Related papers: Adaptive non-asymptotic confidence balls in densit…
Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem. This paper surveys the literature on a fast, recursive estimator based on the predictive recursion…
Neural network-based methods for (un)conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical…
Recent methods in quantile regression have adopted a classification perspective to handle challenges posed by heteroscedastic, multimodal, or skewed data by quantizing outputs into fixed bins. Although these regression-as-classification…
A $d$-dimensional nonparametric additive regression model with dependent observations is considered. Using the marginal integration technique and wavelets methodology, we develop a new adaptive estimator for a component of the additive…
Bayesian density deconvolution using nonparametric prior distributions is a useful alternative to the frequentist kernel based deconvolution estimators due to its potentially wide range of applicability, straightforward uncertainty…
We derive an adaptive hierarchical method of estimating high dimensional probability density functions. We call this method of density estimation the "adaptive cluster expansion" or ACE for short. We present an application of this approach,…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
This work presents a novel simulation-based approach for constructing confidence regions in parametric models, which is particularly suited for generative models and situations where limited data and conventional asymptotic approximations…
The fundamental task of general density estimation $p(x)$ has been of keen interest to machine learning. In this work, we attempt to systematically characterize methods for density estimation. Broadly speaking, most of the existing methods…
One key issue in several astrophysical problems is the evaluation of the density probability function underlying an observational discrete data set. We here review two non-parametric density estimators which recently appeared in the…
In a linear regression model of fixed dimension $p \leq n$, we construct confidence regions for the unknown parameter vector based on the Lasso estimator that uniformly and exactly hold the prescribed in finite samples as well as in an…
We consider clinical trials in which an experimental treatment is compared with a control in pre-specified patient subpopulations. In such settings, adaptive enrichment designs allow the enrolled population to be modified at an interim…
Density based spatial clustering of points in $\mathbb{R}^n$ has a myriad of applications in a variety of industries. We generalise this problem to the density based clustering of lines in high-dimensional spaces, keeping in mind there…
We develop honest and locally adaptive confidence bands for probability densities. They provide substantially improved confidence statements in case of inhomogeneous smoothness, and are easily implemented and visualized. The article…
We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on $\mathbb{R}^p$ and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and…
We consider the problem of constructing Bayesian based confidence sets for linear functionals in the inverse Gaussian white noise model. We work with a scale of Gaussian priors indexed by a regularity hyper-parameter and apply the…
We consider a nonparametric Bayesian approach to estimation and testing for a multivariate monotone density. Instead of following the conventional Bayesian route of putting a prior distribution complying with the monotonicity restriction,…
The problem of adaptive sampling for estimating probability mass functions (pmf) uniformly well is considered. Performance of the sampling strategy is measured in terms of the worst-case mean squared error. A Bayesian variant of the…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
We investigate the estimation of a weighted density taking the form $g=w(F)f$, where $f$ denotes an unknown density, $F$ the associated distribution function and $w$ is a known (non-negative) weight. Such a class encompasses many examples,…