Related papers: Unbiased risk estimation and scoring rules
An unbiased estimator for the ellipticity of an object in a noisy image is given in terms of the image moments. Three assumptions are made: i) the pixel noise is normally distributed, although with arbitrary covariance matrix, ii) the image…
Measuring incomplete sets of mutually unbiased bases constitutes a sensible approach to the tomography of high-dimensional quantum systems. The unbiased nature of these bases optimizes the uncertainty hypervolume. However, imposing…
This work studies the problem of learning unbiased algorithms from biased feedback for recommendation. We address this problem from a novel distribution shift perspective. Recent works in unbiased recommendation have advanced the…
The best linear unbiased estimator (BLUE) is a popular statistical method adopted to combine multiple measurements of the same observable taking into account individual uncertainties and their correlation. The method is unbiased by…
We show that the Bregman divergence provides a rich framework to estimate unnormalized statistical models for continuous or discrete random variables, that is, models which do not integrate or sum to one, respectively. We prove that recent…
We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates…
We propose a standardized version of fairness measures for continuous scores with a reasonable interpretation based on the Wasserstein distance. Our measures are easily computable and well suited for quantifying and interpreting the…
Using Stein's method techniques, we develop a framework which allows one to bound the error terms arising from approximation by the Laplace distribution and apply it to the study of random sums of mean zero random variables. As a corollary,…
Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…
This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…
Many applications involve estimating the mean of multiple binomial outcomes as a common problem -- assessing intergenerational mobility of census tracts, estimating prevalence of infectious diseases across countries, and measuring…
Considering two random variables with different laws to which we only have access through finite size iid samples, we address how to reweight the first sample so that its empirical distribution converges towards the true law of the second…
We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…
This article discusses a generalization of the 1-dimensional multi-reference alignment problem. The goal is to recover a hidden signal from many noisy observations, where each noisy observation includes a random translation and random…
Statistics is sometimes described as the science of reasoning under uncertainty. Statistical models provide one view of this uncertainty, but what is frequently neglected is the 'invisible' portion of uncertainty: that assumed not to exist…
We consider the problem of distributedly estimating Gaussian processes in multi-agent frameworks. Each agent collects few measurements and aims to collaboratively reconstruct a common estimate based on all data. Agents are assumed with…
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…
We study the effective degrees of freedom of the lasso in the framework of Stein's unbiased risk estimation (SURE). We show that the number of nonzero coefficients is an unbiased estimate for the degrees of freedom of the lasso--a…
How might a smooth probability distribution be estimated, with accurately quantified uncertainty, from a limited amount of sampled data? Here we describe a field-theoretic approach that addresses this problem remarkably well in one…
This paper presents a theoretical analysis of sample selection bias correction. The sample bias correction technique commonly used in machine learning consists of reweighting the cost of an error on each training point of a biased sample to…