Related papers: Statistical Inference for Networks of High-Dimensi…

A subjective expected utility policy making centre, managing complex, dynamic systems, needs to draw on the expertise of a variety of disparate panels of experts and integrate this information coherently. To achieve this, diverse supporting…

We introduce a model-independent approximation for the branching ratio of Hawkes self-exciting point processes. Our estimator requires knowing only the mean and variance of the event count in a sufficiently large time window, statistics…

The Hawkes process (HP) is commonly used to model event sequences with self-reinforcing dynamics, including electronic health records (EHRs). Traditional HPs capture self-reinforcement via parametric impact functions that can be inspected…

The Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process is in general non-Markovian. The linear Hawkes process has…

Aggressive behavior in autistic inpatient youth often arises in temporally clustered bursts complicating efforts to distinguish external triggers from internal escalation. The sample population branching factor-the expected number of new…

Many events occur in the world. Some event types are stochastically excited or inhibited---in the sense of having their probabilities elevated or decreased---by patterns in the sequence of previous events. Discovering such patterns can help…

The Hawkes model is suitable for describing self and mutually exciting random events. In addition, the exponential decay in the Hawkes process allows us to calculate the moment properties in the model. However, due to the complexity of the…

A multivariate Hawkes process enables self- and cross-excitations through a triggering matrix that behaves like an asymmetrical covariance structure, characterizing pairwise interactions between the event types. Full-rank estimation of all…

Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…

High-dimensional time series datasets are becoming increasingly common in many areas of biological and social sciences. Some important applications include gene regulatory network reconstruction using time course gene expression data, brain…

Given a stationary point process, an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate. It might signal a local non-stationarity or the presence of an external…

Network datasets appear across a wide range of scientific fields, including biology, physics, and the social sciences. To enable data-driven discoveries from these networks, statistical inference techniques like estimation and hypothesis…

Permutation tests have been proposed by Albert et al. (2015) to detect dependence between point processes, modeling in particular spike trains, that is the time occurrences of action potentials emitted by neurons. Our present work focuses…

The Hawkes process is a widely used model in many areas, such as finance, seismology, neuroscience, epidemiology, and social sciences. Estimation of the Hawkes process from continuous observations of a sample path is relatively…

The problem of statistical inference in its various forms has been the subject of decades-long extensive research. Most of the effort has been focused on characterizing the behavior as a function of the number of available samples, with far…

Inference and prediction are fundamental to the study of complex systems, where network data are often incomplete, inaccurate or obtained indirectly. In this paper, we review recent advances in network sampling and comparison, as well as in…

We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each nodes of the process, but also disentangles the…

The apparent stochasticity of in-vivo neural circuits has long been hypothesized to represent a signature of ongoing stochastic inference in the brain. More recently, a theoretical framework for neural sampling has been proposed, which…

To understand how neural networks process information, it is important to investigate how neural network dynamics varies with respect to different stimuli. One challenging task is to design efficient statistical approaches to analyze…

We propose a novel approach to marked Hawkes kernel inference which we name the moment-based neural Hawkes estimation method. Hawkes processes are fully characterized by their first and second order statistics through a Fredholm integral…