Related papers: High-dimensional maximum-entropy phase space tomog…
The standard implementation of the Maximum Entropy Method (MEM) follows Bryan and deploys a Singular Value Decomposition (SVD) to limit the dimensionality of the underlying solution space apriori. Here we present arguments based on the…
This paper introduces multidimensional algorithms for simulating multiphase flows, leveraging the wave structure of the Euler equations in characteristic space and the physical properties of variables in physical space. The algorithm…
The best techniques for the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a variety of concave continuous relaxations of the objective function. A standard…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…
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…
Recent years have seen the rise of convolutional neural network techniques in exemplar-based image synthesis. These methods often rely on the minimization of some variational formulation on the image space for which the minimizers are…
State estimation is crucial for the performance and safety of numerous robotic applications. Among the suite of estimation techniques, particle filters have been identified as a powerful solution due to their non-parametric nature. Yet, in…
The maximum entropy method has been used to reconstruct images in a wide range of astronomical fields, but in its traditional form it is restricted to the reconstruction of strictly positive distributions. We present an extension of the…
We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…
The best practical techniques for exact solution of instances of the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a branch-and-bound framework, working with a…
We consider the problem of reconstructing 2D images from randomly under-sampled confocal microscopy samples. The well known and widely celebrated total variation regularization, which is the L1 norm of derivatives, turns out to be…
A numerical code is described for constructing Doppler maps from the orbital variation of line profiles of (mass transfering) binaries. It uses an algorithm related to Richardson-Lucy iteration, and is much faster than the standard…
We revisit the classical problem of inverting dimension-reducing linear mappings using the maximum entropy (MaxEnt) criterion. In the literature, solutions are problem-dependent, inconsistent, and use different entropy measures. We propose…
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…
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…
This paper shows how to evolve numerically the maximum entropy probability distributions for a given set of constraints, which is a variational calculus problem. An evolutionary algorithm can obtain approximations to some well-known…
The reconstruction of images from a small number of projections using the maximum-entropy method (MEM) with the Shannon entropy is considered. MEM provides higher-quality image reconstruction for sources with extended components than the…
Transformers suffer from the computational overhead of their quadratic dependence on the length of sequences processed. We present three methods, all adding an intermediate step between training and inference/generation, which extend the…
We develop a method for multidimensional optimisation using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimising functional correspond to fixed points of the…