Related papers: Maximum-entropy moment-closure for stochastic syst…
Contact processes describe the transmission of distinct properties of nodes via the links of a network. They provide a simple framework for many phenomena, such as epidemic spreading and opinion formation. Combining contact processes with…
When an expert operates a perilous dynamic system, ideal constraint information is tacitly contained in their demonstrated trajectories and controls. The likelihood of these demonstrations can be computed, given the system dynamics and task…
Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains. The analysis of such processes is,…
Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…
A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived. Most results in the literature are either focused on…
Generating samples from limited information is a fundamental problem across scientific domains. Classical maximum entropy methods provide principled uncertainty quantification from moment constraints but require sampling via MCMC or…
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…
Maximum-entropy moment methods allow for the modelling of gases from the continuum regime to strongly rarefied conditions. The development of approximated solutions to the entropy maximization problem has made these methods computationally…
In many realistic systems, maximum entropy principle (MEP) analysis provides an effective characterization of the probability distribution of network states. However, to implement the MEP analysis, a sufficiently long-time data recording in…
The method of maximum entropy is quite a powerful tool to solve the generalized moment problem, which consists of determining the probability density of a random variable X from the knowledge of the expected values of a few functions of the…
Efficient approximation lies at the heart of large-scale machine learning problems. In this paper, we propose a novel, robust maximum entropy algorithm, which is capable of dealing with hundreds of moments and allows for computationally…
We present a technique for entropy optimization to calculate a distribution from its moments. The technique is based upon maximizing a discretized form of the Shannon entropy functional by mapping the problem onto a dual space where an…
Power moments, modified moments, and optimized moments are powerful tools for solving microscopic models of macroscopic systems; however the expansion of the density of states as a continued fraction does not converge to the macroscopic…
We propose a high-order stochastic-statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. The statistical moment…
A brief discussion is given of the traditional version of the Maximum Entropy Method, including a review of some of the criticism that has been made in regard to its use in statistical inference. Motivated by these questions, a modified…
The moments of spatial probabilistic systems are often given by an infinite hierarchy of coupled differential equations. Moment closure methods are used to approximate a subset of low order moments by terminating the hierarchy at some order…
Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
We present a systematic study of the reconstruction of a non-negative function via maximum entropy approach utilizing the information contained in a finite number of moments of the function. For testing the efficacy of the approach, we…
The Chemical Master Equation (CME) is used to stochastically model biochemical reaction networks, under the Markovian assumption. The low-order statistical moments induced by the CME are often the key quantities that one is interested in.…