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A two-class mixture model, where the density of one of the components is known, is considered. We address the issue of the nonparametric adaptive estimation of the unknown probability density of the second component. We propose a randomly…
This paper provides a framework for estimating the mean and variance of a high-dimensional normal density. The main setting considered is a fixed number of vector following a high-dimensional normal distribution with unknown mean and…
One key issue in several astrophysical problems is the evaluation of the density probability function underlying an observational discrete data set. We here review two non-parametric density estimators which recently appeared in the…
Our article addresses the problem of flexibly estimating a multivariate density while also attempting to estimate its marginals correctly. We do so by proposing two new estimators that try to capture the best features of mixture of normals…
In this paper, we study the Bernstein polynomial model for estimating the multivariate distribution functions and densities with bounded support. As a mixture model of multivariate beta distributions, the maximum (approximate) likelihood…
We introduce a lightweight, flexible and end-to-end trainable probability density model parameterized by a constrained Fourier basis. We assess its performance at approximating a range of multi-modal 1D densities, which are generally…
Kernel density estimators with circular data have been studied extensively for decades, as they allow flexible estimations even when the shape of the underlying density is complex. Many recent studies have examined bias correction methods;…
Accurate density estimation methodologies play an integral role in a variety of scientific disciplines, with applications including simulation models, decision support tools, and exploratory data analysis. In the past, histograms and kernel…
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,…
Kernel estimation of a probability density function supported on the unit interval has proved difficult, because of the well known boundary bias issues a conventional kernel density estimator would necessarily face in this situation.…
A common feature of methods for analyzing samples of probability density functions is that they respect the geometry inherent to the space of densities. Once a metric is specified for this space, the Fr\'echet mean is typically used to…
The bivariate normal density with unit variance and correlation $\rho$ is well-known. We show that by integrating out $\rho$, the result is a function of the maximum norm. The Bayesian interpretation of this result is that if we put a…
Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…
Deep hashing converts high-dimensional feature vectors into compact binary codes, enabling efficient large-scale retrieval. A fundamental challenge in deep hashing stems from the discrete nature of quantization in generating the codes.…
The nonparametric formulation of density-based clustering, known as modal clustering, draws a correspondence between groups and the attraction domains of the modes of the density function underlying the data. Its probabilistic foundation…
Kernel estimation techniques, such as mean shift, suffer from one major drawback: the kernel bandwidth selection. The bandwidth can be fixed for all the data set or can vary at each points. Automatic bandwidth selection becomes a real…
Sampling-based methods, e.g., Deep Ensembles and Bayesian Neural Nets have become promising approaches to improve the quality of uncertainty estimation and robust generalization. However, they suffer from a large model size and high latency…
We present sparse tree-based and list-based density estimation methods for binary/categorical data. Our density estimation models are higher dimensional analogies to variable bin width histograms. In each leaf of the tree (or list), the…
We investigate the problem of estimating a smooth invertible transformation f when observing independent samples X_1, ..., X_n ~ P \circ f, where P is a known measure. We focus on the two dimensional case where P and f are defined on R^2.…
We consider a continuous-time stochastic volatility model. The model contains a stationary volatility process, the multivariate density of the finite dimensional distributions of which we aim to estimate. We assume that we observe the…