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Extreme mass ratio inspirals (EMRIs) are thought to be one of the most exciting gravitational wave sources to be detected with LISA. Due to their complicated nature and weak amplitudes the detection and parameter estimation of such sources…
The expectation-maximization (EM) algorithm is an iterative computational method to calculate the maximum likelihood estimators (MLEs) from the sample data. It converts a complicated one-time calculation for the MLE of the incomplete data…
In this paper, we consider nonparametric multidimensional finite mixture models and we are interested in the semiparametric estimation of the population weights. Here, the i.i.d. observations are assumed to have at least three components…
The Expectation-Maximization (EM) algorithm (Dempster, Laird and Rubin, 1977) is a popular method for computing maximum likelihood estimates (MLEs) in problems with missing data. Each iteration of the al- gorithm formally consists of an…
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…
Estimators derived from a divergence criterion such as $\varphi-$divergences are generally more robust than the maximum likelihood ones. We are interested in particular in the so-called MD$\varphi$DE, an estimator built using a dual…
We study the approximation of expectations $\E(f(X))$ for Gaussian random elements $X$ with values in a separable Hilbert space $H$ and Lipschitz continuous functionals $f \colon H \to \R$. We consider restricted Monte Carlo algorithms,…
This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…
The EM algorithm is one of the most popular algorithm for inference in latent data models. The original formulation of the EM algorithm does not scale to large data set, because the whole data set is required at each iteration of the…
Experimental design is a classical statistics problem and its aim is to estimate an unknown $m$-dimensional vector $\beta$ from linear measurements where a Gaussian noise is introduced in each measurement. For the combinatorial experimental…
The EMD algorithm, first proposed in [11], made more robust as well as more versatile in [12], is a technique that aims to decompose into their building blocks functions that are the superposition of a (reasonably) small number of…
Data clustering has received a lot of attention and numerous methods, algorithms and software packages are available. Among these techniques, parametric finite-mixture models play a central role due to their interesting mathematical…
This paper studies the optimal rate of estimation in a finite Gaussian location mixture model in high dimensions without separation conditions. We assume that the number of components $k$ is bounded and that the centers lie in a ball of…
Maximum likelihood estimators are proposed for the parameters and the densities in a semiparametric density ratio model in which the nonparametric baseline density is approximated by the Bernstein polynomial model. The EM algorithm is used…
Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an…
We study the problem of list-decodable Gaussian mean estimation and the related problem of learning mixtures of separated spherical Gaussians. We develop a set of techniques that yield new efficient algorithms with significantly improved…
Let $f(y|\theta), \; \theta \in \Omega$ be a parametric family, $\eta(\theta)$ a given function, and $G$ an unknown mixing distribution. It is desired to estimate $E_G (\eta(\theta))\equiv \eta_G$ based on independent observations…
The Expectation-Maximization (EM) algorithm is a commonly used method for finding the maximum likelihood estimates of the parameters in a mixture model via coordinate ascent. A serious pitfall with the algorithm is that in the case of…
Given a source of iid samples of edges of an input graph $G$ with $n$ vertices and $m$ edges, how many samples does one need to compute a constant factor approximation to the maximum matching size in $G$? Moreover, is it possible to obtain…
Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from…