Related papers: Conjugate continuous-discrete projection filter vi…
In many scientific domains, clustering aims to reveal interpretable latent structure that reflects relevant subpopulations or processes. Widely used Bayesian mixture models for model-based clustering often produce overlapping or redundant…
Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…
In this paper, we propose a new efficient method for a sparse Gaussian graphical model with hidden clustering structures by extending a dual spectral projected gradient (DSPG) method proposed by Nakagaki et al.~(2020). We establish the…
The probability hypothesis density (PHD) filter alleviates the computational expense of the optimal Bayesian multi-target filtering by approximating the intensity function of the random finite set (RFS) of targets in time. However, as a…
In this work we tackle the problem of estimating the density $f_X$ of a random variable $X$ by successive smoothing, such that the smoothed random variable $Y$ fulfills $(\partial_t - \Delta_1)f_Y(\,\cdot\,, t) = 0$, $f_Y(\,\cdot\,, 0) =…
In this article, we complement recent results on the convergence of the state estimate obtained by applying the discrete-time Kalman filter on a time-sampled continuous-time system. As the temporal discretization is refined, the estimate…
Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…
For recursive circular filtering based on circular statistics, we introduce a general framework for estimation of a circular state based on different circular distributions, specifically the wrapped normal distribution and the von Mises…
Sparse-view Computed Tomography (CT) is an emerging protocol designed to reduce X-ray dose radiation in medical imaging. Traditional Filtered Back Projection algorithm reconstructions suffer from severe artifacts due to sparse data. In…
Recently, there has been a surge of interest in incorporating neural networks into particle filters, e.g. differentiable particle filters, to perform joint sequential state estimation and model learning for non-linear non-Gaussian…
Computing the unregularized Wasserstein barycenter for measure-valued data is a challenging optimization task. Recent algorithms have been tailored to either discrete measures as point clouds or continuous measures discretized on regular…
Solving semiparametric models can be computationally challenging because the dimension of parameter space may grow large with increasing sample size. Classical Newton's method becomes quite slow and unstable with intensive calculation of…
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…
Deterministic interpolation and quadrature methods are often unsuitable to address Bayesian inverse problems depending on computationally expensive forward mathematical models. While interpolation may give precise posterior approximations,…
We present a robust and efficient numerical framework based on a median filter scheme for solving a broad class of interface-related optimization problems, from image segmentation to topology optimization. A key innovation of our work is…
In this paper, we propose and analyze a fully discrete finite element projection method for the magnetohydrodynamic (MHD) equations. A modified Crank--Nicolson method and the Galerkin finite element method are used to discretize the model…
Can stochastic gradient methods track a moving target? We study the problem of tracking multidimensional time-varying parameters under noisy observations and possible model misspecification. Gradient-based filters update the time-varying…
This paper proposes a probabilistic approach to the problem of intrinsic filtering of a system on a matrix Lie group with invariance properties. The problem of an invariant continuous-time model with discrete-time measurements is cast into…
The projection predictive variable selection is a decision-theoretically justified Bayesian variable selection approach achieving an outstanding trade-off between predictive performance and sparsity. Its projection problem is not easy to…
Compressed Sensing (CS) is a novel technique for simultaneous signal sampling and compression based on the existence of a sparse representation of signal and a projected dictionary $PD$, where $P\in\mathbb{R}^{m\times d}$ is the projection…