Related papers: Maximum Caliber: a general variational principle f…
Schr\"odinger bridges have emerged as an enabling framework for unveiling the stochastic dynamics of systems based on marginal observations at different points in time. The terminology "bridge'' refers to a probability law that suitably…
After the justification of the maximum entropy approach for equilibrium thermodynamic system, and of a maximum path entropy algorithm for nonequilibrium thermodynamic systems by virtue of the principle of virtual work, we present in this…
The principle of maximum entropy (Maxent) is often used to obtain prior probability distributions as a method to obtain a Gibbs measure under some restriction giving the probability that a system will be in a certain state compared to the…
The foundations of Statistical Mechanics can be recovered almost in their entirety from the Principle of Maximum Entropy. In this work we show that its non-equilibrium generalization, the Principle of Maximum Caliber (Jaynes, 1980), when…
MaxEnt's variational principle, in conjunction with Shannon's logarithmic information measure, yields only exponential functional forms in straightforward fashion. In this communication we show how to overcome this limitation via the…
Although compartmental dynamical systems are used in many different areas of science, model selection based on the maximum entropy principle (MaxEnt) is challenging because of the lack of methods for quantifying the entropy for this type of…
We derive a closed-form geometric functional for kernel dynamics on finite graphs by applying the Maximum Caliber (MaxCal) variational principle to the spectral transfer function h(lambda) of the graph Laplacian eigenbasis. The main result…
A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively…
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…
In most data-scientific approaches, the principle of Maximum Entropy (MaxEnt) is used to a posteriori justify some parametric model which has been already chosen based on experience, prior knowledge or computational simplicity. In a…
A theory for non-equilibrium systems is derived from a maximum entropy approach similar in spirit to the equilibrium theory given by Gibbs. Requiring Hamilton's principle of stationary action to be satisfied on average during a trajectory,…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
Distribution functions of many static transport equations are found using the Maximum Entropy Principle. The equations of constraint which contain the relevant dynamical information are simply the low-lying moments of the distributions.…
In this study we apply the maximum entropy principle to derive the properly scaled velocity distribution function of Boltzmann equations for mixtures, which leads to a non-isothermal Maxwell-Stefan diffusion model. We also analyze the…
Random walks are fundamental tools for analyzing complex networked systems, including social networks, biological systems, and communication infrastructures. While classical random walks focus on pairwise interactions, many real-world…
The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…
Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to…
A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…
Maximum entropy (maxEnt) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic dynamical systems, the effect of state space topology and path-dependent constraints on…
We show that the principle of maximum entropy, a variational method appearing in statistical inference, statistical physics, and the analysis of stochastic dynamical systems, admits a geometric description from gauge theory. Using the…