Related papers: Adaptive density estimation for clustering with Ga…

Finite mixture models are widely used in econometric analyses to capture unobserved heterogeneity. This paper shows that maximum likelihood estimation of finite mixtures of parametric densities can suffer from substantial finite-sample bias…

This paper studies statistical aggregation procedures in regression setting. A motivating factor is the existence of many different methods of estimation, leading to possibly competing estimators. We consider here three different types of…

Mixtures of multivariate normal inverse Gaussian (MNIG) distributions can be used to cluster data that exhibit features such as skewness and heavy tails. However, for cluster analysis, using a traditional finite mixture model framework,…

Target tracking represents a state estimation problem recurrent in many practical scenarios like air traffic control, autonomous vehicles, marine radar surveillance and so on. In a Bayesian perspective, when phenomena like clutter are…

We give an efficient algorithm for robustly clustering of a mixture of two arbitrary Gaussians, a central open problem in the theory of computationally efficient robust estimation, assuming only that the the means of the component Gaussians…

Matrix valued data has become increasingly prevalent in many applications. Most of the existing clustering methods for this type of data are tailored to the mean model and do not account for the dependence structure of the features, which…

Bayesian mixture models are widely used for clustering of high-dimensional data with appropriate uncertainty quantification. However, as the dimension of the observations increases, posterior inference often tends to favor too many or too…

Mixture models are commonly used in applications with heterogeneity and overdispersion in the population, as they allow the identification of subpopulations. In the Bayesian framework, this entails the specification of suitable prior…

We study the nonparametric estimation of the jump density of a compound Poisson process from the discrete observation of one trajectory over $[0,T]$. We consider the microscopic regime when the sampling rate $\Delta=\Delta_T\rightarrow0$ as…

Gaussian mixture models (GMMs) are ubiquitous in statistical learning, particularly for unsupervised problems. While full GMMs suffer from the overparameterization of their covariance matrices in high-dimensional spaces, spherical GMMs…

This paper proposes a novel method for testing observability in Gaussian models using discrete density approximations (deterministic samples) of (multivariate) Gaussians. Our notion of observability is defined by the existence of the…

We study the problem of learning mixtures of Gaussians with censored data. Statistical learning with censored data is a classical problem, with numerous practical applications, however, finite-sample guarantees for even simple latent…

We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general…

Although discrete mixture modeling has formed the backbone of the literature on Bayesian density estimation, there are some well known disadvantages. We propose an alternative class of priors based on random nonlinear functions of a uniform…

We study the pointwise maximum likelihood estimation rates for a class of Gaussian mixtures that are invariant under the action of some isometry group. This model is also known as multi-reference alignment, where random isometries of a…

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…

We investigate the convergence properties of the EM algorithm when applied to overspecified Gaussian mixture models -- that is, when the number of components in the fitted model exceeds that of the true underlying distribution. Focusing on…

Gaussian Mixture models (GMMs) are a powerful tool for clustering, classification and density estimation when clustering structures are embedded in the data. The presence of missing values can largely impact the GMMs estimation process,…

Mixtures of Gaussian factors are powerful tools for modeling an unobserved heterogeneous population, offering - at the same time - dimension reduction and model-based clustering. Unfortunately, the high prevalence of spurious solutions and…

Density estimation is an interdisciplinary topic at the intersection of statistics, theoretical computer science and machine learning. We review some old and new techniques for bounding the sample complexity of estimating densities of…