相关论文: Correction algorithm for finite sample statistics
Ranking populations such as institutions based on certain characteristics is often of interest, and these ranks are typically estimated using samples drawn from the populations. Due to sample randomness, it is important to quantify the…
Given an equidistribution for probabilities p(i)=1/N, i=1..N. What is the expected corresponding rank ordered frequency distribution f(i), i=1..N, if an ensemble of M events is drawn?
It is well known that to estimate the Shannon entropy for symbolic sequences accurately requires a large number of samples. When some aspects of the data are known it is plausible to attempt to use this to more efficiently compute entropy.…
Ranked set sampling is a sampling design which has a wide range of applications in industrial statistics, and environmental and ecological studies, etc.. It is well known that ranked set samples provide more Fisher information than simple…
We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…
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…
Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…
We describe a new method that is both physically explicable and quantitatively accurate in describing the multifractal characteristics of intermittent events based on groupings of rank-ordered fluctuations. The generic nature of such…
The R\'enyi entropy is a generalization of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We consider estimation of the quadratic R\'enyi…
The mutual information (MI) between two random variables is an important correlation measure in data analysis. The Shannon entropy of a joint probability distribution is the variable part under fixed marginals. We aim to minimize and…
We investigate Bayesian predictive inference for finite population quantities when there are unequal probabilities of selection. Only limited information about the sample design is available; i.e., only the first-order selection…
Feature selection, in the context of machine learning, is the process of separating the highly predictive feature from those that might be irrelevant or redundant. Information theory has been recognized as a useful concept for this task, as…
Due to the complexity of order statistics, the finite sample behaviour of robust statistics is generally not analytically solvable. While the Monte Carlo method can provide approximate solutions, its convergence rate is typically very slow,…
Partially rank-ordered set (PROS) sampling is a generalization of ranked set sampling in which rankers are not required to fully rank the sampling units in each set, hence having more flexibility to perform the necessary judgemental ranking…
Let $M_n$ be a random $n\times n$ matrix with i.i.d. $\text{Bernoulli}(1/2)$ entries. We show that for fixed $k\ge 1$, \[\lim_{n\to \infty}\frac{1}{n}\log_2\mathbb{P}[\text{corank }M_n\ge k] = -k.\]
Machine learning classification tasks often benefit from predicting a set of possible labels with confidence scores to capture uncertainty. However, existing methods struggle with the high-dimensional nature of the data and the lack of…
We present an algorithmic approach to estimate the value distributions of random variables of probabilistic loops whose statistical moments are (partially) known. Based on these moments, we apply two statistical methods, Maximum Entropy and…
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…
We introduce a method based on Conformal Prediction (CP) to quantify the uncertainty of full ranking algorithms. We focus on a specific scenario where $n+m$ items are to be ranked by some ``black box'' algorithm. It is assumed that the…
We wish to estimate the total number of classes in a population based on sample counts, especially in the presence of high latent diversity. Drawing on probability theory that characterizes distributions on the integers by ratios of…