a popular and efficient repulsion approach that prevents collapse by repelling each node from a sample of dissimilar nodes. In this work, we show that when repulsion is most needed and the embeddings approach collapse, SGNS node-wise repulsion is, in the aggregate, an approximate re-centering of the node embedding dimensions. Such dimension operations are more scalable than node operations and produce a simpler geometric interpretation of the repulsion. Our theoretical result establishes dimension regularization as an effective and more efficient, compared to skip-gram node contrast, approach to enforcing dissimilarity among embeddings of nodes. We use this result to propose a flexible algorithm augmentation framework that improves the scalability of any existing algorithm using SGNS. The framework prioritizes node attraction and replaces SGNS with dimension regularization. We instantiate this generic framework for LINE and node2vec and show that the augmented algorithms preserve downstream link-prediction performance while reducing GPU memory usage by up to 33.3% and training time by 23.4%. Moreover, we show that completely removing repulsion (a special case of our augmentation framework) in LINE reduces training time by 70.9% on average, while increasing link prediction performance, especially for graphs that are globally sparse but locally dense. Global sparsity slows down dimensional collapse, while local density ensures that node attraction brings the nodes near their neighbors. In general, however, repulsion is needed, and dimension regularization provides an efficient alternative to SGNS.

Instant runoff voting (IRV) has recently gained popularity as an alternative to plurality voting for political elections, with advocates claiming a range of advantages, including that it produces more moderate winners than plurality and could thus help address polarization. However, there is little theoretical backing for this claim, with existing evidence focused on case studies and simulations. In this work, we prove that IRV has a moderating effect relative to plurality voting in a precise sense, developed in a 1-dimensional Euclidean model of voter preferences. We develop a theory of exclusion zones, derived from properties of the voter distribution, which serve to show how moderate and extreme candidates interact during IRV vote tabulation. The theory allows us to prove that if voters are symmetrically distributed and not too concentrated at the extremes, IRV cannot elect an extreme candidate over a moderate. In contrast, we show plurality can and validate our results computationally. Our methods provide new frameworks for the analysis of voting systems, deriving exact winner distributions geometrically and establishing a connection between plurality voting and stick-breaking processes.

A common network inference problem, arising from real-world data constraints, is how to infer a dynamic network from its time-aggregated adjacency matrix and time-varying marginals (i.e., row and column sums). Prior approaches to this problem have repurposed the classic iterative proportional fitting (IPF) procedure, also known as Sinkhorn’s algorithm, with promising empirical results. However, the statistical foundation for using IPF has not been well understood: under what settings does IPF provide principled estimation of a dynamic network from its marginals, and how well does it estimate the network? In this work, we establish such a setting, by identifying a generative network model whose maximum likelihood estimates are recovered by IPF. Our model both reveals implicit assumptions on the use of IPF in such settings and enables new analyses, such as structure-dependent error bounds on IPF’s parameter estimates. When IPF fails to converge on sparse network data, we introduce a principled algorithm that guarantees IPF converges under minimal changes to the network structure. Finally, we conduct experiments with synthetic and real-world data, which demonstrate the practical value of our theoretical and algorithmic contributions.

Off-policy evaluation, and the complementary problem of policy learning, use historical data collected under a logging policy to estimate and/or optimize the value of a target policy. Methods for these tasks typically assume overlap between the target and logging policy, enabling solutions based on importance weighting and/or imputation. Absent such an overlap assumption, existing work either relies on a well-specified model or optimizes needlessly conservative bounds. In this work, we develop methods for no-overlap policy evaluation without a well-specified model, relying instead on non-parametric assumptions on the expected outcome, with a particular focus on Lipschitz smoothness. Under such assumptions we are able to provide sharp bounds on the off-policy value, along with optimal estimators of those bounds. For Lipschitz smoothness, we construct a pair of linear programs that upper and lower bound the contribution of the no-overlap region to the off-policy value. We show that these programs have a concise closed form solution, and that their solutions converge under the Lipschitz assumption to the sharp partial identification bounds at a minimax optimal rate, up to log factors. We demonstrate the effectiveness our methods on two semi-synthetic examples, and obtain informative and valid bounds that are tighter than those possible without smoothness assumptions.

In many contexts involving ranked preferences, agents submit partial orders over available alternatives. Statistical models often treat these as marginal in the space of total orders, but this approach overlooks information contained in the list length itself. In this work, we introduce and taxonomize approaches for jointly modeling distributions over top-k partial orders and list lengths k, considering two classes of approaches: composite models that view a partial order as a truncation of a total order, and augmented ranking models that model the construction of the list as a sequence of choice decisions, including the decision to stop. For composite models, we consider three dependency structures for joint modeling of order and truncation length. For augmented ranking models, we consider different assumptions on how the stop-token choice is modeled. Using data consisting of partial rankings from San Francisco school choice and San Francisco ranked choice elections, we evaluate how well the models predict observed data and generate realistic synthetic datasets. We find that composite models, explicitly modeling length as a categorical variable, produce synthetic datasets with accurate length distributions, and an augmented model with position-dependent item utilities jointly models length and preferences in the training data best, as measured by negative log loss. Methods from this work have significant implications on the simulation and evaluation of real-world social systems that solicit ranked preferences.

Multilayer networks describe the rich ways in which nodes are related by accounting for different relationships in separate layers. These multiple relationships are naturally represented by an adjacency tensor. In this work we study the use of the nonnegative Tucker decomposition (NNTuck) of such tensors under a KL loss as an expressive factor model that naturally generalizes existing stochastic block models of multilayer networks. Quantifying interdependencies between layers can identify redundancies in the structure of a network, indicate relationships between disparate layers, and potentially inform survey instruments for collecting social network data. We propose definitions of layer independence, dependence, and redundancy based on likelihood ratio tests between nested nonnegative Tucker decompositions. Using both synthetic and real-world data, we evaluate the use and interpretation of the NNTuck as a model of multilayer networks. Algorithmically, we show that using expectation maximization (EM) to maximize the log-likelihood under the NNTuck is step-by-step equivalent to tensorial multiplicative updates for the NNTuck under a KL loss, extending a previously known equivalence from nonnegative matrices to nonnegative tensors.

Many policies in the US are determined locally, e.g., at the county-level. Local policy regimes provide flexibility between regions, but may become less effective in the presence of geographic spillovers, where populations circumvent local restrictions by traveling to less restricted regions nearby. Due to the endogenous nature of policymaking, there have been few opportunities to reliably estimate causal spillover effects or evaluate their impact on local policies. In this work, we identify a novel setting and develop a suitable methodology that allow us to make unconfounded estimates of spillover effects of local policies. Focusing on California’s Blueprint for a Safer Economy, we leverage how county-level mobility restrictions were deterministically set by public COVID-19 severity statistics, enabling a regression discontinuity design framework to estimate spillovers between counties. We estimate these effects using a mobility network with billions of timestamped edges and find significant spillover movement, with larger effects in retail, eating places, and gyms. Contrasting local and global policy regimes, our spillover estimates suggest that county-level restrictions are only 54% as effective as statewide restrictions at reducing mobility. However, an intermediate strategy of macro-county restrictions---where we optimize county partitions by solving a minimum k-cut problem on a graph weighted by our spillover estimates---can recover over 90% of statewide mobility reductions, while maintaining substantial flexibility between counties.

Instant runoff voting (IRV) is an increasingly-popular alternative to traditional plurality voting in which voters submit rankings over the candidates rather than single votes. In practice, elections using IRV often restrict the ballot length, the number of candidates a voter is allowed to rank on their ballot. We theoretically and empirically analyze how ballot length can influence the outcome of an election, given fixed voter preferences. We show that there exist preference profiles over k candidates such that up to k-1 different candidates win at different ballot lengths. We derive exact lower bounds on the number of voters required for such profiles and provide a construction matching the lower bound for unrestricted voter preferences. Additionally, we characterize which sequences of winners are possible over ballot lengths and provide explicit profile constructions achieving any feasible winner sequence. We also examine how classic preference restrictions influence our results—for instance, single-peakedness makes k-1 different winners impossible but still allows at least Ω(√k). Finally, we analyze a collection of 168 real-world elections, where we truncate rankings to simulate shorter ballots. We find that shorter ballots could have changed the outcome in one quarter of these elections. Our results highlight ballot length as a consequential degree of freedom in the design of IRV elections.

School choice mechanism designers use discrete choice models to understand and predict families' preferences. The most widely-used choice model, the multinomial logit (MNL), is linear in school and/or household attributes. While the model is simple and interpretable, it assumes the ranked preference lists arise from a choice process that is uniform throughout the ranking, from top to bottom. In this work, we introduce two strategies for rank-heterogeneous choice modeling tailored for school choice. First, we adapt a context-dependent random utility model (CDM), considering down-rank choices as occurring in the context of earlier up-rank choices. Second, we consider stratifying the choice modeling by rank, regularizing rank-adjacent models towards one another when appropriate. Using data on household preferences from the San Francisco Unified School District (SFUSD) across multiple years, we show that the contextual models considerably improve our out-of-sample evaluation metrics across all rank positions over the non-contextual models in the literature. Meanwhile, stratifying the model by rank can yield more accurate first-choice predictions while down-rank predictions are relatively unimproved. These models provide performance upgrades that school choice researchers can adopt to improve predictions and counterfactual analyses.

Peer review assignment algorithms aim to match research papers to suitable expert reviewers, working to maximize the quality of the resulting reviews. A key challenge in designing effective assignment policies is evaluating how changes to the assignment algorithm map to changes in review quality. In this work, we leverage recently proposed policies that introduce randomness in peer-review assignment—in order to mitigate fraud—as a valuable opportunity to evaluate counterfactual assignment policies. Specifically, we exploit how such randomized assignments provide a positive probability of observing the reviews of many assignment policies of interest. To address challenges in applying standard off-policy evaluation methods, such as violations of positivity, we introduce novel methods for partial identification based on monotonicity and Lipschitz smoothness assumptions for the mapping between reviewer-paper covariates and outcomes. We apply our methods to peer-review data from two computer science venues: the TPDP'21 workshop (95 papers and 35 reviewers) and the AAAI'22 conference (8,450 papers and 3,145 reviewers). We consider estimates of (i) the effect on review quality when changing weights in the assignment algorithm, e.g., weighting reviewers' bids vs. textual similarity (between the review's past papers and the submission), and (ii) the "cost of randomization", capturing the difference in expected quality between the perturbed and unperturbed optimal match. We find that placing higher weight on text similarity results in higher review quality and that introducing randomization in the reviewer-paper assignment only marginally reduces the review quality. Our methods for partial identification may be of independent interest, while our off-policy approach can likely find use in evaluating a broad class of algorithmic matching systems.

Standard methods in preference learning involve estimating the parameters of discrete choice models from data of selections (choices) made by individuals from a discrete set of alternatives (the choice set). While there are many models for individual preferences, existing learning methods overlook how choice set assignment affects the data. Often, the choice set itself is influenced by an individual's preferences; for instance, a consumer choosing a product from an online retailer is often presented with options from a recommender system that depend on information about the consumer's preferences. Ignoring these assignment mechanisms can mislead choice models into making biased estimates of preferences, a phenomenon that we call choice set confounding. We demonstrate the presence of such confounding in widely-used choice datasets.

Balanced graph partitioning is a critical step for many large-scale distributed computations with relational data. As graph datasets have grown in size and density, a range of highly-scalable balanced partitioning algorithms have appeared to meet varied demands across different domains. As the starting point for the present work, we observe that two recently introduced families of iterative partitioners---those based on restreaming and those based on balanced label propagation (including Facebook's Social Hash Partitioner)---can be viewed through a common modular framework of design decisions. With the help of this modular perspective, we find that a key combination of design decisions leads to a novel family of algorithms with notably better empirical performance than any existing highly-scalable algorithm on a broad range of real-world graphs. The resulting prioritized restreaming algorithms employ a constraint management strategy based on multiplicative weights, borrowed from the restreaming literature, while adopting notions of priority from balanced label propagation to optimize the ordering of the streaming process. Our experimental results consider a range of stream orders, where a dynamic ordering based on what we call ambivalence is broadly the most performative in terms of the cut quality of the resulting balanced partitions, with a static ordering based on degree being nearly as good.

Many prediction problems on social networks, from recommendations to anomaly detection, can be approached by modeling network data as a sequence of relational events and then leveraging the resulting model for prediction. Conditional logit models of discrete choice are a natural approach to modeling relational events as "choices'' in a framework that envelops and extends many long-studied models of network formation. The conditional logit model is simplistic, but it is particularly attractive because it allows for efficient consistent likelihood maximization via negative sampling, something that isn't true for mixed logit and many other richer models. The value of negative sampling is particularly pronounced because choice sets in relational data are often enormous. Given the importance of negative sampling, in this work we introduce a model simplification technique for mixed logit models that we call "de-mixing'', whereby standard mixture models of network formation---particularly models that mix local and global link formation---are reformulated to operate their modes over disjoint choice sets. This reformulation reduces mixed logit models to conditional logit models, opening the door to negative sampling while also circumventing other standard challenges with maximizing mixture model likelihoods. To further improve scalability, we also study importance sampling for more efficiently selecting negative samples, finding that it can greatly speed up inference in both standard and de-mixed models. Together, these steps make it possible to much more realistically model network formation in very large graphs. We illustrate the relative gains of our improvements on synthetic datasets with known ground truth as well as a large-scale dataset of public transactions on the Venmo platform.

Although the foundations of ranking are well established, the ranking literature has primarily been focused on simple, unimodal models, e.g. the Mallows and Plackett-Luce models, that define distributions centered around a single total ordering. Explicit mixture models have provided some tools for modelling multimodal ranking data, though learning such models from data is often difficult. In this work, we contribute a contextual repeated selection (CRS) model that leverages recent advances in choice modeling to bring a natural multimodality and richness to the rankings space. We provide rigorous theoretical guarantees for maximum likelihood estimation under the model through structure-dependent tail risk and expected risk bounds. As a by-product, we also furnish the first tight bounds on the expected risk of maximum likelihood estimators for the multinomial logit (MNL) choice model and the Plackett-Luce (PL) ranking model, as well as the first tail risk bound on the PL ranking model. The CRS model significantly outperforms existing methods for modeling real world ranking data in a variety of settings, from racing to rank choice voting.

Many applications in preference learning assume that decisions come from the maximization of a stable utility function. Yet a large experimental literature shows that individual choices and judgements can be affected by “irrelevant” aspects of the context in which they are made. An important class of such contexts is the composition of the choice set. In this work, our goal is to discover such choice set effects from raw choice data. We introduce an extension of the Multinomial Logit (MNL) model, called the context dependent random utility model (CDM), which allows for a particular class of choice set effects. We show that the CDM can be thought of as a second-order approximation to a general choice system, can be inferred optimally using maximum likelihood and, importantly, is easily interpretable. We apply the CDM to both real and simulated choice data to perform principled exploratory analyses for the presence of choice set effects.

Graph smoothing methods are an extremely popular family of approaches for semi-supervised learning. The choice of graph used to represent relationships in these learning problems is often a more important decision than the particular algorithm or loss function used, yet this choice is less well-studied in the literature. In this work, we demonstrate that for social networks, the basic friendship graph itself may often not be the appropriate graph for predicting node attributes using graph smoothing. More specifically, standard graph smoothing is designed to harness the social phenomenon of homophily whereby individuals are similar to “the company they keep.” We present a decoupled approach to graph smoothing that decouples notions of “identity” and “preference,” resulting in an alternative social phenomenon of monophily whereby individuals are similar to “the company they're kept in,” as observed in recent empirical work. Our model results in a rigorous extension of the Gaussian Markov Random Field (GMRF) models that underlie graph smoothing, interpretable as smoothing on an appropriate auxiliary graph of weighted or unweighted two-hop relationships.

There is a growing need for discrete choice models that account for the complex nature of human choices, escaping traditional behavioral assumptions such as the transitivity of pairwise preferences. Recently, several parametric models of intransitive comparisons have been proposed, but in all cases the model log-likelihood is non-concave, making inference difficult. In this work we generalize this trend, showing that there cannot exist an parametric model that both (i) has a log-likelihood function that is concave in item-level parameters and (ii) can exhibit intransitive preferences. Given this observation, we also contribute a new simple model for analyzing intransitivity in pairwise comparisons, taking inspiration from the Condorcet method (majority vote) in social choice theory. The majority vote model we analyze is defined as a voting process over independent Random Utility Models (RUMs). We infer a multidimensional embedding of each object or player, in contrast to the traditional one-dimensional embedding used by models such as the Thurstone or Bradley-Terry-Luce (BTL) models. We show that a three-dimensional majority vote model is capable of modeling arbitrarily strong and long intransitive cycles, and can also represent arbitrary pairwise comparison probabilities on any triplet. We provide experimental results that substantiate our claims regarding the effectiveness of our model in capturing intransitivity for various pairwise choice tasks such as predicting choices in recommendation systems, winners in online video games, and elections.

We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a “choice” made by a node to connect to another node, based on (generic) features of the other nodes available to make a connection. This perspective on network formation unifies existing models such as preferential attachment, triadic closure, and node fitness, which are all special cases, and thereby provides a flexible means for conceptualizing, estimating, and comparing models. The lens of discrete choice theory also provides several new tools for analyzing social network formation; for example, the significance of node features can be evaluated in a statistically rigorous manner, and mixtures of existing models can be estimated by adapting known expectation-maximization algorithms. We demonstrate the flexibility of our framework through examples that analyze a number of synthetic and real-world datasets. For example, we provide rigorous methods for estimating preferential attachment models and show how to separate the effects of preferential attachment and triadic closure. Non-parametric estimates of the importance of degree show a highly linear trend, and we expose the importance of looking carefully at nodes with degree zero. Examining the formation of a large citation graph, we find evidence for an increased role of degree when accounting for age.

The BDM mechanism, introduced by Becker, DeGroot, and Marschack in the 1960's, employs a second-price auction against a random bidder to elicit the willingness to pay of a consumer. The BDM mechanism has been recently used as a treatment assignment mechanism in order to estimate the treatment effects of policy interventions while simultaneously measuring the demand for the intervention. In this work, we develop a personalized extension of the classic BDM mechanism, using modern machine learning algorithms to predict an individual's willingness to pay and personalize the "random bidder" based on covariates associated with each individual. We show through a mock experiment on Amazon Mechanical Turk that our personalized BDM mechanism results in a lower cost for the experimenter, provides better balance over covariates that are correlated with both the outcome and willingness to pay, and eliminates biases induced by ad-hoc boundaries in the classic BDM algorithm. We expect our mechanism to be of use for policy evaluation and market intervention experiments, in particular in development economics. Personalization can provide more efficient resource allocation when running experiments while maintaining statistical correctness.

A broad range of on-line behaviors are mediated by interfaces in which people make choices among sets of options. A rich and growing line of work in the behavioral sciences indicate that human choices follow not only from the utility of alternatives, but also from the choice set in which alternatives are presented. In this work we study comparison-based choice functions, a simple but surprisingly rich class of functions capable of exhibiting so-called choice-set effects. Motivated by the challenge of predicting complex choices, we study the query complexity of these functions in a variety of settings. We consider settings that allow for active queries or passive observation of a stream of queries, and give analyses both at the granularity of individuals or populations that might exhibit heterogeneous choice behavior. Our main result is that any comparison-based choice function in one dimension can be inferred as efficiently as a basic maximum or minimum choice function across many query contexts, suggesting that choice-set effects need not entail any fundamental algorithmic barriers to inference. We also introduce a class of choice functions we call distance-comparison-based functions, and briefly discuss the analysis of such functions. The framework we outline provides intriguing connections between human choice behavior and a range of questions in the theory of sorting.

As datasets capturing human choices grow in richness and scale, particularly in online domains, there is an increasing need for choice models flexible enough to handle data that violate traditional choice-theoretic axioms such as regularity, stochastic transitivity, or Luce's choice axiom. In this work we introduce the Pairwise Choice Markov Chain (PCMC) model of discrete choice, an inferentially tractable model that does not assume these traditional axioms while still satisfying the foundational axiom of uniform expansion, which can be viewed as a weaker version of Luce's axiom. We show that the PCMC model significantly outperforms the Multinomial Logit (MNL) model in prediction tasks on two empirical data sets known to exhibit violations of Luce's axiom. Our analysis also synthesizes several recent observations connecting the Multinomial Logit model and Markov chains; the PCMC model retains the Multinomial Logit model as a special case.

The "wisdom of crowds" dictates that aggregate predictions from a large crowd can be surprisingly accurate, rivaling predictions by experts. Crowds, meanwhile, are highly heterogeneous in their expertise. In this work, we study how the heterogeneous uncertainty of a crowd can be directly elicited and harnessed to produce more efficient aggregations from a crowd, or provide the same efficiency from smaller crowds. We present and evaluate a novel strategy for eliciting sufficient information about an individual's uncertainty: allow individuals to make multiple simultaneous guesses, and reward them based on the accuracy of their closest guess. We show that our multiple guesses scoring rule is an incentive-compatible elicitation strategy for aggregations across populations under the reasonable technical assumption that the individuals all hold symmetric log-concave belief distributions that come from the same location-scale family. We first show that our multiple guesses scoring rule is strictly proper for a fixed set of quantiles of any log-concave belief distribution. With properly elicited quantiles in hand, we show that when the belief distributions are also symmetric and all belong to a single location-scale family, we can use interquantile ranges to furnish weights for certainty-weighted crowd aggregation. We evaluate our multiple guesses framework empirically through a series of incentivized guessing experiments on Amazon Mechanical Turk, and find that certainty-weighted crowd aggregations using multiple guesses outperform aggregations using single guesses without certainty weights.

Partitioning large graphs is difficult, especially when performed in the limited models of computation afforded to modern large scale computing systems. In this work we introduce restreaming graph partitioning and develop algorithms that scale similarly to streaming partitioning algorithms yet empirically perform as well as fully offline algorithms. In streaming partitioning, graphs are partitioned serially in a single pass. Restreaming partitioning is motivated by scenarios where approximately the same dataset is routinely streamed, making it possible to transform streaming partitioning algorithms into an iterative procedure.

A/B testing is a standard approach for evaluating the effect of online experiments; the goal is to estimate the `average treatment effect' of a new feature or condition by exposing a sample of the overall population to it. A drawback with A/B testing is that it is poorly suited for experiments involving social interference, when the treatment of individuals spills over to neighboring individuals along an underlying social network. In this work, we propose a novel methodology using graph clustering to analyze average treatment effects under social interference. To begin, we characterize graph-theoretic conditions under which individuals can be considered to be `network exposed' to an experiment. We then show how graph cluster randomization admits an efficient exact algorithm to compute the probabilities for each vertex being network exposed under several of these exposure conditions. Using these probabilities as inverse weights, a Horvitz-Thompson estimator can then provide an effect estimate that is unbiased, provided that the exposure model has been properly specified.

Partitioning graphs at scale is a key challenge for any application that involves distributing a graph across disks, machines, or data centers. Graph partitioning is a very well studied problem with a rich literature, but existing algorithms typically can not scale to billions of edges, or can not provide guarantees about partition sizes.

A growing set of on-line applications are generating data that can be viewed as very large collections of small, dense social graphs --- these range from sets of social groups, events, or collaboration projects to the vast collection of graph neighborhoods in large social networks. A natural question is how to usefully define a domain-independent 'coordinate system' for such a collection of graphs, so that the set of possible structures can be compactly represented and understood within a common space. In this work, we draw on the theory of graph homomorphisms to formulate and analyze such a representation, based on computing the frequencies of small induced subgraphs within each graph. We find that the space of subgraph frequencies is governed both by its combinatorial properties --- based on extremal results that constrain all graphs --- as well as by its empirical properties --- manifested in the way that real social graphs appear to lie near a simple one-dimensional curve through this space.

Latent variable mixture models are a powerful tool for exploring the structure in large datasets. A common challenge for interpreting such models is a desire to impose sparsity, the natural assumption that each data point only contains few latent features. Since mixture distributions are constrained in their L1 norm, typical sparsity techniques based on L1 regularization become toothless, and concave regularization becomes necessary. Unfortunately concave regularization typically results in EM algorithms that must perform problematic non-concave M-step maximizations. In this work, we introduce a technique for circumventing this difficulty, using the so-called Mountain Pass Theorem to provide easily verifiable conditions under which the M-step is well-behaved despite the lacking concavity. We also develop a correspondence between logarithmic regularization and what we term the pseudo-Dirichlet distribution, a generalization of the ordinary Dirichlet distribution well-suited for inducing sparsity. We demonstrate our approach on a text corpus, inferring a sparse topic mixture model for 2,406 weblogs.