Estimating Parameters of Large CTMP from Single Trajectory with Application to Stochastic Network Epidemics ModelsGraph dynamical systems (GDS) model dynamic processes on a (static) graph.
Stochastic GDS has been used for network-based epidemics models such as the
contact process and the reversible contact process. In this paper, we consider
stochastic GDS that are also continuous-time Markov processes (CTMP), whose
transition rates are linear functions of some dynamics parameters $θ$ of
interest (i.e., healing, exogeneous, and endogeneous infection rates). Our goal
is to estimate $θ$ from a single, finite-time, continuously observed
trajectory of the CTMP. Parameter estimation of CTMP is challenging when the
state space is large; for GDS, the number of Markov states are
\emph{exponential} in the number of nodes of the graph. We showed that holding
classes (i.e., Markov states with the same holding time distribution) give
efficient partitions of the state space of GDS. We derived an upperbound on the
number of holding classes for the contact process, which is polynomial in the
number of nodes. We utilized holding classes to solve a smaller system of
linear equations to find $θ$. Experimental results show that finding
reasonable results can be achieved even for short trajectories, particularly
for the contact process. In fact, trajectory length does not significantly
affect estimation error.
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