Related papers: Modeling event cascades using networks of additive…

The availability of large scale streaming network data has reinforced the ubiquity of power-law distributions in observations and enabled precision measurements of the distribution parameters. The increased accuracy of these measurements…

We wish to estimate the total number of classes in a population based on sample counts, especially in the presence of high latent diversity. Drawing on probability theory that characterizes distributions on the integers by ratios of…

Threshold models of global cascades have been extensively used to model real-world collective behavior, such as the contagious spread of fads and the adoption of new technologies. A common property of those cascade models is that a…

We develop a new class of dynamic multivariate Poisson count models that allow for fast online updating and we refer to these models as multivariate Poisson-scaled beta (MPSB). The MPSB model allows for serial dependence in the counts as…

We consider the task of estimating a network cascade as fast as possible. The cascade is assumed to spread according to a general Susceptible-Infected process with heterogeneous transmission rates from an unknown source in the network.…

In order to improve the resilience of computer infrastructure against cyber attacks and finding ways to mitigate their impact we need to understand their structure and dynamics. Here we propose a novel network-based influence spreading…

Real count data time series often show the phenomenon of the underdispersion and overdispersion. In this paper, we develop two extensions of the first-order integer-valued autoregressive process with Poisson innovations, based on binomial…

We consider $N$ events that are defined on a common probability space. Those events shell have a common probability function that is symmetric with respect to interchanging the events. We ask for the probability distribution of the number…

Cascade processes are responsible for many important phenomena in natural and social sciences. Simple models of irreversible dynamics on graphs, in which nodes activate depending on the state of their neighbors, have been successfully…

The repeated presentation of an identical visual stimulus in the receptive field of a neuron may evoke different spiking patterns at each trial. Probabilistic methods are essential to understand the functional role of this variance within…

By the method of Poissonization we confirm some existing results concerning consistent estimation of the structural distribution function in the situation of a large number of rare events. Inconsistency of the so called natural estimator is…

We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random…

We present a mixture Poisson model for claims counts in which the number of components in the mixture are estimated by reversible jump MCMC methods.

We tackle a new task, event graph completion, which aims to predict missing event nodes for event graphs. Existing link prediction or graph completion methods have difficulty dealing with event graphs because they are usually designed for a…

Cascading chains of events are a salient feature of many real-world social, biological, and financial networks. In social networks, social reciprocity accounts for retaliations in gang interactions, proxy wars in nation-state conflicts, or…

Motivated by the fundamental problem of measuring species diversity, this paper introduces the concept of a cluster structure to define an exchangeable cluster probability function that governs the joint distribution of a random count and…

Burstiness, the tendency of interaction events to be heterogeneously distributed in time, is critical to information diffusion in physical and social systems. However, an analytical framework capturing the effect of burstiness on generic…

We develop a method to decompose causal effects on a social network into an indirect effect mediated by the network, and a direct effect independent of the social network. To handle the complexity of network structures, we assume that…

Results of numerical procedure of constructing confidence intervals for parameter of the Poisson distribution of signal events in the presence of background events with known value of parameter of Poisson distribution are presented. It is…

This paper develops the theory and methods for modeling a stationary count time series via Gaussian transformations. The techniques use a latent Gaussian process and a distributional transformation to construct stationary series with very…