Related papers: High-dimensional maximum-entropy phase space tomog…
Constructing reduced representations of high-dimensional systems is a fundamental problem in physical chemistry. Many unsupervised machine learning methods can automatically find such low-dimensional representations. However, an often…
This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative…
This paper focuses on multi-block optimization problems over transport polytopes, which underlie various applications including strongly correlated quantum physics and machine learning. Conventional block coordinate descent-type methods for…
Three-dimensional phase contrast imaging of multiply-scattering samples in X-ray and electron microscopy is extremely challenging, due to small numerical apertures, the unavailability of wavefront shaping optics, and the highly nonlinear…
The Spreading Projection Algorithm for Rapid K-space samplING, or SPARKLING, is an optimization-driven method that has been recently introduced for accelerated 2D T2*-w MRI using compressed sensing. It has then been extended to address 3D…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
The maximum-entropy sampling problem is the NP-hard problem of maximizing the (log) determinant of an order-$s$ principle submatrix of a given order $n$ covariance matrix $C$. Exact algorithms are based on a branch-and-bound framework. The…
We present a novel method that integrates subspace modeling with an adaptive generative image prior for high-dimensional MR image reconstruction. The subspace model imposes an explicit low-dimensional representation of the high-dimensional…
Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that is routinely generated. In applications that are constrained by memory and computational intensity, excessively large…
We study the problem of overcoming exponential sample complexity in differential entropy estimation under Gaussian convolutions. Specifically, we consider the estimation of the differential entropy $h(X+Z)$ via $n$ independently and…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
Markov Chain Monte Carlo (MCMC) methods sample from unnormalized probability distributions and offer guarantees of exact sampling. However, in the continuous case, unfavorable geometry of the target distribution can greatly limit the…
This paper presents reconstructions of homogeneous targets from the 2D and 3D Fresnel databases by one-step imaging methods based on the computation of topological derivative and topological energy fields. The electromagnetic inverse…
Data augmentation improves the convergence of iterative algorithms, such as the EM algorithm and Gibbs sampler by introducing carefully designed latent variables. In this article, we first propose a data augmentation scheme for the…
Any given density matrix can be represented as an infinite number of ensembles of pure states. This leads to the natural question of how to uniquely select one out of the many, apparently equally suitable, possibilities. Following Jaynes'…
This note is a geometric commentary on maximum-entropy proofs. Its purpose is to illustrate the geometric structures involved in such proofs, to explain more in detail why the maximization of the entropy can be turned into the minimization…
Enhanced sampling algorithms have emerged as powerful methods to extend the utility of molecular dynamics simulations and allow the sampling of larger portions of the configuration space of complex systems in a given amount of simulation…
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…
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…
The reconstruction of high-dimensional sparse signals is a challenging task in a wide range of applications. In order to deal with high-dimensional problems, efficient sparse fast Fourier transform algorithms are essential tools. The second…