Related papers: Density Ratio Estimation via Sampling along Genera…
When random effects are correlated with sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no…
Consider a density $f$ on $[0,1]$ that must be estimated from an i.i.d. sample $X_1,...,X_n$ drawn from $f$. In this note, we study binary-tree-based histogram estimates that use recursive splitting of intervals. If the decision to split an…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
The ability to backpropagate stochastic gradients through continuous latent distributions has been crucial to the emergence of variational autoencoders and stochastic gradient variational Bayes. The key ingredient is an unbiased and…
Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein…
In this work, we study non-parametric estimation of joint probabilities of a given set of discrete and continuous random variables from their (empirically estimated) 2D marginals, under the assumption that the joint probability could be…
We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian…
We present a method based on unsupervised machine learning to identify regions of interest using particle velocity distributions as a signature pattern. An automatic density estimation technique is applied to particle distributions provided…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
We study the Bayesian density estimation of data living in the offset of an unknown submanifold of the Euclidean space. In this perspective, we introduce a new notion of anisotropic H\"older for the underlying density and obtain posterior…
We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates…
There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health…
We extend the application of Hamiltonian Monte Carlo to allow for sampling from probability distributions defined over symmetric or Hermitian positive definite matrices. To do so, we exploit the Riemannian structure induced by Cartan's…
Discrepancies play an important role in the study of uniformity properties of point sets. Their probability distributions are a help in the analysis of the efficiency of the Quasi Monte Carlo method of numerical integration, which uses…
This paper proposes a novel method for testing observability in Gaussian models using discrete density approximations (deterministic samples) of (multivariate) Gaussians. Our notion of observability is defined by the existence of the…
In population studies, it is standard to sample data via designs in which the population is divided into strata, with the different strata assigned different probabilities of inclusion. Although there have been some proposals for including…
We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…
This paper develops a density deconvolution estimator that assumes the density of interest is a member of the generalized skew-symmetric (GSS) family of distributions. Estimation occurs in two parts: a skewing function, as well as location…
In many statistical and econometric applications, we gather individual samples from various interconnected populations that undeniably exhibit common latent structures. Utilizing a model that incorporates these latent structures for such…