We introduce the Gamma-Exponential Process (GEP), a prior over a large family of continuous time stochastic processes. A hierarchical version of this prior (HGEP; the Hierarchical GEP) yields a useful model for analyzing complex time series. Models based on HGEPs display many attractive properties: conjugacy, exchangeability and closed-form predictive distribution for the waiting times, and exa...

Determinantal point processes (DPPs) are random point processes well-suited for modeling repulsion. In machine learning, the focus of DPP-based models has been on diverse subset selection from a discrete and finite base set. This discrete setting admits an efficient sampling algorithm based on the eigendecomposition of the defining kernel matrix. Recently, there has been growing interest in usi...

A variational formula for positive functionals of a Poisson random measure and Brownian motion is proved. The formula is based on the relative entropy representation for exponential integrals, and can be used to prove large deviation type estimates. A general large deviation result is proved, and illustrated with an example. 1 Introduction In this paper we prove a variational representation for...

In this paper we study the α-stable continuous-state branching processes (for α ∈ (1, 2]) and the α-stable continuous-state branching processes conditioned never to become extinct in the light of positive self-similarity. Understanding the interaction of the Lamperti transformation for continuous-state branching processes and the Lamperti transformation for positive, self-similar Markov process...

We present an approach to solving structured continuous-time Markov decision processes. We approximate the the optimal value function by a compact linear form, resulting in a linear program. The main difficulty arises from the number of constraints that grow exponentially with the number of variables in the system. We exploit the representation of continuous-time Bayesian networks (CTBNs) to de...

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 study “multi-person simple random walks” on a graph G with n vertices. There are n persons distributed randomly at the vertices of G. In each step of this di...

Gaussian ARMA processes with continuous time parameter, otherwise known as stationary continuous-time Gaussian processes with rational spectral density , have been of interest for many years. In the last twenty years there has been a resurgence of interest in continuous-time processes, partly as a result of the very successful application of stochastic diierential equation models to problems in...

This paper presents two approximations for the problem of Bayes linear estimation of continuous vector-valued stochastic processes. The problem of interpolating time series is treated as a particular application. Expressions for errors of approximations are obtained. In particular, our general conditions for zero error lead to a characterization of a generalized ARC!) process.

This paper describes an extension to the RAP system task-net semantics and representation language to enable the effective control of continuous processes. The representation addresses the problems of synchronizing plan expansion with events in the world, coping with multiple, non-deterministic task outcomes, and the description of a simple form of clean-up task. It is also pointed out that suc...

In recent years, various metrics have been developed for measuring the behavioural similarity of states in probabilistic transition systems [Desharnais et al., Proceedings of CONCUR, (1999), pp. 258-273, van Breugel and Worrell, Proceedings of ICALP, (2001), pp. 421-432]. In the context of finite Markov decision processes, we have built on these metrics to provide a robust quantitative analogue...