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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…

We study the task of agnostic learning of multiclass linear classifiers under the Gaussian distribution. Given labeled examples $(x, y)$ from a distribution over $\mathbb{R}^d \times [k]$, with Gaussian $x$-marginal, the goal is to output a…

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…

We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…

Bosonic Gaussian unitaries are fundamental building blocks of central continuous-variable quantum technologies such as quantum-optic interferometry and bosonic error-correction schemes. In this work, we present the first time-efficient…

We develop optimal algorithms for learning undirected Gaussian trees and directed Gaussian polytrees from data. We consider both problems of distribution learning (i.e. in KL distance) and structure learning (i.e. exact recovery). The first…

We study the problem of learning mixtures of linear classifiers under Gaussian covariates. Given sample access to a mixture of $r$ distributions on $\mathbb{R}^n$ of the form $(\mathbf{x},y_{\ell})$, $\ell\in [r]$, where…

Polynomial regression is a basic primitive in learning and statistics. In its most basic form the goal is to fit a degree $d$ polynomial to a response variable $y$ in terms of an $n$-dimensional input vector $x$. This is extremely…

In this paper, we consider mixtures of multinomial logistic models (MNL), which are known to $\epsilon$-approximate any random utility model. Despite its long history and broad use, rigorous results are only available for learning a uniform…

The assumption of Gaussian or Gaussian mixture data has been extensively exploited in a long series of precise performance analyses of machine learning (ML) methods, on large datasets having comparably numerous samples and features. To…

We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…

This paper studies how to recover parameters in diagonal Gaussian mixture models using tensors. High-order moments of the Gaussian mixture model are estimated from samples. They form incomplete symmetric tensors generated by hidden…

Deep embedded clustering has become a dominating approach to unsupervised categorization of objects with deep neural networks. The optimization of the most popular methods alternates between the training of a deep autoencoder and a k-means…

This paper is about variable selection, clustering and estimation in an unsupervised high-dimensional setting. Our approach is based on fitting constrained Gaussian mixture models, where we learn the number of clusters $K$ and the set of…

We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…

Machine learning algorithms frequently require careful tuning of model hyperparameters, regularization terms, and optimization parameters. Unfortunately, this tuning is often a "black art" that requires expert experience, unwritten rules of…

The learning of Gaussian Mixture Models (also referred to simply as GMMs) plays an important role in machine learning. Known for their expressiveness and interpretability, Gaussian mixture models have a wide range of applications, from…

We consider a simulation optimization problem for a context-dependent decision-making. A Gaussian mixture model is proposed to capture the performance clustering phenomena of context-dependent designs. Under a Bayesian framework, we develop…

Gaussian Mixture Models are a powerful tool in Data Science and Statistics that are mainly used for clustering and density approximation. The task of estimating the model parameters is in practice often solved by the Expectation…

It is well-known that polynomial reproduction is not possible when approximating with Gaussian kernels. Quasi-interpolation schemes have been developed which use a finite number of Gaussians at different scales, which then reproduce…