Related papers: Statistical guarantees for the EM algorithm: From …
The controlled branching process is a generalization of the classical Bienaym\'e-Galton-Watson branching process. It is a useful model for describing the evolution of populations in which the population size at each generation needs to be…
In this paper, we firstly give a brief introduction of expectation maximization (EM) algorithm, and then discuss the initial value sensitivity of expectation maximization algorithm. Subsequently, we give a short proof of EM's convergence.…
The EM algorithm is one of many important tools in the field of statistics. While often used for imputing missing data, its widespread applications include other common statistical tasks, such as clustering. In clustering, the EM algorithm…
This paper tackles the problem of missing data imputation for noisy and non-Gaussian data. A classical imputation method, the Expectation Maximization (EM) algorithm for Gaussian mixture models, has shown interesting properties when…
Recently, a so-called E-MS algorithm was developed for model selection in the presence of missing data. Specifically, it performs the Expectation step (E step) and Model Selection step (MS step) alternately to find the minimum point of the…
The expectation--maximization (EM) algorithm combines global monotonicity, local linear convergence, and strong practical robustness, but these features are usually analyzed separately. Global descent is nonlinear, whereas local convergence…
We study mixture of linear regression (random coefficient) models, which capture population heterogeneity by allowing the regression coefficients to follow an unknown distribution $G^*$. In contrast to common parametric methods that fix the…
Expectation Maximization (EM) is the standard method to learn Gaussian mixtures. Yet its classic, centralized form is often infeasible, due to privacy concerns and computational and communication bottlenecks. Prior work dealt with data…
We study Bayesian inverse problems with mixed noise, modeled as a combination of additive and multiplicative Gaussian components. While traditional inference methods often assume fixed or known noise characteristics, real-world…
Many applications require that we learn the parameters of a model from data. EM is a method used to learn the parameters of probabilistic models for which the data for some of the variables in the models is either missing or hidden. There…
Regression analysis with missing data is a long-standing and challenging problem, particularly when there are many missing variables with arbitrary missing patterns. Likelihood-based methods, although theoretically appealing, are often…
Capture-recapture experiments are widely used to estimate the abundance of a finite population. Based on capture-recapture data, the empirical likelihood (EL) method has been shown to outperform the conventional conditional likelihood (CL)…
We present a new framework for analysing the Expectation Maximization (EM) algorithm. Drawing on recent advances in the theory of gradient flows over Euclidean-Wasserstein spaces, we extend techniques from alternating minimization in…
Despite the extent of recent advances in Machine Learning (ML) and Neural Networks, providing formal guarantees on the behavior of these systems is still an open problem, and a crucial requirement for their adoption in regulated or…
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…
Neural networks trained with standard objectives exhibit behaviors characteristic of probabilistic inference: soft clustering, prototype specialization, and Bayesian uncertainty tracking. These phenomena appear across architectures -- in…
A non linear regression approach which consists of a specific regression model incorporating a latent process, allowing various polynomial regression models to be activated preferentially and smoothly, is introduced in this paper. The model…
Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled \emph{with} replacement. In practice, however, sampling \emph{without} replacement is very common, easier to…
In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…
A maximum likelihood methodology for the parameters of models with an intractable likelihood is introduced. We produce a likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm to maximize the…