Online EM for functional data

- A mixture of deformable models for functional data (curves and shapes).
- Inference is conducted using a novel approach, the Monte Carlo online EM algorithm.
- Templates from data with high time/geometric dispersion.
- Processing observations on the fly, MCoEM is more efficient than batch EM algorithms.

A novel approach to perform unsupervised sequential learning for functional data is proposed. The goal is to extract reference shapes (referred to as templates) from noisy, deformed and censored realizations of curves and images. The proposed model generalizes the Bayesian dense deformable template model, 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 (EM) algorithm. The designed 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 the methodology.