Related papers: Maximum Caliber: a general variational principle f…

Simplified mechanistic models in ecology have been criticized for the fact that a good fit to data does not imply the mechanism is true: pattern does not equal process. In parallel, the maximum entropy principle (MaxEnt) has been applied in…

Trajectory optimization and model predictive control are essential techniques underpinning advanced robotic applications, ranging from autonomous driving to full-body humanoid control. State-of-the-art algorithms have focused on data-driven…

We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing…

Making statistical predictions requires tackling two problems: one must assign appropriate probability distributions and then one must calculate a variety of expected values. The method of maximum entropy is commonly used to address the…

Ill-posed inverse problems of the form y = X p where y is J-dimensional vector of a data, p is m-dimensional probability vector which cannot be measured directly and matrix X of observable variables is a known J,m matrix, J < m, are…

A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…

Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization…

Dynamics of inelastic gases are studied within the framework of random collision processes. The corresponding Boltzmann equation with uniform collision rates is solved analytically for gases, impurities, and mixtures. Generally, the energy…

The concept of Shannon Entropy for probability distributions and associated Maximum Entropy Principle are extended here to the concepts of Relative Divergence of one Grading Function from another and Maximum Relative Divergence Principle…

Turbulence may appear as a complex process with a multitude of scales and flow patterns, but still obeys simple physical principles such as the conservation of momentum, of energy, and the maximum entropy principle. The latter states that…

Dissipative processes cause collisionless plasmas in many systems to develop nonthermal particle distributions with broad power-law tails. The prevalence of power-law energy distributions in space/astrophysical observations and kinetic…

In this paper an alternative approach to statistical mechanics based on the maximum information entropy principle (MaxEnt) is examined, specifically its close relation with the Gibbs method of ensembles. It is shown that the MaxEnt…

Recursive max-linear vectors model causal dependence between its components by expressing each node variable as a max-linear function of its parental nodes in a directed acyclic graph and some exogenous innovation. Motivated by extreme…

Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input…

The ability of many powerful machine learning algorithms to deal with large data sets without compromise is often hampered by computationally expensive linear algebra tasks, of which calculating the log determinant is a canonical example.…

Many Imitation and Reinforcement Learning approaches rely on the availability of expert-generated demonstrations for learning policies or value functions from data. Obtaining a reliable distribution of trajectories from motion planners is…

Cells are often considered input-output devices that maximize the transmission of information by converting extracellular stimuli (input) via signaling pathways (communication channel) to cell behavior (output). However, in biological…

We show that the naive application of the maximum entropy principle can yield answers which depend on the level of description, i.e. the result is not invariant under coarse-graining. We demonstrate that the correct approach, even for…

In this paper we show how to exploit interventional data to acquire the joint conditional distribution of all the variables using the Maximum Entropy principle. To this end, we extend the Causal Maximum Entropy method to make use of…

We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with…