Related papers: Estimating statistical distributions using an inte…
In this paper, we study the classification problem by estimating the conditional probability function of the given data. Different from the traditional expected risk estimation theory on empirical data, we calculate the probability via…
A framework for robust optimization under uncertainty based on the use of the generalized inverse distribution function (GIDF), also called quantile function, is here proposed. Compared to more classical approaches that rely on the usage of…
Estimating the temperature and metal abundance of the intracluster and the intragroup media is crucial to determine their global metal content and to determine fundamental cosmological parameters. When a spatially resolved temperature or…
Multiple importance sampling estimators are widely used for computing intractable constants due to its reliability and robustness. The celebrated balance heuristic estimator belongs to this class of methods and has proved very successful in…
We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…
The randomized unbiased estimators of Rhee and Glynn (Operations Research:63(5), 1026-1043, 2015) can be highly efficient at approximating expectations of path functionals associated with stochastic differential equations (SDEs). However,…
Efficient and accurate estimation of multivariate empirical probability distributions is fundamental to the calculation of information-theoretic measures such as mutual information and transfer entropy. Common techniques include variations…
Stochastic variational inference makes it possible to approximate posterior distributions induced by large datasets quickly using stochastic optimization. The algorithm relies on the use of fully factorized variational distributions.…
This article proposes a new method to estimate an existing mutual information based dependence measure using histogram density estimates. Finding a suitable bin length for histogram is an open problem. We propose a new way of computing the…
It is not unusual for a data analyst to encounter data sets distributed across several computers. This can happen for reasons such as privacy concerns, efficiency of likelihood evaluations, or just the sheer size of the whole data set. This…
Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…
We develop a general method for power spectrum analysis of three dimensional redshift surveys. We present rigorous analytical estimates for the statistical uncertainty in the power and we are able to derive a rigorous optimal weighting…
When we use simulation to evaluate the performance of a stochastic system, the simulation often contains input distributions estimated from real-world data; therefore, there is both simulation and input uncertainty in the performance…
We study the problem of estimating the sum of $n$ elements, each with weight $w(i)$, in a structured universe. Our goal is to estimate $W = \sum_{i=1}^n w(i)$ within a $(1 \pm \epsilon)$ factor using a sublinear number of samples, assuming…
We introduce the Mutual Information Machine (MIM), a novel formulation of representation learning, using a joint distribution over the observations and latent state in an encoder/decoder framework. Our key principles are symmetry and mutual…
In the framework of Multifractal Diffusion Entropy Analysis we propose a method for choosing an optimal bin-width in histograms generated from underlying probability distributions of interest. The method presented uses techniques of…
Compositional data, which is data consisting of fractions or probabilities, is common in many fields including ecology, economics, physical science and political science. If these data would otherwise be normally distributed, their spread…
The Hoover index is a widely used measure of inequality with an intuitive interpretation, yet little is known about the finite-sample properties of its empirical estimator. In this paper, we derive a simple expression for the expected value…
The noncentral Wishart distribution has become more mainstream in statistics as the prevalence of applications involving sample covariances with underlying multivariate Gaussian populations as dramatically increased since the advent of…
The advent of data science has spurred interest in estimating properties of distributions over large alphabets. Fundamental symmetric properties such as support size, support coverage, entropy, and proximity to uniformity, received most…