相关论文: On the best approximation by finite Gaussian mixtu…

Computing the posterior distribution of a probabilistic program is a hard task for which no one-fit-for-all solution exists. We propose Gaussian Semantics, which approximates the exact probabilistic semantics of a bounded program by means…

This work considers the computation of risk measures for quantities of interest governed by PDEs with Gaussian random field parameters using Taylor approximations. While efficient, Taylor approximations are local to the point of expansion,…

Gaussian variational approximations are widely used for summarizing posterior distributions in Bayesian models, especially in high-dimensional settings. However, a drawback of such approximations is the inability to capture skewness or more…

Expanding a lower-dimensional problem to a higher-dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, namely how to improve inference…

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…

We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…

In this paper, we study stochastic ordering results between two finite mixtures with single and multiple outliers, assuming subpopulations follow general exponentiated location-scale distributions. For single-outlier mixtures, several…

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…

Non-Gaussian and multimodal distributions are an important part of many recent robust sensor fusion algorithms. In difference to robust cost functions, they are probabilistically founded and have good convergence properties. Since their…

We consider the problem of recovering an unknown matching between a set of $n$ randomly placed points in $\mathbb{R}^d$ and random perturbations of these points. This can be seen as a model for particle tracking and more generally, entity…

We propose the finite mixture of skewed sub-Gaussian stable distributions. The maximum likelihood estimator for the parameters of proposed finite mixture model is computed through the expectation-maximization algorithm. The proposed model…

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…

We consider the problem of identifying the parameters of an unknown mixture of two arbitrary $d$-dimensional gaussians from a sequence of independent random samples. Our main results are upper and lower bounds giving a computationally…

The posterior distribution of the number of components k in a finite mixture satisfies a set of inequality constraints. The result holds irrespective of the parametric form of the mixture components and under assumptions on the prior…

This paper studies identifiability and convergence behaviors for parameters of multiple types in finite mixtures, and the effects of model fitting with extra mixing components. First, we present a general theory for strong identifiability,…

We compute quantitative bounds for measuring the discrepancy between the distribution of two min-max statistics involving either pairs of Gaussian random matrices, or one Gaussian and one Gaussian-subordinated random matrix. In the fully…

The question of polynomial learnability of probability distributions, particularly Gaussian mixture distributions, has recently received significant attention in theoretical computer science and machine learning. However, despite major…

While mixtures of Gaussian distributions have been studied for more than a century (Pearson, 1894), the construction of a reference Bayesian analysis of those models still remains unsolved, with a general prohibition of the usage of…

Detection of sparse signals arises in a wide range of modern scientific studies. The focus so far has been mainly on Gaussian mixture models. In this paper, we consider the detection problem under a general sparse mixture model and obtain…

We prove that $\tilde{\Theta}(k d^2 / \varepsilon^2)$ samples are necessary and sufficient for learning a mixture of $k$ Gaussians in $\mathbb{R}^d$, up to error $\varepsilon$ in total variation distance. This improves both the known upper…