Online EM for Functional Data
Abstract
A novel approach to perform unsupervised sequential learning for functional data is proposed. Our goal is to extract reference shapes (referred to as templates) from noisy, deformed and censored realizations of curves and images. Our model generalizes the Bayesian dense deformable template model (Allassonni\`ere et al., 2007), a hierarchical model in which the template is the function to be estimated and the deformation is a nuisance, assumed to be random with a known prior distribution. The templates are estimated using a Monte Carlo version of the online Expectation-Maximization algorithm, extending the work from Capp\'e and Moulines (2009). Our sequential inference framework is significantly more computationally efficient than equivalent batch learning algorithms, especially when the missing data is high-dimensional. Some numerical illustrations on curve registration problem and templates extraction from images are provided to support our findings.
Cite
@article{arxiv.1604.00570,
title = {Online EM for Functional Data},
author = {Florian Maire and Eric Moulines and Sidonie Lefebvre},
journal= {arXiv preprint arXiv:1604.00570},
year = {2016}
}