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Automatic estimation of piano fingering is important for understanding thecomputational process of music performance and applicable to performanceassistance and education systems. While a natural way to formulate the qualityof fingerings is to construct models of the constraints/costs of performance,it is generally difficult to find appropriate parameter values for thesemodels. Here we study an alternative data-driven approach based on statisticalmodeling in which the appropriateness of a given fingering is described byprobabilities. Specifically, we construct two types of hidden Markov models(HMMs) and their higher-order extensions. We also study deep neural network(DNN)-based methods for comparison. Using a newly released dataset of fingeringannotations, we conduct systematic evaluations of these models as well as arepresentative constraint-based method. We find that the methods based onhigh-order HMMs outperform the other methods in terms of estimation accuracies.We also quantitatively study individual difference of fingering and proposeevaluation measures that can be used with multiple ground truth data. Weconclude that the HMM-based methods are currently state of the art and generateacceptable fingerings in most parts and that they have certain limitations suchas ignorance of phrase boundaries and interdependence of the two hands.

Statistical Learning and Estimation of Piano Fingering