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In recent years there has been a substantial increase in the availability of datasets which contain information about the location and timing of an event or group of events and the application of methods to analyse spatio-temporal datasets…
Progressive diseases worsen over time and are characterised by monotonic change in features that track disease progression. Here we connect ideas from two formerly separate methodologies -- event-based and hidden Markov modelling -- to…
Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
A study of time homogeneous, real valued Markov processes with a special property and a non-atomic initial distribution is provided. The new notion of a function of evolution of distribution which determines the dependency between one…
Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems. In particular, the…
In evolving complex systems such as air traffic and social organizations, collective effects emerge from their many components' dynamic interactions. While the dynamic interactions can be represented by temporal networks with nodes and…
Threshold based models have been widely used in characterizing collective behavior on social networks. An individual's threshold indicates the minimum level of influence that must be exerted, by other members of the population engaged in…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
Temporal Point Processes (TPP) are probabilistic generative frameworks. They model discrete event sequences localized in continuous time. Generally, real-life events reveal descriptive information, known as marks. Marked TPPs model time and…
We develop a new family of marked point processes by focusing the characteristic properties of marked Hawkes processes exclusively to the space of marks, providing the freedom to specify a different model for the occurrence times. This is…
We propose a novel probabilistic framework to model continuous-time interaction events data. Our goal is to infer the \emph{implicit} community structure underlying the temporal interactions among entities, and also to exploit how the…
Cross-sectional studies are widely prevalent since they are more feasible to conduct compared to longitudinal studies. However, cross-sectional data lack the temporal information required to study the evolution of the underlying processes.…
Compartment models with delay terms are widely used across a range of disciplines. The motivation to include delay terms varies across different contexts. In epidemiological and pharmacokinetic models, the delays are often used to represent…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…
Models for cross-sectional network data have become increasingly well-developed in recent decades, and are widely used. This has led to a growing interest in the connection between such cross-sectional models and the behavioral processes…
Determinantal point processes are models for regular spatial point patterns, with appealing probabilistic properties. We present their spatio-temporal counterparts and give examples of these models, based on spatio-temporal covariance…
Optimising probabilistic models is a well-studied field in statistics. However, its connection with the training of generative models remains largely under-explored. In this paper, we show that the evolution of time-varying generative…
Although static networks have been extensively studied in machine learning, data mining, and AI communities for many decades, the study of dynamic networks has recently taken center stage due to the prominence of social media and its…
Many biological and medical questions can be modeled using time-to-event data in finite-state Markov chains, with the phase-type distribution describing intervals between events. We solve the inverse problem: given a phase-type…