Related papers: Strong Gaussian approximation of the mixture Rasch…
This paper investigates the stochastic program with the chance constraint on a quadratic form of random variables following multivariate Gaussian mixture distribution (GMD). Under some mild conditions, it is proved that the asymptotic…
Identification-robust hypothesis tests are commonly based on the continuous updating GMM objective function. When the number of moment conditions grows proportionally with the sample size, the large-dimensional weighting matrix prohibits…
The large-system performance of MAP estimation is studied considering a general distortion function when the observation vector is received through a linear system with additive white Gaussian noise. The analysis considers the system matrix…
We consider the Bayesian estimation of the parameters of a finite mixture model from independent order statistics arising from imperfect ranked set sampling designs. As a cost-effective method, ranked set sampling enables us to incorporate…
Standard Gaussian graphical models (GGMs) implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected form heterogeneous…
Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles,…
A comprehensive class of models is proposed that can be used for continuous, binary, ordered categorical and count type responses. The difficulty of items is described by difficulty functions, which replace the item difficulty parameters…
Gaussian Quadrature is a well known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums have found some new interest. In this paper we apply these ideas to…
As with the advancement of geographical information systems, non-Gaussian spatial data sets are getting larger and more diverse. This study develops a general framework for fast and flexible non-Gaussian regression, especially for…
Learning a Gaussian mixture model (GMM) is a fundamental problem in machine learning, learning theory, and statistics. One notion of learning a GMM is proper learning: here, the goal is to find a mixture of $k$ Gaussians $\mathcal{M}$ that…
We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
Random graph mixture models are now very popular for modeling real data networks. In these setups, parameter estimation procedures usually rely on variational approximations, either combined with the expectation-maximisation (\textsc{em})…
We give a necessary and sufficient condition for symmetric infinitely divisible distribution to have Gaussian component. The result can be applied to approximation the distribution of finite sums of random variables. Particularly, it shows…
The random coefficients model is an extension of the linear regression model that allows for unobserved heterogeneity in the population by modeling the regression coefficients as random variables. Given data from this model, the statistical…
We derive a Gaussian approximation result for the maximum of a sum of random vectors under $(2+\iota)$-th moments. Our main theorem is abstract and nonasymptotic, and can be applied to a variety of statistical learning problems. The proof…
Finding a suitable measurement matrix is an important topic in compressed sensing. Though the known random matrix, whose entries are drawn independently from a certain probability distribution, can be used as a measurement matrix and…
Many methods for machine learning rely on approximate inference from intractable probability distributions. Variational inference approximates such distributions by tractable models that can be subsequently used for approximate inference.…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object. Instead, suitable distributional approximations can be used, where…