Related papers: A Bayesian Approach Toward Robust Multidimensional…
A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…
Real-world network applications must cope with failing nodes, malicious attacks, or nodes facing corrupted data - data classified as outliers. Our work addresses these concerns in the scope of the sensor network localization problem where,…
An efficient method for finding a better maximizer of computationally extensive probability distributions is proposed on the basis of a Bayesian optimization technique. A key idea of the proposed method is to use extreme values of…
Problems that require the parameterization of closed contours arise frequently in computer vision applications. This article introduces a new curve parameterization algorithm that is able to fit a closed curve to a set of points while being…
In this paper, we develop a Bayesian multiscale approach based on a multiscale finite element method. Because of scale disparity in many multiscale applications, computational models can not resolve all scales. Various subgrid models are…
Simultaneous localization and tracking (SLAT) in sensor networks aims to determine the positions of sensor nodes and a moving target in a network, given incomplete and inaccurate range measurements between the target and each of the…
In this paper, the multiple-source ellipsoidal localization problem based on acoustic energy measurements is investigated via set-membership estimation theory. When the probability density function of measurement noise is…
Collision avoidance in the presence of dynamic obstacles in unknown environments is one of the most critical challenges for unmanned systems. In this paper, we present a method that identifies obstacles in terms of ellipsoids to estimate…
We introduce a new numerical method based on machine learning to approximate the solution of elliptic partial differential equations with collocation using a set of sigmoidal functions. We show that a feedforward neural network with a…
We introduce a novel and scalable Bayesian framework for multivariate-density-density regression (DDR), designed to model relationships between multivariate distributions. Our approach addresses the critical issue of distributions residing…
A weighted likelihood technique for robust estimation of a multivariate Wrapped Normal distribution for data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise…
We introduce a methodology for robust Bayesian estimation with robust divergence (e.g., density power divergence or {\gamma}-divergence), indexed by a single tuning parameter. It is well known that the posterior density induced by robust…
The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…
High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…
Most existing robust fitting methods are designed for classical models, such as lines, circles, and planes. In contrast, fewer methods have been developed to robustly handle non-classical models, such as spiral curves, procedural character…
Bayesian estimation is a vital tool in robotics as it allows systems to update the robot state belief using incomplete information from noisy sensors. To render the state estimation problem tractable, many systems assume that the motion and…
This paper presents a new approach to a robust Gaussian process (GP) regression. Most existing approaches replace an outlier-prone Gaussian likelihood with a non-Gaussian likelihood induced from a heavy tail distribution, such as the…
We introduce Cayley transform ellipsoid fitting (CTEF), an algorithm that uses the Cayley transform to fit ellipsoids to noisy data in any dimension. Unlike many ellipsoid fitting methods, CTEF is ellipsoid specific, meaning it always…
This paper is concerned with the online estimation of a nonlinear dynamic system from a series of noisy measurements. The focus is on cases wherein outliers are present in-between normal noises. We assume that the outliers follow an unknown…
We apply a linear Bayesian model to seismic tomography, a high-dimensional inverse problem in geophysics. The objective is to estimate the three-dimensional structure of the earth's interior from data measured at its surface. Since this…