Related papers: Consistent Density Estimation Under Discrete Mixtu…

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…

Modeling large dependent datasets in modern time series analysis is a crucial research area. One effective approach to handle such datasets is to transform the observations into density functions and apply statistical methods for further…

The authors consider the problem of estimating the density $g$ of independent and identically distributed variables $X\_i$, from a sample $Z\_1, ..., Z\_n$ where $Z\_i=X\_i+\sigma\epsilon\_i$, $i=1, ..., n$, $\epsilon$ is a noise…

We show how one can test the cosmological Poisson equation by requiring only the validity of three main assumptions: the energy-momentum conservation equations of matter, the equivalence principle, and the cosmological principle. We first…

Although continuous density estimation has received abundant attention in the Bayesian nonparametrics literature, there is limited theory on multivariate mixed scale density estimation. In this note, we consider a general framework to…

Probabilistic machine learning techniques can learn both complex relations between input features and output quantities of interest as well as take into account stochasticity or uncertainty within a data set. In this initial work, we…

While the problem of estimating a probability density function (pdf) from its observations is classical, the estimation under additional shape constraints is both important and challenging. We introduce an efficient, geometric approach for…

Despite the huge success of deep neural networks (NNs), finding good mechanisms for quantifying their prediction uncertainty is still an open problem. Bayesian neural networks are one of the most popular approaches to uncertainty…

Density estimation, which estimates the distribution of data, is an important category of probabilistic machine learning. A family of density estimators is mixture models, such as Gaussian Mixture Model (GMM) by expectation maximization.…

Assessing the predictive uncertainty of deep neural networks is crucial for safety-related applications of deep learning. Although Bayesian deep learning offers a principled framework for estimating model uncertainty, the common approaches…

We study the likelihood ratio test in general mixture models where the base density is parametric, the null is a known fixed mixing distribution, and the alternative is a general mixing distribution supported on a bounded parameter space.…

Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a…

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 f-divergence estimation is important in the fields of machine learning, information theory, and statistics. While several nonparametric divergence estimators exist, relatively few have known convergence properties. In…

Probabilistic conditioning is concerned with the identification of a distribution of a random variable $X$ given a random variable $Y$. It is a cornerstone of scientific and engineering applications where modeling uncertainty is key. This…

We consider maximum likelihood estimation of finite mixture of uniform distributions. We prove that maximum likelihood estimator is strongly consistent, if the scale parameters of the component uniform distributions are restricted from…

In this paper, we construct a moment inequality for mixing dependent random variables, it is of independent interest. As applications, the consistency of the kernel density estimation is investigated. Several limit theorems are established:…

Density estimation is a crucial component of many machine learning methods, and manifold learning in particular, where geometry is to be constructed from data alone. A significant practical limitation of the current density estimation…

Finite mixture models are widely used in econometric analyses to capture unobserved heterogeneity. This paper shows that maximum likelihood estimation of finite mixtures of parametric densities can suffer from substantial finite-sample bias…

Let $X$ be a discrete random variable with support $S$ and $f : S \to S^\prime$ be a bijection. Then it is well-known that the entropy of $X$ is the same as the entropy of $f(X)$. This entropy preservation property has been well-utilized to…