Related papers: Local Minima Structures in Gaussian Mixture Models

When searching for global optima of nonconvex unconstrained optimization problems, it is desirable that every local minimum be a global minimum. This property of having no spurious local minima is true in various problems of interest…

Testing a covariance matrix following a Gaussian graphical model (GGM) is considered in this paper based on observations made at a set of distributed sensors grouped into clusters. Ordered transmissions are proposed to achieve the same…

Mixture models are widely used in modeling heterogeneous data populations. A standard approach of mixture modeling assumes that the mixture component takes a parametric kernel form. In many applications, making parametric assumptions on the…

Maxima of the linear density field form a point process that can be used to understand the spatial distribution of virialized halos that collapsed from initially overdense regions. However, owing to the peak constraint, clustering…

Necessary optimality conditions in Lagrangian form and the sequential minimization framework are extended to mixed-integer nonlinear optimization, without any convexity assumptions. Building upon a recently developed notion of local…

Gaussian graphical models (GGMs) are probabilistic tools of choice for analyzing conditional dependencies between variables in complex systems. Finding changepoints in the structural evolution of a GGM is therefore essential to detecting…

We evaluate the misclustering probability of a spectral clustering algorithm under a Gaussian mixture model with a general covariance structure. The algorithm partitions the data into two groups based on the sign of the first principal…

Ising formulations are widely utilized to solve combinatorial optimization problems, and a variety of quantum or semiconductor-based hardware has recently been made available. In combinatorial optimization problems, the existence of local…

We consider the question of estimating multi-dimensional Gaussian mixtures (GM) with compactly supported or subgaussian mixing distributions. Minimax estimation rate for this class (under Hellinger, TV and KL divergences) is a long-standing…

Neural networks in general, from MLPs and CNNs to attention-based Transformers, are constructed from layers of linear combinations followed by nonlinear operations such as ReLU, Sigmoid, or Softmax. Despite their strength, these…

Local search algorithms for combinatorial search problems frequently encounter a sequence of states in which it is impossible to improve the value of the objective function; moves through these regions, called plateau moves, dominate the…

Expectation Maximization (EM) is among the most popular algorithms for maximum likelihood estimation, but it is generally only guaranteed to find its stationary points of the log-likelihood objective. The goal of this article is to present…

Skew-symmetric functions are a class of functions defined on a product space $M \times M$ that are antisymmetric with respect to the order of their inputs. In [13], the authors proved that non-deterministic skew-symmetric Gaussian fields…

This paper addresses the statistical estimation of Gaussian Mixture Models (GMMs) with unknown diagonal covariances from independent and identically distributed samples. We employ the Beurling-LASSO (BLASSO), a convex optimization framework…

Multidimensional data is often associated with uncertainties that are not well-described by normal distributions. In this work, we describe how such distributions can be projected to a low-dimensional space using uncertainty-aware principal…

Many experiments in medicine and ecology can be conveniently modeled by finite Gaussian mixtures but face the problem of dealing with small data sets. We propose a robust version of the estimator based on self-regression and sparsity…

Although extensive research exists in spatial modeling, few studies have addressed finite mixture model-based clustering methods for spatial data. Finite mixture models, especially Gaussian mixture models, particularly suffer from high…

We consider the problem of spherical Gaussian Mixture models with $k \geq 3$ components when the components are well separated. A fundamental previous result established that separation of $\Omega(\sqrt{\log k})$ is necessary and sufficient…

We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…

It is shown that $3$ disjoint sets with fixed Gaussian volumes that partition $\mathbb{R}^{n}$ with nearly minimum total Gaussian surface area must be close to adjacent $120$ degree sectors, when $n\geq2$. These same results hold for any…