Dynamic Bayesian Networks for Symbolic Polyphonic Pitch Modeling

Symbolic pitch modeling is a way of incorporating knowledge about relations between pitches into the process of analyzing musical information or signals. In this paper, we propose a family of probabilistic symbolic polyphonic pitch models, which account for both the "horizontal" and the &q...

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Vydáno v:	IEEE transactions on audio, speech, and language processing Ročník 21; číslo 9; s. 1830 - 1840
Hlavní autoři:	Raczyński, Stanisław A., Vincent, Emmanuel, Sagayama, Shigeki
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Piscataway, NJ IEEE 01.09.2013 Institute of Electrical and Electronics Engineers
Témata:	Accuracy Acoustics Applied sciences Audio signals Bayes methods Computer Science Context modeling Data models Detection, estimation, filtering, equalization, prediction Dynamic Bayesian Networks Engineering Sciences Estimation Exact sciences and technology Hidden Markov models Horizontal Information theory Information, signal and communications theory Interpolation Mathematical models multipitch analysis Music Pitch estimation Signal and communications theory Signal and Image Processing Signal, noise symbolic pitch modeling Telecommunications and information theory Training Transaction processing Performance evaluation Linear interpolation Dynamic Bayesian Networks Probabilistic approach Acoustic signal Signal estimation Entropy Matrix factorization Modeling Information analysis Accuracy Non negative matrix Audio signal Linear combination symbolic pitch modeling multipitch analysis Bayes network Musical sound Pitch(acoustics)
ISSN:	1558-7916, 1558-7924
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Abstract	Symbolic pitch modeling is a way of incorporating knowledge about relations between pitches into the process of analyzing musical information or signals. In this paper, we propose a family of probabilistic symbolic polyphonic pitch models, which account for both the "horizontal" and the "vertical" pitch structure. These models are formulated as linear or log-linear interpolations of up to five sub-models, each of which is responsible for modeling a different type of relation. The ability of the models to predict symbolic pitch data is evaluated in terms of their cross-entropy, and of a newly proposed "contextual cross-entropy" measure. Their performance is then measured on synthesized polyphonic audio signals in terms of the accuracy of multiple pitch estimation in combination with a Nonnegative Matrix Factorization-based acoustic model. In both experiments, the log-linear combination of at least one "vertical" (e.g., harmony) and one "horizontal" (e.g., note duration) sub-model outperformed a pitch-dependent Bernoulli prior by more than 60% in relative cross-entropy and 3% in absolute multiple pitch estimation accuracy. This work provides a proof of concept of the usefulness of model interpolation, which may be used for improved symbolic modeling of other aspects of music in the future.
AbstractList	Symbolic pitch modelling is a way of incorporating knowledge about relations between pitches into the process of analysing musical information or signals. In this paper, we propose a family of probabilistic symbolic polyphonic pitch models, which account for both the ''horizontal'' and the ''vertical'' pitch structure. These models are formulated as linear or log-linear interpolations of up to five sub-models, each of which is responsible for modelling a different type of relation. The ability of the models to predict symbolic pitch data is evaluated in terms of their cross-entropy, and of a newly proposed ''contextual cross-entropy'' measure. Their performance is then measured on synthesised polyphonic audio signals in terms of the accuracy of multiple pitch estimation in combination with a Nonnegative Matrix Factorisation-based acoustic model. In both experiments, the log-linear combination of at least one ''vertical'' (e.g., harmony) and one ''horizontal'' (e.g., note duration) sub-model outperformed a pitch-dependent Bernoulli prior by more than 60% in relative cross-entropy and 3% in absolute multiple pitch estimation accuracy. This work provides a proof of concept of the usefulness of model interpolation, which may be used for improved symbolic modelling of other aspects of music in the future. Symbolic pitch modeling is a way of incorporating knowledge about relations between pitches into the process of analyzing musical information or signals. In this paper, we propose a family of probabilistic symbolic polyphonic pitch models, which account for both the "horizontal" and the "vertical" pitch structure. These models are formulated as linear or log-linear interpolations of up to five sub-models, each of which is responsible for modeling a different type of relation. The ability of the models to predict symbolic pitch data is evaluated in terms of their cross-entropy, and of a newly proposed "contextual cross-entropy" measure. Their performance is then measured on synthesized polyphonic audio signals in terms of the accuracy of multiple pitch estimation in combination with a Nonnegative Matrix Factorization-based acoustic model. In both experiments, the log-linear combination of at least one "vertical" (e.g., harmony) and one "horizontal" (e.g., note duration) sub-model outperformed a pitch-dependent Bernoulli prior by more than 60% in relative cross-entropy and 3% in absolute multiple pitch estimation accuracy. This work provides a proof of concept of the usefulness of model interpolation, which may be used for improved symbolic modeling of other aspects of music in the future.
Author	Sagayama, Shigeki Vincent, Emmanuel Raczyński, Stanisław A.
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Keywords	Performance evaluation Linear interpolation Dynamic Bayesian Networks Probabilistic approach Acoustic signal Signal estimation Entropy Matrix factorization Modeling Information analysis Accuracy Non negative matrix Audio signal Linear combination symbolic pitch modeling multipitch analysis Bayes network Musical sound Pitch(acoustics)
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Snippet	Symbolic pitch modeling is a way of incorporating knowledge about relations between pitches into the process of analyzing musical information or signals. In... Symbolic pitch modelling is a way of incorporating knowledge about relations between pitches into the process of analysing musical information or signals. In...
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SubjectTerms	Accuracy Acoustics Applied sciences Audio signals Bayes methods Computer Science Context modeling Data models Detection, estimation, filtering, equalization, prediction Dynamic Bayesian Networks Engineering Sciences Estimation Exact sciences and technology Hidden Markov models Horizontal Information theory Information, signal and communications theory Interpolation Mathematical models multipitch analysis Music Pitch estimation Signal and communications theory Signal and Image Processing Signal, noise symbolic pitch modeling Telecommunications and information theory Training Transaction processing
Title	Dynamic Bayesian Networks for Symbolic Polyphonic Pitch Modeling
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