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Density estimates based on point processes are often restrained to regions with irregular boundaries or holes. We propose a density estimator, the lattice-based density estimator, which produces reasonable density estimates under these…
Parameterless stopping criteria for recursive polynomial expansions to construct the density matrix in electronic structure calculations are proposed. Based on convergence order estimation the new stopping criteria automatically and…
Given a random sample of points from some unknown distribution, we propose a new data-driven method for estimating its probability support S. Under the mild assumption that S is r-convex, the smallest r-convex set which contains the sample…
We propose a fast algorithm for the probabilistic solution of boundary value problems (BVPs), which are ordinary differential equations subject to boundary conditions. In contrast to previous work, we introduce a Gauss--Markov prior and…
The need for parameter estimation with massive datasets has reinvigorated interest in stochastic optimization and iterative estimation procedures. Stochastic approximations are at the forefront of this recent development as they yield…
For quantitative seismic imaging, iterative least-squares reverse time migration is the recommended approach. The existence of an inverse of the forward modelling operator would considerably reduce the number of required iterations. In the…
In this paper, we develop a general theory of truncated inverse binomial sampling. In this theory, the fixed-size sampling and inverse binomial sampling are accommodated as special cases. In particular, the classical Chernoff-Hoeffding…
This paper describes recursive algorithms for state estimation of linear dynamical systems when measurements are noisy with unknown bias and/or outliers. For situations with noisy and biased measurements, algorithms are proposed that…
The spectacular success of deep generative models calls for quantitative tools to measure their statistical performance. Divergence frontiers have recently been proposed as an evaluation framework for generative models, due to their ability…
We present some new results on the dynamic regressor extension and mixing parameter estimators for linear regression models recently proposed in the literature. This technique has proven instrumental in the solution of several open problems…
We develop the Bayesian Wasserstein repulsive Gaussian mixture model that promotes well-separated clusters. Unlike existing repulsive mixture approaches that focus on separating the component means, our method encourages separation between…
We estimate the density and its derivatives using a local polynomial approximation to the logarithm of an unknown density $f$. The estimator is guaranteed to be nonnegative and achieves the same optimal rate of convergence in the interior…
Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely…
In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…
Beta-binomial/Poisson models have been used by many authors to model multivariate count data. Lora and Singer (Statistics in Medicine, 2008) extended such models to accommodate repeated multivariate count data with overdipersion in the…
Using a capacity approach, and the theory of measure's perturbation of Dirichlet forms, we give the probabilistic representation of the General Robin boundary value problems on an arbitrary domain $\Omega$, involving smooth measures, which…
We extend balloon and sample-smoothing estimators, two types of variable-bandwidth kernel density estimators, by a shift parameter and derive their asymptotic properties. Our approach facilitates the unified study of a wide range of density…
In this paper, a method for recursively computing approximate modal paths is developed. A recursive formulation of the modal path can be obtained either by backward or forward dynamic programming. By combining both methods, a ``two-filter''…
We consider the challenge of finding a deterministic policy for a Markov decision process that uniformly (in all states) maximizes one reward subject to a probabilistic constraint over a different reward. Existing solutions do not fully…
This paper introduces a new simulation-based inference procedure to model and sample from multi-dimensional probability distributions given access to i.i.d.\ samples, circumventing the usual approaches of explicitly modeling the density…