Related papers: Time-like graphical models
We study Markov processes where the "time" parameter is replaced by paths in a directed graph from an initial vertex to a terminal one. Along each directed path the process is Markov and has the same distribution as the one along any other…
Graph processes that unfold in continuous time are of obvious theoretical and practical interest. Particularly useful are those whose long-term behavior converges to a graph distribution of known form. Here, we review some of the conditions…
We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series…
We study continuous time Markov processes on graphs. The notion of frequency is introduced, which serves well as a scaling factor between any Markov time of a continuous time Markov process and that of its jump chain. As an application, we…
In this paper, we propose Continuous Graph Flow, a generative continuous flow based method that aims to model complex distributions of graph-structured data. Once learned, the model can be applied to an arbitrary graph, defining a…
Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical data analysis and signal processing and (ii) characterising classes of dynamical…
Representing the conditional independences present in a multivariate random vector via graphs has found widespread use in applications, and such representations are popularly known as graphical models or Markov random fields. These models…
Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing.…
Many real-world objects can be modeled as a stream of events on the nodes of a graph. In this paper, we propose a class of graphical event models named temporal point process graphical models for representing the temporal dependencies among…
Let $X = \{X_{u}\}_{u \in U}$ be a real-valued Gaussian process indexed by a set $U$. It can be thought of as an undirected graphical model with every random variable $X_{u}$ serving as a vertex. We characterize this graph in terms of the…
We introduce an algorithmic model of heat conduction, the thermodynamic graph. The thermodynamic graph is analogous to meshes in the finite difference method in the sense that the calculation of temperature is carried out at the vertices of…
This paper introduces graphemes for constructing and analyzing stochastic processes that describe the evolution of large dynamic graphs. Unlike graphons, which capture the static properties of dense graphs via exchangeability or subgraph…
In this paper, we establish the partial correlation graph for multivariate continuous-time stochastic processes, assuming only that the underlying process is stationary and mean-square continuous with expectation zero and spectral density…
The concept of a random process has been recently extended to graph signals, whereby random graph processes are a class of multivariate stochastic processes whose coefficients are matrices with a \textit{graph-topological} structure. The…
This paper contributes to the multivariate analysis of marked spatio-temporal point process data by introducing different partial point characteristics and extending the spatial dependence graph model formalism. Our approach yields a…
In recent years, a growing number of method and application works have adapted and applied the causal-graphical-model framework to time series data. Many of these works employ time-resolved causal graphs that extend infinitely into the past…
We consider a class of graph-valued stochastic processes in which each vertex has a type that fluctuates randomly over time. Collectively, the paths of the vertex types up to a given time determine the probabilities that the edges are…
Neural marked temporal point processes have been a valuable addition to the existing toolbox of statistical parametric models for continuous-time event data. These models are useful for sequences where each event is associated with a single…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
We propose a method to approximate continuous-time, continuous-state stochastic processes by a discrete-time Markov chain defined on a nonuniform grid. Our method provides exact moment matching for processes whose first and second moments…