Related papers: Local Minima Structures in Gaussian Mixture Models

This article introduces a nonlinear generalized matrix factor model (GMFM) that allows for mixed-type variables, extending the scope of linear matrix factor models (LMFM) that are so far limited to handling continuous variables. We…

Gaussian mixture alignment is a family of approaches that are frequently used for robustly solving the point-set registration problem. However, since they use local optimisation, they are susceptible to local minima and can only guarantee…

Mixture models with Gamma and or inverse-Gamma distributed mixture components are useful for medical image tissue segmentation or as post-hoc models for regression coefficients obtained from linear regression within a Generalised Linear…

We study the gradient Expectation-Maximization (EM) algorithm for Gaussian Mixture Models (GMM) in the over-parameterized setting, where a general GMM with $n>1$ components learns from data that are generated by a single ground truth…

In this article, we discuss two specific classes of models - Gaussian Mixture Copula models and Mixture of Factor Analyzers - and the advantages of doing inference with gradient descent using automatic differentiation. Gaussian mixture…

This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…

This work focuses on the mixed membership models for multivariate categorical data widely used for analyzing survey responses and population genetics data. These grade of membership (GoM) models offer rich modeling power but present…

Cluster-weighted modeling (CWM) is a mixture approach for modeling the joint probability of a response variable and a set of explanatory variables. The parameters are estimated by means of the expectation-maximization algorithm according to…

Deriving from the gradient vector of a generative model of local features, Fisher vector coding (FVC) has been identified as an effective coding method for image classification. Most, if not all, FVC implementations employ the Gaussian…

In this work we propose an approximate Minimum Mean-Square Error (MMSE) filter for linear dynamic systems with Gaussian Mixture noise. The proposed estimator tracks each component of the Gaussian Mixture (GM) posterior with an individual…

The paper considers the problem of network-based computation of global minima in smooth nonconvex optimization problems. It is known that distributed gradient-descent-type algorithms can achieve convergence to the set of global minima by…

We study the complexity of learning $k$-mixtures of Gaussians ($k$-GMMs) on $\mathbb{R}^d$. This task is known to have complexity $d^{\Omega(k)}$ in full generality. To circumvent this exponential lower bound on the number of components,…

Finite mixture models provide a flexible framework for approximating and estimating multivariate probability densities. We study mixtures formed from translated and rescaled copies of a fixed density kernel and obtain explicit results for…

In the mixture modeling frame, this paper presents the polynomial Gaussian cluster-weighted model (CWM). It extends the linear Gaussian CWM, for bivariate data, in a twofold way. Firstly, it allows for possible nonlinear dependencies in the…

Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of…

Community detection has attracted increasing attention during the past decade, and many algorithms have been proposed to find the underlying community structure in a given network. Many of these algorithms are based on modularity…

Finite mixture models are among the most popular statistical models used in different data science disciplines. Despite their broad applicability, inference under these models typically leads to computationally challenging non-convex…

We consider clustering based on significance tests for Gaussian Mixture Models (GMMs). Our starting point is the SigClust method developed by Liu et al. (2008), which introduces a test based on the k-means objective (with k = 2) to decide…

We perform a detailed investigation of the statistical properties of the projected distribution of galaxy clusters obtained in Cold Dark Matter (CDM) models with both Gaussian and skewed primordial density fluctuations. We use N-body…

In regional economics research, a problem of interest is to detect similarities between regions, and estimate their shared coefficients in economics models. In this article, we propose a mixture of finite mixtures (MFM) clustered regression…