Uncertainty Quantification in Melody Estimation using Histogram Representation

Abstract

Confidence estimation can improve the reliability of melody estimation by indicating which predictions are likely incorrect. The existing classification-based approach provides confidence for predicted pitch classes but fails to capture the magnitude of deviation from the ground truth. To address this limitation, we reformulate melody estimation as a regression problem and propose a novel approach to estimate uncertainty directly from the histogram representation of the pitch values, which correlates well with the deviation between the prediction and the ground-truth. We design three methods to model pitch on a continuous support range of histogram, which introduces the challenge of handling the discontinuity of unvoiced from the voiced pitch values. The first two methods address the abrupt discontinuity by mapping the pitch values to a continuous range, while the third adopts a fully Bayesian formulation, which models voicing detection as a classification and voiced pitch estimation as a regression task. Experimental results demonstrate that regression-based formulations yield more reliable uncertainty estimates compared to classification-based approaches in identifying incorrect pitch predictions. Comparing the proposed methods with a state-of-the-art regression model, it is observed that the Bayesian method performs the best at estimating both the melody and its associated uncertainty.