Related papers: Eigenvalue distribution from bootstrap estimates
Accurate uncertainty estimates can significantly improve the performance of iterative design of experiments, as in Sequential and Reinforcement learning. For many such problems in engineering and the physical sciences, the design task…
The Bethe free energy approximation provides an effective way for relaxing NP-hard problems of probabilistic inference. However, its accuracy depends on the model parameters and particularly degrades if a phase transition in the model…
The eigenstate thermalization hypothesis provides a framework for understanding thermalization in isolated quantum many-body systems by characterizing statistical properties of local observables in energy eigenstates. Here we demonstrate…
Networks are often studied using the eigenvalues of their adjacency matrix, a powerful mathematical tool with a wide range of applications. Since in real systems the exact graph structure is not known, researchers resort to random graphs to…
We discuss the use of the replica ansatz in computing free energies in random matrix theory, and confirm a conjectured condition on analytic continuation in the replica index at large-N.
We develop a method to fit high-temperature Gibbs free energy data for the development of interatomic potentials for atomic systems. The approach is based on Hamiltonian thermodynamic integration, enabling the identification of suitable…
Given a sequence of observations from a discrete-time, finite-state hidden Markov model, we would like to estimate the sampling distribution of a statistic. The bootstrap method is employed to approximate the confidence regions of a…
The quantum mechanical expression relating two commuting operators is reformulated such that the power method (also called method of moments) for iteratively calculating eigenvalues and eigenvectors becomes applicable. The new iterative…
By quenching into the metastable region of the three-dimensional Ising model, we investigate the paths that the magnetization (energy) takes as a function of time. We accumulate the magnetization (energy) paths into time-dependent…
Inspired by Kubo-Anderson Markov processes, we introduce a new class of transfer matrices whose largest eigenvalue is determined by a simple explicit algebraic equation. Applications include the free energy calculation for various…
Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…
We describe a novel method to obtain thermodynamic properties of quantum systems using Baysian Inference -- Maximum Entropy techniques. The method is applicable to energy values sampled at a discrete set of temperatures from Quantum Monte…
While widely used as a general method for uncertainty quantification, the bootstrap method encounters difficulties that raise concerns about its validity in practical applications. This paper introduces a new resampling-based method, termed…
In this paper we develop a complete analytical framework based on Random Matrix Theory for the performance evaluation of Eigenvalue-based Detection. While, up to now, analysis was limited to false-alarm probability, we have obtained an…
We derive the optimal estimates of the free energies of an arbitrary number of thermodynamic states from nonequilibrium work measurements; the work data are collected from forward and reverse switching processes and obey a fluctuation…
In the study of phase transitions a very few models are accessible to exact solution. In the most cases analytical simplifications have to be done or some numerical technique has to be used to get insight about their critical properties.…
Importance sampling of target probability distributions belonging to a given convex class is considered. Motivated by previous results, the cost of importance sampling is quantified using the relative entropy of the target with respect to…
This paper considers the problem of estimating the population spectral distribution from a sample covariance matrix in large dimensional situations. We generalize the contour-integral based method in Mestre (2008) and present a local moment…
Accurate calculations of solvation free energies remain a central challenge in molecular simulations, often requiring extensive sampling and numerous alchemical intermediates to ensure sufficient overlap between phase-space distributions of…
Network models are applied in numerous domains where data can be represented as a system of interactions among pairs of actors. While both statistical and mechanistic network models are increasingly capable of capturing various dependencies…