Related papers: Density estimation for biased data
In this paper, we study a class of non-parametric density estimators under Bayesian settings. The estimators are piecewise constant functions on binary partitions. We analyze the concentration rate of the posterior distribution under a…
Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…
Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a…
In many applications, different populations are compared using data that are sampled in a biased manner. Under sampling biases, standard methods that estimate the difference between the population means yield unreliable inferences. Here we…
An evolving problem in the field of spatial and ecological statistics is that of preferential sampling, where biases may be present due to a relationship between sample data locations and a response of interest. This field of research bears…
An important estimation problem that is closely related to large-scale multiple testing is that of estimating the null density and the proportion of nonnull effects. A few estimators have been introduced in the literature; however, several…
Estimating prevalence, the fraction of a population with a certain medical condition, is fundamental to epidemiology. Traditional methods rely on classification of test samples taken at random from a population. Such approaches to…
This paper focuses on the problem of unbounded density ratio estimation -- an understudied yet critical challenge in statistical learning -- and its application to covariate shift adaptation. Much of the existing literature assumes that the…
Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…
We review some aspects of Bayesian and frequentist interval estimation, focusing first on their relative strengths and weaknesses when used in "clean" or "textbook" contexts. We then turn attention to observational-data situations which are…
The question of how best to estimate a continuous probability density from finite data is an intriguing open problem at the interface of statistics and physics. Previous work has argued that this problem can be addressed in a natural way…
Bayesian predictive densities when the observed data $x$ and the target variable $y$ to be predicted have different distributions are investigated by using the framework of information geometry. The performance of predictive densities is…
We consider statistical models where functional data are artificially contaminated by independent Wiener processes in order to satisfy privacy constraints. We show that the corrupted observations have a Wiener density which determines the…
Given a random sample of points from some unknown density, we propose a data-driven method for estimating density level sets under the r-convexity assumption. This shape condition generalizes the convexity property. However, the main…
We consider nonparametric measurement error density deconvolution subject to heteroscedastic measurement errors as well as symmetry about zero and shape constraints, in particular unimodality. The problem is motivated by applications where…
One-step ahead prediction for the multinomial model is considered. The performance of a predictive density is evaluated by the average Kullback-Leibler divergence from the true density to the predictive density. Asymptotic approximations of…
Estimating mutual information (MI) from samples is a fundamental problem in statistics, machine learning, and data analysis. Recently it was shown that a popular class of non-parametric MI estimators perform very poorly for strongly…
Nonprobability (convenience) samples are increasingly sought to reduce the estimation variance for one or more population variables of interest that are estimated using a randomized survey (reference) sample by increasing the effective…
Divergence estimators based on direct approximation of density-ratios without going through separate approximation of numerator and denominator densities have been successfully applied to machine learning tasks that involve distribution…
Density Ratio Estimation has attracted attention from the machine learning community due to its ability to compare the underlying distributions of two datasets. However, in some applications, we want to compare distributions of random…