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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…
The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with latent variables. Many authors modified its simple design to fit more specific situations. For instance, the Expectation (E) step…
We develop a novel approach to tackle the common but challenging problem of conformal inference for missing data in machine learning, focusing on Missing at Random (MAR) data. We propose a new procedure Conformal prediction for Missing data…
Computational efficient evaluation of penalized estimators of multivariate exponential family distributions is sought. These distributions encompass among others Markov random fields with variates of mixed type (e.g. binary and continuous)…
Most practical data science problems encounter missing data. A wide variety of solutions exist, each with strengths and weaknesses that depend upon the missingness-generating process. Here we develop a theoretical framework for training and…
Missing covariates are not uncommon in capture-recapture studies. When covariate information is missing at random in capture-recapture data, an empirical full likelihood method has been demonstrated to outperform…
We consider the problem of estimating the inverse covariance matrix by maximizing the likelihood function with a penalty added to encourage the sparsity of the resulting matrix. We propose a new approach based on the split Bregman method to…
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…
Beta regression is commonly employed when the outcome variable is a proportion. Since its conception, the approach has been widely used in applications spanning various scientific fields. A series of extensions have been proposed over time,…
We consider a least absolute deviation (LAD) approach to the robust phase retrieval problem that aims to recover a signal from its absolute measurements corrupted with sparse noise. To solve the resulting non-convex optimization problem, we…
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…
A new approach for signal parametrization, which consists of a specific regression model incorporating a discrete hidden logistic process, is proposed. The model parameters are estimated by the maximum likelihood method performed by a…
Multiple imputation (MI) is a popular method for handling missing data. Auxiliary variables can be added to the imputation model(s) to improve MI estimates. However, the choice of which auxiliary variables to include in the imputation model…
In this letter, we employ and design the expectation--conditional maximization either (ECME) algorithm, a generalisation of the EM algorithm, for solving the maximum likelihood direction finding problem of stochastic sources, which may be…
We study the problem of consistently recovering the sparsity pattern of a regression parameter vector from correlated observations governed by deterministic missing data patterns using Lasso. We consider the case in which the observed…
In this paper we study the computation of the nonparametric maximum likelihood estimator (NPMLE) in multivariate mixture models. Our first approach discretizes this infinite dimensional convex optimization problem by fixing the support…
To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation-Maximization algorithm for general latent variable models is proposed. For exponential models the algorithm is shown…
This paper provides an alternative to penalized estimators for estimation and vari- able selection in high dimensional linear regression models with measurement error or missing covariates. We propose estimation via bias corrected least…
Maximum Likelihood Estimation (MLE) and Likelihood Ratio Test (LRT) are widely used methods for estimating the transition probability matrix in Markov chains and identifying significant relationships between transitions, such as equality.…
This paper proposes a new interpretation of sparse penalties such as the elastic-net and the group-lasso. Beyond providing a new viewpoint on these penalization schemes, our approach results in a unified optimization strategy. Our…