Related papers: Recent progress in log-concave density estimation
In this paper, we study the approximation and estimation of $s$-concave densities via R\'enyi divergence. We first show that the approximation of a probability measure $Q$ by an $s$-concave densities exists and is unique via the procedure…
In the context of estimating local modes of a conditional density based on kernel density estimators, we show that existing bandwidth selection methods developed for kernel density estimation are unsuitable for mode estimation. We propose…
Reconstruction of sets from a random sample of points intimately related to them is the goal of set estimation theory. Within this context, a particular problem is the one related with the reconstruction of density level sets and…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
For sampling from a log-concave density, we study implicit integrators resulting from $\theta$-method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the…
The inference of evolutionary histories is a central problem in evolutionary biology. The analysis of a sample of phylogenetic trees can be conducted in Billera-Holmes-Vogtmann tree space, which is a CAT(0) metric space of phylogenetic…
Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…
Kernel density estimation is a well known method involving a smoothing parameter (the bandwidth) that needs to be tuned by the user. Although this method has been widely used the bandwidth selection remains a challenging issue in terms of…
Sampling from Gibbs distributions and computing their log-partition function are fundamental tasks in statistics, machine learning, and statistical physics. While efficient algorithms are known for log-concave densities, the worst-case…
We present some new density estimation algorithms obtained by bootstrap aggregation like Bagging. Our algorithms are analyzed and empirically compared to other methods found in the statistical literature, like stacking and boosting for…
We study nonparametric maximum likelihood estimation for two classes of multivariate distributions that imply strong forms of positive dependence; namely log-supermodular (MTP$_2$) distributions and log-$L^\#$-concave (LLC) distributions.…
The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of…
Length-biased data are a particular case of weighted data, which arise in many situations: biomedicine, quality control or epidemiology among others. In this paper we study the theoretical properties of kernel density estimation in the…
This paper proposes a new method of bandwidth selection in kernel estimation of density and distribution functions motivated by the connection between maximisation of the entropy of probability integral transforms and maximum likelihood in…
Motivated by studies in biological sciences to detect differentially expressed genes, a semiparametric two-component mixture model with one known component is being studied in this paper. Assuming the density of the unknown component to be…
Density level sets are mainly estimated using one of three methodologies: plug-in, excess mass, or a hybrid approach. The plug-in methods are based on replacing the unknown density by some nonparametric estimator, usually the kernel. Thus,…
The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…
We study the approximation of arbitrary distributions $P$ on $d$-dimensional space by distributions with log-concave density. Approximation means minimizing a Kullback--Leibler-type functional. We show that such an approximation exists if…
This article proposes a novel density estimation based algorithm for carrying out supervised machine learning. The proposed algorithm features O(n) time complexity for generating a classifier, where n is the number of sampling instances in…
In the this paper, the authors propose to estimate the density of a targeted population with a weighted kernel density estimator (wKDE) based on a weighted sample. Bandwidth selection for wKDE is discussed. Three mean integrated squared…