## A VOCABULARY-FREE INFINITY-GRAM MODEL FOR NONPARAMETRIC BAYESIAN CHORD PROGRESSION ANALYSIS

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@MISC{Yoshii_avocabulary-free,

author = {Kazuyoshi Yoshii and Masataka Goto},

title = {A VOCABULARY-FREE INFINITY-GRAM MODEL FOR NONPARAMETRIC BAYESIAN CHORD PROGRESSION ANALYSIS},

year = {}

}

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### Abstract

This paper presents probabilistic n-gram models for symbolic chord sequences. To overcome the fundamental limitations in conventional models—that the model optimality is not guaranteed, that the value of n is fixed uniquely, and that a vocabulary of chord types (e.g., major, minor, ···)is defined in an arbitrary way—we propose a vocabulary-free infinity-gram model based on Bayesian nonparametrics. It accepts any combinations of notes as chord types and allows each chord appearing in a sequence to have an unbounded and variable-length context. All possibilities of n are taken into account when calculating the predictive probability of a next chord given a particular context, and when an unseen chord type emerges we can avoid out-of-vocabulary error by adaptively evaluating the 0-gram probability, i.e., the combinatorial probability of note components. Our experiments using Beatles songs showed that the predictive performance of the proposed model is better than that of the state-of-theart models and that we could find stochastically-coherent chord patterns by sorting variable-length n-grams in a line according to their generative probabilities. 1.

### Citations

924 | An empirical study of smoothing techniques for language modeling
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Citation Context ...exponentially with increasing n. Therefore, the naive estimates of the probabilities of unobserved n-grams are zero. To avoid such overfitting, various heuristic smoothing methods have been developed =-=[7]-=-. In this paper we focus on three fundamental limitations of conventional n-gram models: 1) n-gram models based on heuristic smoothing methods have no solid theoretical foundation, 2) the value of n s... |

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Citation Context ...sed and component-based notations to represent chord sequences (Table 1). 2.1 Label-based Notation The conventional label-based notation is based on intuitive shorthand labels defined by Harte et al. =-=[14]-=-. There are 17 chord labels with an attached root note, which is one of 12 pitch classes. 1 In this paper we do not distinguish C# from Db because they are in the same pitch class. This is a standard ... |

32 | Simultaneous estimation of chords and musical context from audio
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Citation Context ...ication is automatic chord recognition, where a vocabulary of chord labels is given. For example, an infinitygram model could be fused with a joint probabilistic model of keys, chords, and bass notes =-=[12]-=-. Another novel application is automatic music transcription, where a vocabulary is not given. We plan to use a vocabulary-free model as a prior distribution on a probabilistic acoustic model for mult... |

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Citation Context ...odels is that we need to define a finite vocabulary even though in the real world the vocabulary is growing steadily. To solve this problem in the context of word sequence modeling, Mochihashi et al. =-=[10]-=- proposed a nested PY language model (NPYLM) by formulating a global base measure G0 over a countably 64812th International Society for Music Information Retrieval Conference (ISMIR 2011) infinite nu... |

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17 | A Probabilistic Model for Chord Progressions
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Citation Context ...rting variable-length n-grams in a line according to their generative probabilities. 1. INTRODUCTION Chord progression analysis is an important task for contentbased music information retrieval (MIR) =-=[1,2]-=-. Because the chord patterns used in musical pieces are closely related to the composer styles [3] and musical genres [4], it is useful to build statistical models of chord patterns from symbolic chor... |

15 | B.: Discovering chord idioms through Beatles and Real Book songs
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Citation Context ...ese metits enable our model to not only attain the best performance but also find “stochasticallycoherent” variable-length chord patterns that are not always simply the ones used most frequently (cf. =-=[11]-=-). The innovative models of symbolic chord sequences (an infinity-gram model and its vocabulary-free extension) are useful for probabilistic modeling of music audio signals. A typical application is a... |

14 |
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Citation Context ...ysis is an important task for contentbased music information retrieval (MIR) [1,2]. Because the chord patterns used in musical pieces are closely related to the composer styles [3] and musical genres =-=[4]-=-, it is useful to build statistical models of chord patterns from symbolic chord sequences. In addition, accurate models of chord sequences (called language models in analogy with automatic speech rec... |

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Citation Context ...In addition, accurate models of chord sequences (called language models in analogy with automatic speech recognition) could improve the accuracy of automatic chord recognition for music audio signals =-=[5, 6]-=-. So far, n-gram models have often been used as language models of chord sequences [2–6]. An n-gram is a subsequence of n chords in a given chord sequence, and n-gram Permission to make digital or har... |

11 | F.: Robust modelling of musical chord sequences using probabilistic n-grams
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Citation Context ...rting variable-length n-grams in a line according to their generative probabilities. 1. INTRODUCTION Chord progression analysis is an important task for contentbased music information retrieval (MIR) =-=[1,2]-=-. Because the chord patterns used in musical pieces are closely related to the composer styles [3] and musical genres [4], it is useful to build statistical models of chord patterns from symbolic chor... |

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Citation Context ...ls in [8]). 3.3 Variable-Order Pitman-Yor Language Model A problem of the HPYLM is that all M customers are forced to enter restaurants of fixed depth n−1. To solve the problem, Mochihashi and Sumita =-=[9]-=- proposed a variable-order PY language model (VPYLM) that allows each customer to enter a restaurant of variable depth. Each chord xm is associated with a latent variable zm that indicates the value o... |

6 | Automatic chord recognition for music classification and retrieval
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Citation Context ...In addition, accurate models of chord sequences (called language models in analogy with automatic speech recognition) could improve the accuracy of automatic chord recognition for music audio signals =-=[5, 6]-=-. So far, n-gram models have often been used as language models of chord sequences [2–6]. An n-gram is a subsequence of n chords in a given chord sequence, and n-gram Permission to make digital or har... |

6 | Infinite latent harmonic allocation: A nonparametric bayesian approach to multipitch analysis
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- 2010
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Citation Context ...plication is automatic music transcription, where a vocabulary is not given. We plan to use a vocabulary-free model as a prior distribution on a probabilistic acoustic model for multipitch estimation =-=[13]-=-, and jointly optimize the both models. This means that chords and their progressions (now “chords” are combinations of notes, not text labels) are self-organized in an unsupervised manner and are use... |

4 |
n-gram chord profiles for composer style representation
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Citation Context ... Chord progression analysis is an important task for contentbased music information retrieval (MIR) [1,2]. Because the chord patterns used in musical pieces are closely related to the composer styles =-=[3]-=- and musical genres [4], it is useful to build statistical models of chord patterns from symbolic chord sequences. In addition, accurate models of chord sequences (called language models in analogy wi... |