Distribution-free prediction intervals with conformal prediction for acoustical estimation

Acoustical parameter estimation is a routine task in many domains. The performance of existing estimation methods is affected by external uncertainty, yet the methods provide no measure of confidence in the estimates. Hence, it is crucial to quantify estimate uncertainty before real-world deployment. Conformal prediction (CP) generates statistically valid prediction intervals for any estimation model using calibration data; a limitation is that calibration data needed by CP must come from the same distribution as the test-time data. In this work, we propose to use CP to obtain statistically valid uncertainty intervals for acoustical parameter estimation using a data-driven model or an analytical model without training data. We consider direction-of-arrival estimation and localization of sources. The performance is validated on plane wave data with different sources of uncertainty, including ambient noise, interference, and sensor location uncertainty. The application of CP for data-driven and traditional propagation models is demonstrated. Results show that CP can be used for statistically valid uncertainty quantification with proper calibration data.