arXiv subjects

Aaron Schein

Publications and source records attributed to Aaron Schein.

25 records · Page 2Linked to original sources

arXiv2019

Poisson-Randomized Gamma Dynamical Systems

This paper presents the Poisson-randomized gamma dynamical system (PRGDS), a model for sequentially observed count tensors that encodes a strong inductive bias toward sparsity and burstiness. The PRGDS is based on a new motif in Bayesian latent variable modeling, an alternating chain of discrete Poisson and continuous gamma latent states that is analytically convenient and computationally tractable. This motif yields closed-form complete conditionals for all variables by way of the Bessel distribution and a novel discrete distribution that we call the shifted confluent hypergeometric distribution. We draw connections to closely related models and compare the PRGDS to these models in studies of real-world count data sets of text, international events, and neural spike trains. We find that a sparse variant of the PRGDS, which allows the continuous gamma latent states to take values of exactly zero, often obtains better predictive performance than other models and is uniquely capable of inferring latent structures that are highly localized in time.

stat.ML↗

arXiv2019

Locally Private Bayesian Inference for Count Models

We present a general method for privacy-preserving Bayesian inference in Poisson factorization, a broad class of models that includes some of the most widely used models in the social sciences. Our method satisfies limited precision local privacy, a generalization of local differential privacy, which we introduce to formulate privacy guarantees appropriate for sparse count data. We develop an MCMC algorithm that approximates the locally private posterior over model parameters given data that has been locally privatized by the geometric mechanism (Ghosh et al., 2012). Our solution is based on two insights: 1) a novel reinterpretation of the geometric mechanism in terms of the Skellam distribution (Skellam, 1946) and 2) a general theorem that relates the Skellam to the Bessel distribution (Yuan & Kalbfleisch, 2000). We demonstrate our method in two case studies on real-world email data in which we show that our method consistently outperforms the commonly-used naive approach, obtaining higher quality topics in text and more accurate link prediction in networks. On some tasks, our privacy-preserving method even outperforms non-private inference which conditions on the true data.

stat.ML↗

arXiv2018

The Hyperedge Event Model

We introduce the hyperedge event model (HEM)---a generative model for events that can be represented as directed edges with one sender and one or more receivers or one receiver and one or more senders. We integrate a dynamic version of the exponential random graph model (ERGM) of edge structure with a survival model for event timing to jointly understand who interacts with whom, and when. The HEM offers three innovations with respect to the literature---first, it extends a growing class of dynamic network models to model hyperedges. The current state-of-the-art approach to dealing with hyperedges is to inappropriately break them into separate edges/events. Second, our model involves a novel receiver selection distribution that is based on established edge formation models, but assures non-empty receiver lists. Third, the HEM integrates separate, but interacting, equations governing edge formation and event timing. We use the HEM to analyze emails sent among department managers in Montgomery County government in North Carolina. Our application demonstrates that the model is effective at predicting and explaining time-stamped network data involving edges with multiple receivers. We present an out-of-sample prediction experiment to illustrate how researchers can select between different specifications of the model.

stat.ME↗

arXiv2017

Poisson--Gamma Dynamical Systems

We introduce a new dynamical system for sequentially observed multivariate count data. This model is based on the gamma--Poisson construction---a natural choice for count data---and relies on a novel Bayesian nonparametric prior that ties and shrinks the model parameters, thus avoiding overfitting. We present an efficient MCMC inference algorithm that advances recent work on augmentation schemes for inference in negative binomial models. Finally, we demonstrate the model's inductive bias using a variety of real-world data sets, showing that it exhibits superior predictive performance over other models and infers highly interpretable latent structure.

stat.ML↗

arXiv2016

Bayesian Poisson Tucker Decomposition for Learning the Structure of International Relations

We introduce Bayesian Poisson Tucker decomposition (BPTD) for modeling country--country interaction event data. These data consist of interaction events of the form "country $i$ took action $a$ toward country $j$ at time $t$." BPTD discovers overlapping country--community memberships, including the number of latent communities. In addition, it discovers directed community--community interaction networks that are specific to "topics" of action types and temporal "regimes." We show that BPTD yields an efficient MCMC inference algorithm and achieves better predictive performance than related models. We also demonstrate that it discovers interpretable latent structure that agrees with our knowledge of international relations.

stat.ML↗

arXiv2015

Bayesian Poisson Tensor Factorization for Inferring Multilateral Relations from Sparse Dyadic Event Counts

We present a Bayesian tensor factorization model for inferring latent group structures from dynamic pairwise interaction patterns. For decades, political scientists have collected and analyzed records of the form "country $i$ took action $a$ toward country $j$ at time $t$"---known as dyadic events---in order to form and test theories of international relations. We represent these event data as a tensor of counts and develop Bayesian Poisson tensor factorization to infer a low-dimensional, interpretable representation of their salient patterns. We demonstrate that our model's predictive performance is better than that of standard non-negative tensor factorization methods. We also provide a comparison of our variational updates to their maximum likelihood counterparts. In doing so, we identify a better way to form point estimates of the latent factors than that typically used in Bayesian Poisson matrix factorization. Finally, we showcase our model as an exploratory analysis tool for political scientists. We show that the inferred latent factor matrices capture interpretable multilateral relations that both conform to and inform our knowledge of international affairs.

stat.ML↗

arXiv2013

Inferring Multilateral Relations from Dynamic Pairwise Interactions

Correlations between anomalous activity patterns can yield pertinent information about complex social processes: a significant deviation from normal behavior, exhibited simultaneously by multiple pairs of actors, provides evidence for some underlying relationship involving those pairs---i.e., a multilateral relation. We introduce a new nonparametric Bayesian latent variable model that explicitly captures correlations between anomalous interaction counts and uses these shared deviations from normal activity patterns to identify and characterize multilateral relations. We showcase our model's capabilities using the newly curated Global Database of Events, Location, and Tone, a dataset that has seen considerable interest in the social sciences and the popular press, but which has is largely unexplored by the machine learning community. We provide a detailed analysis of the latent structure inferred by our model and show that the multilateral relations correspond to major international events and long-term international relationships. These findings lead us to recommend our model for any data-driven analysis of interaction networks where dynamic interactions over the edges provide evidence for latent social structure.

cs.AI↗