  A central task in many applications is reasoning about processes that change
in a continuous time. The mathematical framework of Continuous Time Markov
Processes provides the basic foundations for modeling such systems. Recently,
Nodelman et al introduced continuous time Bayesian networks (CTBNs), which
allow a compact representation of continuous-time processes over a factored
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. In many real life processes, such as
biological and chemical systems, the dynamics of the process can be naturally
described as an interplay between two forces - the tendency of each entity to
change its state, and the overall fitness or energy function of the entire
system. In our model, the first force is described by a continuous-time
proposal process that suggests possible local changes to the state of the
system at different rates. The second force is represented by a Markov network
that encodes the fitness, or desirability, of different states; a proposed
local change is then accepted with a probability that is a function of the
change in the fitness distribution. 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. This allows us
to naturally capture a different type of structure in complex dynamical
processes, such as evolving biological sequences. We describe the semantics of
the representation, its basic properties, and how it compares to CTBNs. We also
provide algorithms for learning such models from data, and discuss its
applicability to biological sequence evolution.
