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We introduce an approach based on mirror descent and sequential Monte Carlo (SMC) to perform joint parameter inference and posterior estimation in latent variable models. This approach is based on minimisation of a functional over the…

We develop a general framework for proving rigorous guarantees on the performance of the EM algorithm and a variant known as gradient EM. Our analysis is divided into two parts: a treatment of these algorithms at the population level (in…

Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…

Finding parameters that minimise a loss function is at the core of many machine learning methods. The Stochastic Gradient Descent algorithm is widely used and delivers state of the art results for many problems. Nonetheless, Stochastic…

In dynamic scenes, images often suffer from dynamic blur due to superposition of motions or low signal-noise ratio resulted from quick shutter speed when avoiding motions. Recovering sharp and clean results from the captured images heavily…

The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of…

When images are statistically described by a generative model we can use this information to develop optimum techniques for various image restoration problems as inpainting, super-resolution, image coloring, generative model inversion, etc.…

In Positron Emission Tomography, movement leads to blurry reconstructions when not accounted for. Whether known a priori or estimated jointly to reconstruction, motion models are increasingly defined in continuum rather that in discrete,…

The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic…

One of the challenges in model-based control of stochastic dynamical systems is that the state transition dynamics are involved, and it is not easy or efficient to make good-quality predictions of the states. Moreover, there are not many…

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…

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…

Dramatic increases in the size and dimensionality of many recent data sets make crucial the need for sophisticated methods that can exploit inherent structure and handle missing values. In this article we derive an expectation-maximization…

The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…

The expectation-maximization (EM) algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The EM is best suited for situations where the…

The Expectation Maximization (EM) algorithm is a versatile tool for model parameter estimation in latent data models. When processing large data sets or data stream however, EM becomes intractable since it requires the whole data set to be…

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…

Maximum likelihood estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with…

The expectation-maximization (EM) algorithm and its variants are widely used in statistics. In high-dimensional mixture linear regression, the model is assumed to be a finite mixture of linear regression and the number of predictors is much…

Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…