Related papers: On Parameter Estimation in Deviated Gaussian Mixtu…

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…

The Gaussian mixture model is widely used in unsupervised learning, owing to its simplicity and interpretability. However, a fundamental limitation of the classical Gaussian mixture model is that it forces each observation to belong to…

We propose a procedure to handle the problem of Gaussian regression when the variance is unknown. We mix least-squares estimators from various models according to a procedure inspired by that of Leung and Barron (2007). We show that in some…

Since Pearson [Philosophical Transactions of the Royal Society of London. A, 185 (1894), pp. 71-110] first applied the method of moments (MM) for modeling data as a mixture of one-dimensional Gaussians, moment-based estimation methods have…

Gaussian processes (GPs) provide a powerful non-parametric framework for reasoning over functions. Despite appealing theory, its superlinear computational and memory complexities have presented a long-standing challenge. State-of-the-art…

We consider the problem of identifying the parameters of an unknown mixture of two arbitrary $d$-dimensional gaussians from a sequence of independent random samples. Our main results are upper and lower bounds giving a computationally…

This paper considers the problem of networks reconstruction from heterogeneous data using a Gaussian Graphical Mixture Model (GGMM). It is well known that parameter estimation in this context is challenging due to large numbers of variables…

The multivariate generalized Gaussian distribution (MGGD), also known as the multivariate exponential power (MEP) distribution, is widely used in signal and image processing. However, estimating MGGD parameters, which is required in…

A principled framework to generalize variational perturbation approximations (VPA's) formulated within the ambit of the nonadditive statistics of Tsallis statistics, is introduced. This is accomplished by operating on the terms constituting…

Mixtures of Gaussian process experts is a class of models that can simultaneously address two of the key limitations inherent in standard Gaussian processes: scalability and predictive performance. In particular, models that use Dirichlet…

Optimum parameter estimation methods require knowledge of a parametric probability density that statistically describes the available observations. In this work we examine Bayesian and non-Bayesian parameter estimation problems under a…

Statistical models are central to machine learning with broad applicability across a range of downstream tasks. The models are controlled by free parameters that are typically estimated from data by maximum-likelihood estimation or…

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…

Mechanistic simulation models are inverted against observations in order to gain inference on modeled processes. However, with the increasing ability to collect high resolution observations, these observations represent more patterns of…

The article addresses a long-standing open problem on the justification of using variational Bayes methods for parameter estimation. We provide general conditions for obtaining optimal risk bounds for point estimates acquired from…

We investigate the problem of center estimation in the high dimensional binary sub-Gaussian Mixture Model with Hidden Markov structure on the labels. We first study the limitations of existing results in the high dimensional setting and…

Mixtures-of-Experts models and their maximum likelihood estimation (MLE) via the EM algorithm have been thoroughly studied in the statistics and machine learning literature. They are subject of a growing investigation in the context of…

We take a new look at parameter estimation for Gaussian Mixture Models (GMMs). In particular, we propose using \emph{Riemannian manifold optimization} as a powerful counterpart to Expectation Maximization (EM). An out-of-the-box invocation…

Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become…

Differential Equation (DE) is a commonly used modeling method in various scientific subjects such as finance and biology. The parameters in DE models often have interesting scientific interpretations, but their values are often unknown and…