Related papers: Sobolev Space Regularised Pre Density Models
Given a set of empirical observations, conditional density estimation aims to capture the statistical relationship between a conditional variable $\mathbf{x}$ and a dependent variable $\mathbf{y}$ by modeling their conditional probability…
The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise, which possesses both Burgers-type and cubic nonlinearities. To discretize the…
We consider the problem of density estimation on Riemannian manifolds. Density estimation on manifolds has many applications in fluid-mechanics, optics and plasma physics and it appears often when dealing with angular variables (such as…
Predictive recursion (PR) is a fast algorithm for nonparametric estimation of a mixing density, with connections to sequential Bayesian updating under a Dirichlet process prior and rigorous frequentist consistency guarantees. Extending PR…
Finite mixture models provide a flexible framework for approximating and estimating multivariate probability densities. We study mixtures formed from translated and rescaled copies of a fixed density kernel and obtain explicit results for…
Density estimation represents one of the most successful applications of Bayesian nonparametrics. In particular, Dirichlet process mixtures of normals are the gold standard for density estimation and their asymptotic properties have been…
A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…
Model-independent searches in particle physics aim at completing our knowledge of the universe by looking for new possible particles not predicted by the current theories. Such particles, referred to as signal, are expected to behave as a…
Stochastic Neighbor Embedding (SNE) methods minimize the divergence between the similarity matrix of a high-dimensional data set and its counterpart from a low-dimensional embedding, leading to widely applied tools for data visualization.…
We propose a novel non-parametric adaptive anomaly detection algorithm for high dimensional data based on rank-SVM. Data points are first ranked based on scores derived from nearest neighbor graphs on n-point nominal data. We then train a…
This paper is concerned with the regularity of solutions to linear and nonlinear evolution equations extending our findings in [22] to domains of polyhedral type. In particular, we study the smoothness in the specific scale…
We develop an optimal regularity theory for parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces. The results extend the classical Schauder estimates to coefficients that are merely measurable in time and…
We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on $\mathbb{R}^p$ and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and…
Most classification algorithms used in high energy physics fall under the category of supervised machine learning. Such methods require a training set containing both signal and background events and are prone to classification errors…
We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…
The density estimation is one of the core problems in statistics. Despite this, existing techniques like maximum likelihood estimation are computationally inefficient due to the intractability of the normalizing constant. For this reason an…
Conditional density estimation generalizes regression by modeling a full density f(yjx) rather than only the expected value E(yjx). This is important for many tasks, including handling multi-modality and generating prediction intervals.…
This paper investigates the statistical estimation of a discrete mixing measure $\mu$0 involved in a kernel mixture model. Using some recent advances in l1-regularization over the space of measures, we introduce a "data fitting and…
In this paper, we consider non-diffusive variational problems with mixed boundary conditions and (distributional and weak) gradient constraints. The upper bound in the constraint is either a function or a Borel measure, leading to the state…
Supervised anomaly detection methods perform well in identifying known anomalies that are well represented in the training set. However, they often struggle to generalise beyond the training distribution due to decision boundaries that lack…