Maximum-entropy moment-closure for stochastic systems on networks
نویسنده
چکیده
Moment-closure methods are popular tools to simplify the mathematical analysis of stochastic models defined on networks, in which high dimensional joint distributions are approximated (often by some heuristic argument) as functions of lower dimensional distributions. Whilst undoubtedly useful, several such methods suffer from issues of non-uniqueness and inconsistency. These problems are solved by an approach based on the maximisation of entropy, which is motivated, derived and implemented in this article. A series of numerical experiments are also presented, detailing the application of the method to the Susceptible-Infective-Recovered model of epidemics, as well as cautionary examples showing the sensitivity of moment-closure techniques in general.
منابع مشابه
Exact and approximate moment closures for non-Markovian network epidemics.
Moment-closure techniques are commonly used to generate low-dimensional deterministic models to approximate the average dynamics of stochastic systems on networks. The quality of such closures is usually difficult to asses and furthermore the relationship between model assumptions and closure accuracy are often difficult, if not impossible, to quantify. Here we carefully examine some commonly u...
متن کاملA Maximum Entropy Principle Based Closure Method for Macro-micro Models of Polymeric Materials
We consider the finite extensible nonlinear elasticity (FENE) dumbbell model in viscoelastic polymeric fluids. We employ the maximum entropy principle for FENE model to obtain the solution which maximizes the entropy of FENE model in stationary situations. Then we approximate the maximum entropy solution using the second order terms in microscopic configuration field to get an probability densi...
متن کاملMaximum-entropy closures for kinetic theories of neuronal network dynamics.
We analyze (1 + 1)D kinetic equations for neuronal network dynamics, which are derived via an intuitive closure from a Boltzmann-like equation governing the evolution of a one-particle (i.e., one-neuron) probability density function. We demonstrate that this intuitive closure is a generalization of moment closures based on the maximum-entropy principle. By invoking maximum-entropy closures, we ...
متن کاملNew stochastic mode reduction strategy for dissipative systems.
We present a new methodology for studying non-Hamiltonian nonlinear systems based on an information theoretical extension of a renormalization group technique using a modified maximum entropy principle. We obtain a rigorous dimensionally reduced description for such systems. The neglected degrees of freedom by this reduction are replaced by a systematically defined stochastic process under a co...
متن کاملConditional Generative Moment-Matching Networks
Maximum mean discrepancy (MMD) has been successfully applied to learn deep generative models for characterizing a joint distribution of variables via kernel mean embedding. In this paper, we present conditional generative moment-matching networks (CGMMN), which learn a conditional distribution given some input variables based on a conditional maximum mean discrepancy (CMMD) criterion. The learn...
متن کامل