Related papers: Learning mixtures of separated nonspherical Gaussi…
We consider the problem of efficiently learning mixtures of a large number of spherical Gaussians, when the components of the mixture are well separated. In the most basic form of this problem, we are given samples from a uniform mixture of…
Gaussian mixture distributions are commonly employed to represent general probability distributions. Despite the importance of using Gaussian mixtures for uncertainty estimation, the entropy of a Gaussian mixture cannot be calculated…
Semi- and non-parametric mixture of regressions are a very useful flexible class of mixture of regressions in which some or all of the parameters are non-parametric functions of the covariates. These models are, however, based on the…
Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise the learning of a mixture of $K$ Gaussians with generic means…
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 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,…
We consider the problem of estimating means of two Gaussians in a 2-Gaussian mixture, which is not balanced and is corrupted by noise of an arbitrary distribution. We present a robust algorithm to estimate the parameters, together with…
Semi- and non-parametric mixture of regressions are a very useful flexible class of mixture of regressions in which some or all of the parameters are non-parametric functions of the covariates. These models are, however, based on the…
We give a new algorithm for learning mixtures of $k$ Gaussians (with identity covariance in $\mathbb{R}^n$) to TV error $\varepsilon$, with quasi-polynomial ($O(n^{\text{poly\,log}\left(\frac{n+k}{\varepsilon}\right)})$) time and sample…
This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition…
The Gaussian mixture model is a classic technique for clustering and data modeling that is used in numerous applications. With the rise of big data, there is a need for parameter estimation techniques that can handle streaming data and…
We systematically study various network Expectation-Maximization (EM) algorithms for the Gaussian mixture model within the framework of decentralized federated learning. Our theoretical investigation reveals that directly extending the…
This paper studies how to learn parameters in diagonal Gaussian mixture models. The problem can be formulated as computing incomplete symmetric tensor decompositions. We use generating polynomials to compute incomplete symmetric tensor…
Even in low dimensions, sampling from multi-modal distributions is challenging. We provide the first sampling algorithm for a broad class of distributions -- including all Gaussian mixtures -- with a query complexity that is polynomial in…
A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the general inverse…
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find…
We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise…
Gaussian mixture models (GMM) are the most widely used statistical model for the $k$-means clustering problem and form a popular framework for clustering in machine learning and data analysis. In this paper, we propose a natural semi-random…
The Expectation-Maximization (EM) algorithm is one of the most popular methods used to solve the problem of parametric distribution-based clustering in unsupervised learning. In this paper, we propose to analyze a generalized EM (GEM)…
Mixtures of high dimensional Gaussian distributions have been studied extensively in statistics and learning theory. While the total variation distance appears naturally in the sample complexity of distribution learning, it is analytically…