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Multivariate geostatistics is based on modelling all covariances between all possible combinations of two or more variables at any sets of locations in a continuously indexed domain. Multivariate spatial covariance models need to be built…
This paper focuses on modeling the dynamic attributes of a dynamic network with a fixed number of vertices. These attributes are considered as time series which dependency structure is influenced by the underlying network. They are modeled…
Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's…
In this paper, we study time-varying graphical models based on data measured over a temporal grid. Such models are motivated by the needs to describe and understand evolving interacting relationships among a set of random variables in many…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from…
Motivated by the need to develop simulation tools for verification and validation of autonomous driving systems operating in traffic consisting of both autonomous and human-driven vehicles, we propose a framework for modeling vehicle…
Due to the complex and changing interactions in dynamic scenarios, motion forecasting is a challenging problem in autonomous driving. Most existing works exploit static road graphs to characterize scenarios and are limited in modeling…
We outline a representation for discrete multivariate distributions in terms of interventional potential functions that are globally normalized. This representation can be used to model the effects of interventions, and the independence…
In this paper, we consider multivariate functional time series with a two-way dependence structure: a serial dependence across time points and a graphical interaction among the multiple functions within each time point. We develop the…
Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…
Undirected graphical models are widely used to model the conditional independence structure of vector-valued data. However, in many modern applications, for example those involving EEG and fMRI data, observations are more appropriately…
This paper explores the observability and estimation capability of dynamical systems using predominantly relative measurements of the system's state-space variables, with minimal to no reliance on absolute measurements of these variables.…
Network graphs have become a popular tool to represent complex systems composed of many interacting subunits; especially in neuroscience, network graphs are increasingly used to represent and analyze functional interactions between neural…
This paper introduces sparse dynamic chain graph models for network inference in high dimensional non-Gaussian time series data. The proposed method parametrized by a precision matrix that encodes the intra time-slice conditional…
We propose here a framework to model real-time components consisting of concurrent real-time tasks running on a single processor, using parametric timed automata. Our framework is generic and modular, so as to be easily adapted to different…
Graph models are widely used to analyse diffusion processes embedded in social contacts and to develop applications. A range of graph models are available to replicate the underlying social structures and dynamics realistically. However,…
Time-varying graph signals are alternative representation of multivariate (or multichannel) signals in which a single time-series is associated with each of the nodes or vertex of a graph. Aided by the graph-theoretic tools, time-varying…
Ordered sequences of univariate or multivariate regressions provide statistical models for analysing data from randomized, possibly sequential interventions, from cohort or multi-wave panel studies, but also from cross-sectional or…
We introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential…