Adapted Variational Bayes for Functional Data Registration, Smoothing, and Prediction

TL;DR

This paper introduces an efficient Bayesian hierarchical model for functional data registration, smoothing, and prediction, utilizing an adapted variational Bayes algorithm to handle high-dimensional inference with improved computational speed.

Contribution

It presents a novel adaptive variational Bayes approach for functional data registration that combines smoothing and registration in a unified probabilistic framework.

Findings

Performs comparably to MCMC in accuracy

Enables separate variability depiction via bootstrapping

Demonstrated on El Niño temperature data

Abstract

We propose a model for functional data registration that compares favorably to the best methods of functional data registration currently available. It also extends current inferential capabilities for unregistered data by providing a flexible probabilistic framework that 1) allows for functional prediction in the context of registration and 2) can be adapted to include smoothing and registration in one model. The proposed inferential framework is a Bayesian hierarchical model where the registered functions are modeled as Gaussian processes. To address the computational demands of inference in high-dimensional Bayesian models, we propose an adapted form of the variational Bayes algorithm for approximate inference that performs similarly to MCMC sampling methods for well-defined problems. The efficiency of the adapted variational Bayes (AVB) algorithm allows variability in a predicted registered, warping, and unregistered function to be depicted separately via bootstrapping. Temperature data related to the el-ni\~no phenomenon is used to demonstrate the unique inferential capabilities for prediction provided by this model.