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We tackle the problem of nonparametric variable selection with a focus on discovering interactions between variables. With $p$ variables there are $O(p^s)$ possible order-$s$ interactions making exhaustive search infeasible. It is…
When the sample path of a Hawkes process is observed discretely, such that only the total event counts in disjoint time intervals are known, the likelihood function becomes intractable. To overcome the challenge of likelihood-based…
Multi-type Markov point processes offer a flexible framework for modelling complex multi-type point patterns where it is pertinent to capture both interactions between points as well as large scale trends depending on observed covariates.…
Interval-censored data solely records the aggregated counts of events during specific time intervals - such as the number of patients admitted to the hospital or the volume of vehicles passing traffic loop detectors - and not the exact…
Event-driven systems in fields such as neuroscience, social networks, and finance often exhibit dynamics influenced by continuously evolving external covariates. Motivated by these applications, we introduce a new class of multivariate…
Spectral methods have greatly advanced the estimation of latent variable models, generating a sequence of novel and efficient algorithms with strong theoretical guarantees. However, current spectral algorithms are largely restricted to…
State-transition models are essential across epidemiology and ecology, but statistical inference remains challenging owing to high-dimensional latent state spaces, temporal dependence, and intractable likelihood functions. Bayesian…
An unsupervised learning procedure based on maximizing the mutual information between the outputs of two networks receiving different but statistically dependent inputs is analyzed (Becker and Hinton, Nature, 355, 92, 161). For a generic…
A nonparametric method to predict non-Markovian time series of partially observed dynamics is developed. The prediction problem we consider is a supervised learning task of finding a regression function that takes a delay embedded…
Over the past few decades, the Hawkes process has become a popular framework for modeling temporal events thanks to its flexibility to capture different dependency structures. The objective of this work is to model call sequences emitted by…
Many self-exciting systems change because endogenous amplification, as opposed to exogenous forcing, varies. We study a Hawkes process with fixed background rate and kernel, but piecewise time-varying productivity. For exponential kernels…
We consider finite systems of $N$ interacting neurons described by non-linear Hawkes processes in a mean field frame. Neurons are described by their membrane potential. They spike randomly, at a rate depending on their potential. In between…
A new class of models for dynamic networks is proposed, called mutually exciting point process graphs (MEG). MEG is a scalable network-wide statistical model for point processes with dyadic marks, which can be used for anomaly detection…
Multi-class event streams arise in numerous real-world applications, where uncovering structured, interpretable inter-event relationships, together with accurate prediction, remains a central challenge. Existing neural point process models…
Hawkes processes have recently gained increasing attention from the machine learning community for their versatility in modeling event sequence data. While they have a rich history going back decades, some of their properties, such as…
We present a non-parametric prognostic framework for individualized event prediction based on joint modeling of both longitudinal and time-to-event data. Our approach exploits a multivariate Gaussian convolution process (MGCP) to model the…
Animal acoustic communication often exhibits temporal dependence, with calls triggering or suppressing subsequent calls within and across call types, individuals, or species. While Hawkes processes provide a natural framework for modeling…
The increasing availability of multiple network data has highlighted the need for statistical models for heterogeneous populations of networks. A convenient framework makes use of metrics to measure similarity between networks. In this…
Modeling the complex interactions of systems of particles or agents is a fundamental scientific and mathematical problem that is studied in diverse fields, ranging from physics and biology, to economics and machine learning. In this work,…
Nonlocal operators with integral kernels have become a popular tool for designing solution maps between function spaces, due to their efficiency in representing long-range dependence and the attractive feature of being resolution-invariant.…