Gaussian Process for Noisy Inputs with Ordering Constraints

TL;DR

This paper introduces a novel Gaussian Process regression method that incorporates ordering constraints on noisy inputs, improving predictive accuracy and computational efficiency in temporal data modeling.

Contribution

It presents a new inference approach using Gaussian variational approximation that enforces ordering constraints, enhancing model accuracy with noisy inputs.

Findings

Outperforms state-of-the-art NIGP in experiments

Reduces computational costs compared to existing methods

Improves predictive performance on synthetic and real data

Abstract

We study the Gaussian Process regression model in the context of training data with noise in both input and output. The presence of two sources of noise makes the task of learning accurate predictive models extremely challenging. However, in some instances additional constraints may be available that can reduce the uncertainty in the resulting predictive models. In particular, we consider the case of monotonically ordered latent input, which occurs in many application domains that deal with temporal data. We present a novel inference and learning approach based on non-parametric Gaussian variational approximation to learn the GP model while taking into account the new constraints. The resulting strategy allows one to gain access to posterior estimates of both the input and the output and results in improved predictive performance. We compare our proposed models to state-of-the-art Noisy Input Gaussian Process (NIGP) and other competing approaches on synthetic and real sea-level rise data. Experimental results suggest that the proposed approach consistently outperforms selected methods while, at the same time, reducing the computational costs of learning and inference.