Model-Based and Model-Free point prediction algorithms for locally stationary random fields

TL;DR

This paper extends Model-Free and Model-Based prediction methods to locally stationary random fields, demonstrating their effectiveness on synthetic data and CIFAR-10 images, with Model-Free methods outperforming Model-Based ones.

Contribution

It introduces novel applications of Model-Free and Model-Based prediction techniques to locally stationary random fields, a previously unexplored context.

Findings

Model-Free prediction outperforms Model-Based in CIFAR-10 images

Both methods are successfully adapted for locally stationary random fields

Synthetic data experiments validate the approaches

Abstract

The Model-free Prediction Principle has been successfully applied to general regression problems, as well as problems involving stationary and locally stationary time series. In this paper we demonstrate how Model-Free Prediction can be applied to handle random fields that are only locally stationary, i.e., they can be assumed to be stationary only across a limited part over their entire region of definition. We construct one-step-ahead point predictors and compare the performance of Model-free to Model-based prediction using models that incorporate a trend and/or heteroscedasticity. Both aspects of the paper, Model-free and Model-based, are novel in the context of random fields that are locally (but not globally) stationary. We demonstrate the application of our Model-based and Model-free point prediction methods to synthetic data as well as images from the CIFAR-10 dataset and in the latter case show that our best Model-free point prediction results outperform those obtained using Model-based prediction.