Related papers: Functional marked point processes -- A natural str…
This paper studies change-points in human brain functional connectivity (FC) and seeks patterns that are common across multiple subjects under identical external stimulus. FC relates to the similarity of fMRI responses across different…
Functional data are frequently accompanied by a parametric template that describes the typical shapes of the functions. However, these parametric templates can incur significant bias, which undermines both utility and interpretability. To…
Symmetric determinantal point processes (DPP's) are a class of probabilistic models that encode the random selection of items that exhibit a repulsive behavior. They have attracted a lot of attention in machine learning, when returning…
Determinantal point processes (DPPs) are an important concept in random matrix theory and combinatorics. They have also recently attracted interest in the study of numerical methods for machine learning, as they offer an elegant "missing…
In the development of stochastic integration and the theory of semimartingales, Markov processes have been a constant source of inspiration. Despite this historical interweaving, it turned out that semimartingales should be considered the…
Functional equations (FE) arise quite naturally in the analysis of stochastic systems of different kinds : queueing and telecommunication networks, random walks, enumeration of planar lattice walks, etc. Frequently, the object is to…
Predictable forward performance processes (PFPPs) are stochastic optimal control frameworks for an agent who controls a randomly evolving system but can only prescribe the system dynamics for a short period ahead. This is a common scenario…
We study the problem of change point localisation and inference for sequentially collected fragmented functional data, where each curve is observed only over discrete grids randomly sampled over a short fragment. The sequence of underlying…
Semi-parametric regression models are used in several applications which require comprehensibility without sacrificing accuracy. Typical examples are spline interpolation in geophysics, or non-linear time series problems, where the system…
This paper presents a focused review of Markov random fields (MRFs)--commonly used probabilistic representations of spatial dependence in discrete spatial domains--for categorical data, with an emphasis on models for binary-valued…
To analyse interaction in marked spatio-temporal point processes (MSTPPs), we introduce marked (cross) second-order reduced moment measures and K-functions for general inhomogeneous second-order intensity reweighted stationary MSTPPs. These…
Determinantal point processes (DPPs) are specific probability distributions over clouds of points that are used as models and computational tools across physics, probability, statistics, and more recently machine learning. Sampling from…
Semantic mapping is the incremental process of "mapping" relevant information of the world (i.e., spatial information, temporal events, agents and actions) to a formal description supported by a reasoning engine. Current research focuses on…
In this research paper, the relationship between finite / countable state space stochastic processes and point processes is explored. Utilizing the known relationship between Poisson processes and continuous time Markov chains, finite /…
We give a short overview of recent results on a specific class of Markov process: the Piecewise Deterministic Markov Processes (PDMPs). We first recall the definition of these processes and give some general results. On more specific cases…
Temporal point processes (TPPs) are widely used to model the timing and occurrence of events in domains such as social networks, transportation systems, and e-commerce. In this paper, we introduce TPP-LLM, a novel framework that integrates…
Spatio-temporal Hawkes point processes are a particularly interesting class of stochastic point processes for modeling self-exciting behavior, in which the occurrence of one event increases the probability of other events occurring. These…
We consider spatially dependent functional data collected under a geostatistics setting, where locations are sampled from a spatial point process. The functional response is the sum of a spatially dependent functional effect and a spatially…
Linear processes on functional spaces were born about fifteen years ago. And this original topic went through the same fast development as the other areas of functional data modeling such as PCA or regression. They aim at generalizing to…
Motivated by modern observational studies, we introduce a class of functional models that expands nested and crossed designs. These models account for the natural inheritance of correlation structure from sampling design in studies where…