  Across many fields, a problem of interest is to predict the transition rates
between nodes of a network, given limited stationary state and dynamical
information. We give a solution using the principle of Maximum Caliber. We find
the transition rate matrix by maximizing the path entropy of a random walker on
the network constrained to reproducing a stationary distribution and a few
dynamical averages. A main finding here is that when constrained only by the
mean jump rate, the rate matrix is given by a square-root dependence of the
rate, $\omega_{ab} \propto \sqrt{p_b/p_a}$, on $p_a$ and $p_b$, the stationary
state populations at nodes a and b. We give two examples of our approach.
First, we show that this method correctly predicts the correlated rates in a
biochemical network of two genes, where we know the exact results from prior
simulation. Second, we show that it correctly predicts rates of peptide
conformational transitions, when compared to molecular dynamics simulations.
This method can be used to infer large numbers of rates on known networks where
smaller numbers of steady-state node populations are known.
