Related papers: Estimating Probability Distributions using "Dirac"…
We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
In this article we propose a method of performing arithmetic operations on varia-bles with unknown distribution. The approach to the evaluation results of arithme-tic operations can select probability intervals of the algebraic equations…
This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, and propagate uncertainties for fairly general stochastic…
Stochastic expansion-based methods of uncertainty quantification, such as polynomial chaos and separated representations, require basis functions orthogonal with respect to the density of random inputs. Many modern engineering problems…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density…
Mixture distributions provide a versatile and widely used framework for modeling random phenomena, and are particularly well-suited to the analysis of geoscientific processes and their attendant risks to society. For continuous mixtures of…
We view sequential design as a model selection problem to determine which new observation is expected to be the most informative, given the existing set of observations. For estimating a probability distribution on a bounded interval, we…
Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…
The probability density function (PDF) associated with a given set of samples is approximated by a piecewise-linear polynomial constructed with respect to a binning of the sample space. The kernel functions are a compactly supported basis…
We describe a method for fitting distributions to data which only requires knowledge of the parametric form of either the signal or the background but not both. The unknown distribution is fit using a non-parametric kernel density…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification. Recently, several estimators of this ratio have been proposed. Most…
The paper studies binary classification and aims at estimating the underlying regression function which is the conditional expectation of the class labels given the inputs. The regression function is the key component of the Bayes optimal…
In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al.…
This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of…
Kernel Estimation provides an unbinned and non-parametric estimate of the probability density function from which a set of data is drawn. In the first section, after a brief discussion on parametric and non-parametric methods, the theory of…
Nonparametric density estimation for compositional data supported on the simplex is examined under a missing at random mechanism. Rather than imputing missing values and estimating the density from a completed data set, we adopt a strategy…
Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…