Related papers: Function reconstruction as a classical moment prob…
We study inverse reinforcement learning (IRL) and imitation learning (IM), the problems of recovering a reward or policy function from expert's demonstrated trajectories. We propose a new way to improve the learning process by adding a…
Distance measurements are currently the most powerful tool to study the expansion history of the universe without specifying its matter content nor any theory of gravitation. Assuming only an isotropic, homogeneous and flat universe, in…
Maximization of an expensive, unimodal function under random observations has been an important problem in hyperparameter tuning. It features expensive function evaluations (which means small budgets) and a high level of noise. We develop…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a…
Network reconstruction is the task of inferring the unseen interactions between elements of a system, based only on their behavior or dynamics. This inverse problem is in general ill-posed, and admits many solutions for the same…
The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates from incomplete data. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed…
A moment body is a linear projection of the spectraplex, the convex set of trace-one positive semidefinite matrices. Determining whether a given point lies within a given moment body is a problem with numerous applications in quantum state…
For many of the physical phenomena around us, we have developed sophisticated models explaining their behavior. Nevertheless, inferring specifics from visual observations is challenging due to the high number of causally underlying physical…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a…
It is a great challenge of nonequilibrium statistical mechanics to calculate entropy production within a microscopic theory. In the framework of linear irreversible thermodynamics, we combine the Mori-Zwanzig-Forster projection operator…
A basic issue in optimization, inverse theory,neural networks, computational chemistry and many other problems is the geometrical characterization of high dimensional functions. In inverse calculations one aims to characterize the set of…
We consider dynamical systems evolving near an equilibrium statistical state where the interest is in modelling long term behavior that is consistent with thermodynamic constraints. We adjust the distribution using an entropy-optimizing…
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…
We present a new framework for recycling independent variational approximations to Gaussian processes. The main contribution is the construction of variational ensembles given a dictionary of fitted Gaussian processes without revisiting any…
In stochastic systems, numerically sampling the relevant trajectories for the estimation of the large deviation statistics of time-extensive observables requires overcoming their exponential (in space and time) scarcity. The optimal way to…
The inverse Ising problem seeks to reconstruct the parameters of an Ising Hamiltonian on the basis of spin configurations sampled from the Boltzmann measure. Over the last decade, many applications of the inverse Ising problem have arisen,…
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…
Conductivity reconstruction in an inverse eddy current problem is considered in the present paper. With the electric field measurement on part of domain boundary, we formulate the reconstruction problem to a constrained optimization problem…