A central task in many applications is reasoning about processes that
change over continuous time. Recently, Nodelman et al. introduced
*continuous time Bayesian networks (CTBNs)*, a structured
representation for representing *Continuous Time Markov Processes*
over a structured state space. In this paper, we introduce
*continuous time Markov networks (CTMNs)*, an alternative
representation language that represents a different type of continuous-time
dynamics, particularly appropriate for
modeling biological and chemical
systems.
In this language, the dynamics of the process is
described as an interplay between two forces: the tendency of
each entity to change its state, which we model using a continuous-time
*proposal process* that suggests possible local changes to the state
of the system at different rates; and a global *fitness* or
*energy* function of the entire system, governing the probability that
a proposed change is accepted, which we capture by a Markov network that
encodes the fitness of different states. We show that the fitness
distribution is also the stationary distribution of the Markov process, so
that this representation provides a characterization of a temporal process
whose stationary distribution has a compact graphical representation. We
describe the semantics of the representation, its basic properties, and how
it compares to CTBNs. We also provide an algorithm for learning such models
from data, and demonstrate its potential benefit over other learning
approaches.

nir@cs.huji.ac.il