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Estimating the Shannon entropy of a discrete distribution from which we have only observed a small sample is challenging. Estimating other information-theoretic metrics, such as the Kullback-Leibler divergence between two sparsely sampled…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
Message importance measure (MIM) is applicable to characterize the importance of information in the scenario of big data, similar to entropy in information theory. In fact, MIM with a variable parameter can make an effect on the…
We introduce the {\alpha}-{\kappa}-{\mu} shadowed ({\alpha}-KMS) fading distribution as a natural generalization of the versatile {\alpha}-{\kappa}-{\mu} and {\alpha}-{\eta}-{\mu} distributions. The {\alpha}-KMS fading distribution unifies…
The gamma distribution arises frequently in Bayesian models, but there is not an easy-to-use conjugate prior for the shape parameter of a gamma. This inconvenience is usually dealt with by using either Metropolis-Hastings moves, rejection…
Transfer entropy is a widely used measure for quantifying directed information flows in complex systems. While the challenges of estimating transfer entropy for continuous data are well known, it has two major shortcomings for data of…
Identifying anomalies and contamination in datasets is important in a wide variety of settings. In this paper, we describe a new technique for estimating contamination in large, discrete valued datasets. Our approach considers the normal…
Numerous approaches are proposed in the literature for non-stationarity marginal extreme value inference, including different model parameterisations with respect to covariate, and different inference schemes. The objective of this article…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
A common approach to statistical learning with big-data is to randomly split it among $m$ machines and learn the parameter of interest by averaging the $m$ individual estimates. In this paper, focusing on empirical risk minimization, or…
Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
We consider parameter estimations with probes being the boundary driven/dissipated non- equilibrium steady states of XXZ spin 1/2 chains. The parameters to be estimated are the dissipation coupling and the anisotropy of the spin-spin…
The major problem in information theoretic analysis of neural responses and other biological data is the reliable estimation of entropy--like quantities from small samples. We apply a recently introduced Bayesian entropy estimator to…
Statistical signal processing applications usually require the estimation of some parameters of interest given a set of observed data. These estimates are typically obtained either by solving a multi-variate optimization problem, as in the…
We study the estimation and concentration on its expectation of the probability to observe data further than a specified distance from a given iid sample in a metric space. The problem extends the classical problem of estimation of the…
In statistical survey analysis, (partial) non-responders are integral elements during data acquisition. Treating missing values during data preparation and data analysis is therefore a non-trivial underpinning. Focusing on different data…
Estimation frameworks for statistical inference are preferred to hypothesis testing when quantifying uncertainty and precise estimation are more valuable than binary decisions about statistical significance. Study design for…
Scientific modeling applications often require estimating a distribution of parameters consistent with a dataset of observations - an inference task also known as source distribution estimation. This problem can be ill-posed, however, since…
We consider the relative configurational entropy per cell S_Delta as a measure of the degree of spatial disorder for systems of finite-sized objects. It is highly sensitive to deviations from the most spatially ordered reference…