Related papers: Fused Density Estimation: Theory and Methods
We propose a generative model that achieves minimax-optimal convergence rates for estimating probability distributions supported on unknown low-dimensional manifolds. Building on Fefferman's solution to the geometric Whitney problem, our…
The density ratio is an important metric for evaluating the relative likelihood of two probability distributions, with extensive applications in statistics and machine learning. However, existing estimation theories for density ratios often…
Among the variety of statistical intervals, highest-density regions (HDRs) stand out for their ability to effectively summarize a distribution or sample, unveiling its distinctive and salient features. An HDR represents the minimum size set…
Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in…
We study mixture of linear regression (random coefficient) models, which capture population heterogeneity by allowing the regression coefficients to follow an unknown distribution $G^*$. In contrast to common parametric methods that fix the…
Existing methods to summarize posterior inference for mixture models focus on identifying a point estimate of the implied random partition for clustering, with density estimation as a secondary goal (Wade and Ghahramani, 2018; Dahl et al.,…
We consider the Grenander estimator that is the maximum likelihood estimator for non-increasing densities. We prove uniform central limit theorems for certain subclasses of bounded variation functions and for H\"older balls of smoothness…
The clustering of bounded data presents unique challenges in statistical analysis due to the constraints imposed on the data values. This paper introduces a novel method for model-based clustering specifically designed for bounded data.…
Given a set of points $P\subset \mathbb{R}^{d}$ and a kernel $k$, the Kernel Density Estimate at a point $x\in\mathbb{R}^{d}$ is defined as $\mathrm{KDE}_{P}(x)=\frac{1}{|P|}\sum_{y\in P} k(x,y)$. We study the problem of designing a data…
A new nonparametric model of maximum-entropy (MaxEnt) copula density function is proposed, which offers the following advantages: (i) it is valid for mixed random vector. By `mixed' we mean the method works for any combination of discrete…
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…
We describe and analyze a broad class of mixture models for real-valued multivariate data in which the probability density of observations within each component of the model is represented as an arbitrary combination of basis functions.…
The estimation of a log-concave density on $\mathbb{R}^d$ represents a central problem in the area of nonparametric inference under shape constraints. In this paper, we study the performance of log-concave density estimators with respect to…
We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…
This paper introduces an intuitive and easy-to-implement nonparametric density estimator based on local polynomial techniques. The estimator is fully boundary adaptive and automatic, but does not require pre-binning or any other…
We study the problem of nonparametric estimation of density functions with a product form on the domain $\triangle=\{( x_1, \ldots, x_d)\in \mathbb{R}^d, 0\leq x_1\leq \dots \leq x_d \leq 1\}$. Such densities appear in the random truncation…
Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…
We formulate an optimization problem to estimate probability densities in the context of multidimensional problems that are sampled with uneven probability. It considers detector sensitivity as an heterogeneous density and takes advantage…
Probabilistic Regression refers to predicting a full probability density function for the target conditional on the features. We present a nonparametric approach to this problem which combines base classifiers (typically gradient boosted…
Current tools for multivariate density estimation struggle when the density is concentrated near a nonlinear subspace or manifold. Most approaches require choice of a kernel, with the multivariate Gaussian by far the most commonly used.…