Bayesian Registration of Functions With a Gaussian Process Prior

ABSTRACT

We present a Bayesian framework for registration of real-valued functional data. At the core of our approach is a series of transformations of the data and functional parameters, developed under a differential geometric framework. We aim to avoid discretization of functional objects for as long as possible, thus minimizing the potential pitfalls associated with high-dimensional Bayesian inference. Approximate draws from the posterior distribution are obtained using a novel Markov chain Monte Carlo (MCMC) algorithm, which is well suited for estimation of functions. We illustrate our approach via pairwise and multiple functional data registration, using both simulated and real datasets. Supplementary material for this article is available online.

KEYWORDS:

• Function registration
• Markov chain Monte Carlo
• Time warping

Acknowledgments

The authors thank the reviewers for their valuable comments that greatly improved the quality of this manuscript. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Funding

This research was partially supported by the following grants: NSF DMS 1209142 (YL and RH), NSF DMS 1407604 (RH), and NSF DMS 1613054 (SK).