Related papers: Probabilistic Constraint Satisfaction with Non-Gau…

We have developed a general Bayesian algorithm for determining the coordinates of points in a three-dimensional space. The algorithm takes as input a set of probabilistic constraints on the coordinates of the points, and an a priori…

We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…

Recent work on Bayesian optimization has shown its effectiveness in global optimization of difficult black-box objective functions. Many real-world optimization problems of interest also have constraints which are unknown a priori. In this…

Mixtures of Gaussian (or normal) distributions arise in a variety of application areas. Many heuristics have been proposed for the task of finding the component Gaussians given samples from the mixture, such as the EM algorithm, a…

Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…

We present an efficient algorithm to compute tight upper bounds of collision probability between two objects with positional uncertainties, whose error distributions are represented with non-Gaussian forms. Our approach can handle noisy…

Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations…

Bayesian optimization works effectively optimizing parameters in black-box problems. However, this method did not work for high-dimensional parameters in limited trials. Parameters can be efficiently explored by nonlinearly embedding them…

This paper deals with Bayesian inference of a mixture of Gaussian distributions. A novel formulation of the mixture model is introduced, which includes the prior constraint that each Gaussian component is always assigned a minimal number of…

Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the…

Optimization problems with uncertain black-box constraints, modeled by warped Gaussian processes, have recently been considered in the Bayesian optimization setting. This work introduces a new class of constraints in which the same…

Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…

We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise…

Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…

In this article, we introduce mixture representations for likelihood ratio ordered distributions. Essentially, the ratio of two probability densities, or mass functions, is monotone if and only if one can be expressed as a mixture of…

The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…

This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…

Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…

A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture…