Related papers: Threshold-free estimation of entropy from a Pearso…
We establish non-asymptotic efficiency guarantees for tensor decomposition-based inference in count data models. Under a Poisson framework, we consider two related goals: (i) parametric inference, the estimation of the full distributional…
The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…
Entanglement entropy is an essential metric for characterizing quantum many-body systems, but its numerical evaluation for neural network representations of quantum states has so far been inefficient and demonstrated only for the restricted…
Assuming that a threshold Ornstein-Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate the parameters. Our theoretical basis is the celebrated ergodic theorem. To use this theorem we…
Bayesian optimal experimental design provides a principled framework for selecting experimental settings that maximize obtained information. In this work, we focus on estimating the expected information gain in the setting where the…
In a recent Letter [1] a framework for estimating entropy was introduced and applied to one-dimensional and two-dimensional systems. In this Comment we show that the method is not well suited for estimating entropy in bidimensional systems…
Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive for high-dimensional problems. Iterative random sparsification methods allow for the estimation of a single dominant eigenvalue at reduced cost by…
We describe a method to determine the eigenvalue density of empirical covariance matrix in the presence of correlations between samples. This is a straightforward generalization of the method developed earlier by the authors for…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
I propose a new algorithm, a free energy Monte Carlo algorithm, for calculations where conventional Monte Carlo simulations struggle with ergodicity problems. The simplest version of the proposed algorithm allows for the determination of…
We develop randomized matrix-free algorithms for estimating partial traces, a generalization of the trace arising in quantum physics and chemistry. Our algorithm improves on the typicality-based approach used in [T. Chen and Y-C. Cheng,…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
In nonlinear dynamics, and to a lesser extent in other fields, a widely used measure of complexity is the Permutation Entropy. But there is still no known method to determine the accuracy of this measure. There has been little research on…
We investigate the concept of orbital free entropy from the viewpoint of matrix liberation process. We will show that many basic questions around the definition of orbital free entropy are reduced to the question of full large deviation…
The concentration of measure phenomenon may be summarized as follows: a function of many weakly dependent random variables that is not too sensitive to any of its individual arguments will tend to take values very close to its expectation.…
We show that the same maximum entropy principle applied to recurrence microstates configures a new way to properly compute the time delay necessary to correctly sample a data set. The new method retrieves results obtained using traditional…
The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions…
The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…
Quantum coherence is the most distinguished signature of quantum mechanics, also recognized to be an essential resource for many promising quantum technologies, playing a central role in phenomena related to quantum information science,…
The purpose of this study was to investigate how the entropy of a neuron cell can be measured using membrane ion current signals, which were recorded from neurons in the mouse medial prefrontal cortex (mPFC). The sample entropy and the…