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Empirical Bayes methods are widely used for large-scale estimation and inference in the Poisson means problem. Existing results establish theoretical properties of the nonparametric maximum likelihood estimator (NPMLE) for optimal posterior…

Statistics Theory · Mathematics 2026-05-06 Taehyun Kim

The EM (Expectation-Maximization) algorithm is regarded as an MM (Majorization-Minimization) algorithm for maximum likelihood estimation of statistical models. Expanding this view, this paper demonstrates that by choosing an appropriate…

Optimization and Control · Mathematics 2026-02-12 Kensuke Asai , Jun-ya Gotoh

Accelerated algorithms for maximum likelihood image reconstruction are essential for emerging applications such as 3D tomography, dynamic tomographic imaging, and other high dimensional inverse problems. In this paper, we introduce and…

Computation · Statistics 2012-01-31 Stéphane Chrétien , Alfred O. Hero

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…

Statistics Theory · Mathematics 2016-08-30 Ji Xu , Daniel Hsu , Arian Maleki

In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…

Applications · Statistics 2011-03-14 François-Xavier Dupé , Jalal Fadili , Jean-Luc Starck

We develop two algorithms, based on maximum likelihood (ML) inference, for estimating the parameters of polarized radio sources which emit at a single rotation measure (RM), e.g., pulsars. These algorithms incorporate the flux density…

Instrumentation and Methods for Astrophysics · Physics 2017-10-25 D. H. F. M. Schnitzeler , K. J. Lee

We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is…

Methodology · Statistics 2013-03-18 Kei Hirose , Michio Yamamoto

In the context of Independent Component Analysis (ICA), noisy mixtures pose a dilemma regarding the desired objective. On one hand, a "maximally separating" solution, providing the minimal attainable Interference-to-Source-Ratio (ISR),…

Applications · Statistics 2019-10-02 Amir Weiss , Arie Yeredor

In the Multiple Measurements Vector (MMV) model, measurement vectors are connected to unknown, jointly sparse signal vectors through a linear regression model employing a single known measurement matrix (or dictionary). Typically, the…

Methodology · Statistics 2024-08-05 Esa Ollila

The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It…

Quantum Physics · Physics 2020-07-08 Iordanis Kerenidis , Alessandro Luongo , Anupam Prakash

A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…

Numerical Analysis · Computer Science 2010-09-03 Adam C. Zelinski , Vivek K Goyal , Elfar Adalsteinsson

We consider a symmetric mixture of linear regressions with random samples from the pairwise comparison design, which can be seen as a noisy version of a type of Euclidean distance geometry problem. We analyze the expectation-maximization…

Statistics Theory · Mathematics 2023-06-23 Abhishek Dhawan , Cheng Mao , Ashwin Pananjady

We propose a continuous non-convex variational model for Single Molecule Localisation Microscopy (SMLM) super-resolution in order to overcome light diffraction barriers. Namely, we consider a variation of the Continuous Exact $\ell_0$…

Image and Video Processing · Electrical Eng. & Systems 2020-10-27 Marta Lazzaretti , Luca Calatroni , Claudio Estatico

The purpose of this note is to show how the method of maximum entropy in the mean (MEM) may be used to improve parametric estimation when the measurements are corrupted by large level of noise. The method is developed in the context on a…

Machine Learning · Computer Science 2021-08-23 Henryk Gzyl , Enrique ter Horst

Motivated by the problem of determining the atomic structure of macromolecules using single-particle cryo-electron microscopy (cryo-EM), we study the sample and computational complexities of the sparse multi-reference alignment (MRA) model:…

Information Theory · Computer Science 2021-09-27 Tamir Bendory , Oscar Mickelin , Amit Singer

We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…

Numerical Analysis · Mathematics 2022-03-24 Darko Volkov

Partially recorded data are frequently encountered in many applications and usually clustered by first removing incomplete cases or features with missing values, or by imputing missing values, followed by application of a clustering…

Methodology · Statistics 2021-10-20 Emily M. Goren , Ranjan Maitra

We address the problem of estimating a random vector X from two sets of measurements Y and Z, such that the estimator is linear in Y. We show that the partially linear minimum mean squared error (PLMMSE) estimator does not require knowing…

Information Theory · Computer Science 2015-05-27 Tomer Michaeli , Daniel Sigalov , Yonina C. Eldar

The paper deals with quantum pulse position modulation (PPM), both in the absence (pure states) and in the presence (mixed states) of thermal noise, using the Glauber representation of coherent laser radiation. The objective is to find…

Quantum Physics · Physics 2009-11-16 G. Cariolaro , G. Pierobon

The mixture model is undoubtedly one of the greatest contributions to clustering. For continuous data, Gaussian models are often used and the Expectation-Maximization (EM) algorithm is particularly suitable for estimating parameters from…

Machine Learning · Statistics 2025-11-25 Zineddine Tighidet , Lazhar Labiod , Mohamed Nadif