Related papers: Statistical mechanical analysis of sparse linear r…
In this paper, we focus on activating only a few sensors, among many available, to estimate the state of a stochastic process of interest. This problem is important in applications such as target tracking and simultaneous localization and…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
The stochastic nature of iterative optimization heuristics leads to inherently noisy performance measurements. Since these measurements are often gathered once and then used repeatedly, the number of collected samples will have a…
A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical equilibrium states are obtained by maximizing the…
This paper provides a statistical analysis of high-dimensional batch Reinforcement Learning (RL) using sparse linear function approximation. When there is a large number of candidate features, our result sheds light on the fact that…
In the setting of entangled single-sample distributions, the goal is to estimate some common parameter shared by a family of distributions, given one \emph{single} sample from each distribution. We study mean estimation and linear…
The SparseStep algorithm is presented for the estimation of a sparse parameter vector in the linear regression problem. The algorithm works by adding an approximation of the exact counting norm as a constraint on the model parameters and…
Sparse Bayesian Learning (SBL) is a powerful framework for attaining sparsity in probabilistic models. Herein, we propose a coordinate ascent algorithm for SBL termed Relevance Matching Pursuit (RMP) and show that, as its noise variance…
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…
We consider tensor factorizations based on sparse measurements of the components of relatively high rank tensors. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful…
Data-driven modelling and computational predictions based on maximum entropy principle (MaxEnt-principle) aim at finding as-simple-as-possible - but not simpler then necessary - models that allow to avoid the data overfitting problem. We…
Sparse wideband sensor array design for sensor location optimisation is highly nonlinear and it is traditionally solved by genetic algorithms, simulated annealing or other similar optimization methods. However, this is an extremely…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
A generic algorithm for the extraction of probabilistic (Bayesian) information about model parameters from data is presented. The algorithm propagates an ensemble of particles in the product space of model parameters and outputs. Each…
High-entropy alloys have attracted attention for their exceptional mechanical properties and thermal stability. However, the combinatorial explosion in the number of possible elemental compositions renders traditional trial-and-error…
We report a multiscale approach of broad applicability to stochastic reconstruction of multiphase materials, including porous ones. The approach devised uses an optimization method, such as the simulated annealing (SA) and the so-called…
In recent years, sparse principal component analysis has emerged as an extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a…
Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this belief, even in the form of examples that are…
Any performance analysis based on stochastic simulation is subject to the errors inherent in misspecifying the modeling assumptions, particularly the input distributions. In situations with little support from data, we investigate the use…
Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…