Related papers: Beyond Black Box Densities: Parameter Learning for…
We revisit the classical problem of deriving convergence rates for the maximum likelihood estimator (MLE) in finite mixture models. The Wasserstein distance has become a standard loss function for the analysis of parameter estimation in…
Mixture distributions are a workhorse model for multimodal data in information theory, signal processing, and machine learning. Yet even when each component density is simple, the differential entropy of the mixture is notoriously hard to…
Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but…
We consider the problem of estimating probability density functions based on sample data, using a finite mixture of densities from some component class. To this end, we introduce the $h$-lifted Kullback--Leibler (KL) divergence as a…
We consider the problem of estimating the mixing density $f$ from $n$ i.i.d. observations distributed according to a mixture density with unknown mixing distribution. In contrast with finite mixtures models, here the distribution of the…
We consider the parameter estimation problem in the deviated Gaussian mixture of experts in which the data are generated from $(1 - \lambda^{\ast}) g_0(Y| X)+ \lambda^{\ast} \sum_{i = 1}^{k_{\ast}} p_{i}^{\ast}…
Suppose $X_1,\dots, X_n$ is a random sample from a bounded and decreasing density $f_0$ on $[0,\infty)$. We are interested in estimating such $f_0$, with special interest in $f_0(0)$. This problem is encountered in various statistical…
We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac…
For data assumed to come from a finite mixture with an unknown number of components, it has become common to use Dirichlet process mixtures (DPMs) not only for density estimation, but also for inferences about the number of components. The…
We study the rates of convergence of the posterior distribution for Bayesian density estimation with Dirichlet mixtures of normal distributions as the prior. The true density is assumed to be twice continuously differentiable. The bandwidth…
Divergence is not only an important mathematical concept in information theory, but also applied to machine learning problems such as low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection. We…
Despite the strong predictive performance achieved by machine learning models across many application domains, assessing their trustworthiness through reliable estimates of predictive confidence remains a critical challenge. This issue…
Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…
We investigate whether the Wigner semi-circle and Marcenko-Pastur distributions, often used for deep neural network theoretical analysis, match empirically observed spectral densities. We find that even allowing for outliers, the observed…
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…
In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…
We study posterior contraction rates for mixing measures in homoscedastic location-scale mixture models with infinitely many components. While posterior convergence at the level of densities is well understood, ensuring convergence of the…
Given a decision process based on the approximate probability density function returned by a data assimilation algorithm, an interaction level between the decision making level and the data assimilation level is designed to incorporate the…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…