Conformal Prediction for Manifold-based Source Localization with Gaussian Processes

We address the problem of uncertainty quantification (UQ) in the localization of a sound source within adverse acoustic environments. Estimating the position of the source is influenced by various factors, such as noise and reverberation, leading to significant uncertainty. Quantifying this uncertainty is essential, particularly when localization outcomes impact critical decision-making processes, such as in robot audition, where the accuracy of location estimates directly influences subsequent actions. Despite this, common localization methods offer point estimates without quantifying the estimation uncertainty. To address this, we employ conformal prediction (CP)—a framework that delivers statistically valid prediction intervals (PIs) with finite-sample guarantees, independent of the data distribution. However, commonly used Inductive CP (ICP) methods require a large amount of labeled data, which can be difficult to obtain in the localization setting. To mitigate this limitation, we incorporate a semi-supervised manifold-based localization method using Gaussian process regression (GPR), with an efficient Transductive CP (TCP) technique, specifically designed for GPR. We demonstrate that our method generates statistically valid PIs across different acoustic conditions, while producing smaller intervals compared to baselines.