Related papers: Time-like graphical models
We construct a family of self-similar Markov martingales with given marginal distributions. This construction uses the self-similarity and Markov property of a reference process to produce a family of Markov processes that possess the same…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
We study a class of graphs that represent local independence structures in stochastic processes allowing for correlated error processes. Several graphs may encode the same local independencies and we characterize such equivalence classes of…
Graph-based models form a fundamental aspect of data representation in Data Sciences and play a key role in modeling complex networked systems. In particular, recently there is an ever-increasing interest in modeling dynamic complex…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
We provide a new kriging procedure of processes on graphs. Based on the construction of Gaussian random processes indexed by graphs, we extend to this framework the usual linear prediction method for spatial random fields, known as kriging.…
When dealing with time series data, causal inference methods often employ structural vector autoregressive (SVAR) processes to model time-evolving random systems. In this work, we rephrase recursive SVAR processes with possible latent…
In this paper, we introduce different concepts of Granger causality and contemporaneous correlation for multivariate stationary continuous-time processes to model different dependencies between the component processes. Several equivalent…
A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so-called local independences, meaning that the intensities of certain types of events are independent of some…
This article introduces autocorrelograms for time series of point processes. Such time series usually arise when a longer temporal or spatio-temporal point process is sliced into smaller time units; for example, when an annual process is…
We study various classes of random processes defined on the regular tree $T_d$ that are invariant under the automorphism group of $T_d$. Most important ones are factor of i.i.d. processes (randomized local algorithms), branching Markov…
We initiate the study of graph algorithms in the streaming setting on massive distributed and parallel systems inspired by practical data processing systems. The objective is to design algorithms that can efficiently process evolving graphs…
Graph burning is a deterministic, discrete-time process that models how influence or contagion spreads in a graph. Associated to each graph is its burning number, which is a parameter that quantifies how quickly the influence spreads. We…
We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Due to the fact that the numbers of annually published papers have witnessed a linear growth in some citation networks, a geometric model is thus proposed to predict some statistical features of those networks, in which the academic…
We propose an analytic approach for the steady-state dynamics of Markov processes on locally tree-like graphs. It is based on time-translation invariant probability distributions for edge trajectories, which we encode in terms of infinite…
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…
We introduce graph gamma process (GGP) linear dynamical systems to model real-valued multivariate time series. For temporal pattern discovery, the latent representation under the model is used to decompose the time series into a…
We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, the known approaches to ascertain the existence of continuous Markov processes are based in the assumption…