## Predictive Models for Music (2008)

### BibTeX

@MISC{A08predictivemodels,

author = {Jean-francois Paiement A and Yves Grandvalet and Samy Bengio and Jean-francois Paiement and Yves Grandvalet and Samy Bengio},

title = {Predictive Models for Music},

year = {2008}

}

### OpenURL

### Abstract

submitted for publication Abstract. Modeling long-term dependencies in time series has proved very difficult to achieve with traditional machine learning methods. This problem occurs when considering music data. In this paper, we introduce generative models for melodies. We decompose melodic modeling into two subtasks. We first propose a rhythm model based on the distributions of distances between subsequences. Then, we define a generative model for melodies given chords and rhythms based on modeling sequences of Narmour features. The rhythm model consistently outperforms a standard Hidden Markov Model in terms of conditional prediction accuracy on two different music databases. Using a similar evaluation procedure, the proposed melodic model consistently outperforms an Input/Output Hidden Markov Model. Furthermore, sampling these models given appropriate musical contexts generates realistic melodies. 2 IDIAP–RR 08-51 1

### Citations

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Citation Context ...ides efficient algorithms for marginalization and various learning algorithms can be used to learn the parameters of a model, given an appropriate dataset. The Expectation-Maximization (EM) algorithm =-=[5]-=- can be used to estimate the conditional probabilities of the hidden variables in a graphical model. Hidden variables are variables that are neither observed during training nor during evaluation of t... |

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Citation Context ...on, symbol 2 can never follow symbol 3. Let A = {1,2,3}; in the remaining of this paper, we assume that x l ∈ A m for all x l ∈ X. Hidden Markov Models (HMMs) are commonly used to model temporal data =-=[21]-=-. In principle, an HMM as described in Section 2.2 is able to capture complex regularities in patterns between subsequences of data, provided its number of hidden states is large enough. Thus, the HMM... |

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Citation Context ...increase the value of the utility function. Obviously, r=1IDIAP–RR 08-51 9 many other methods could have been used to search the space of possible sequences ˆxs,..., ˆxm, such as simulated annealing =-=[12]-=-. Our choice is motivated by simplicity and the fact that it yields excellent results, as reported in the following section. 3 Rhythm Prediction Experiments Two databases from different musical genres... |

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Citation Context ...een subsequences significantly improve prediction accuracy. 2.1 Graphical Models and EM The probabilistic models used in this paper are described using the graphical model framework. Graphical models =-=[13]-=- are useful to define probability distributions where graphs are used as representations for a particular factorization of joint probabilities. Vertices are associated with random variables. A directe... |

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Citation Context ...{n(1) i,j ,...,n(c) i,j } the number of elements in each of these clusters. We initialize the parameters θi,j with w (k) i,j n(k) i,j = n and p (k) i,j = µ(k) i,j . We then follow a standard approach =-=[4]-=- to apply the EM algorithm to the binomial mixture in Eq. (7). Let zl i,j ∈ {1,...,c} be a hidden variable telling which component density generated dli,j . For every iteration of the EM algorithm, we... |

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Citation Context ...terize and constrain the relative distances between various parts of a sequence of bags-of-concepts could be an efficient means to improve performance of automatic systems such as machine translation =-=[17]-=-. On a more general level, learning constraints related to distances between subsequences can boost the performance of “short term memory” models such as the HMM. Finally, with a reliable rhythm model... |

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Citation Context ...t of this paper, we focus on modeling rhythmic sequences, ignoring for the moment other aspects of music such as pitch, timbre and dynamics. Many algorithms have been proposed for audio beat tracking =-=[23, 6]-=-. Here, we consider rhythm modeling as a first step towards full melodic modeling. Our main contribution in this respect is to propose a generative model for distance patterns, specifically designed f... |

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Citation Context ...es, which has proved very difficult to achieve with traditional statistical methods. Note that the problem of long-term dependencies is not limited to music, nor to one particular probabilistic model =-=[3]-=-. In this paper we present graphical models that capture melodic structures in a given musical style using as evidence a limited amount of symbolic MIDI 1 data. A few generative models have already be... |

149 |
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Citation Context ...essions given melodies in a particular musical genre [1, 19]. However, the dual problem that we address in this paper is much more difficult. In Section 4.2, we describe melodic features derived from =-=[15]-=- that put useful constraints on melodies based on musicological substantiation. We then introduce in Section 4.3 a probabilistic model of melodies given chords and rhythms that leads to significantly ... |

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Citation Context ...metrical hierarchy (e.g. sequences of 4, 8 or 16 measures). It is well know in music theory that distance patterns are more important than the actual choice of notes in order to create coherent music =-=[11]-=-. For instance, measure 1 may always be similar to measure 5 in a particular musical genre. In fact, even random music can sound structured and melodic if it is built by repeating random subsequences ... |

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Citation Context ... l 1)pπ(h l 1|ν l 1)po(u l 1|h l gl ∏ 1) pi(ν l t)pō(h l t|h l t−1,ν l t)po(u l t|h l t) . (12) This model, shown in Figure 5, is a specific Input/Output Hidden Markov Model (IOHMM), as introduced by =-=[2]-=-. Usual IOHMMs have additional links connecting directly the input variables (level 1) t=212 IDIAP–RR 08-51 Figure 5: Variant of an IOHMM model for MIDI notes given chords. The variables in level 1 a... |

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Citation Context ...cal models that capture melodic structures in a given musical style using as evidence a limited amount of symbolic MIDI 1 data. A few generative models have already been proposed for music in general =-=[7, 18]-=-. While these models generate impressive musical results, we are not aware of proper quantitative comparisons between generative models of music, that is for instance in terms of out-of-sample predict... |

34 |
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Citation Context ...t of this paper, we focus on modeling rhythmic sequences, ignoring for the moment other aspects of music such as pitch, timbre and dynamics. Many algorithms have been proposed for audio beat tracking =-=[23, 6]-=-. Here, we consider rhythm modeling as a first step towards full melodic modeling. Our main contribution in this respect is to propose a generative model for distance patterns, specifically designed f... |

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Citation Context ...nd actual notes would certainly help to discover long-term musical structures in tonal music. It is fairly easy to generate interesting chord progressions given melodies in a particular musical genre =-=[1, 19]-=-. However, the dual problem that we address in this paper is much more difficult. In Section 4.2, we describe melodic features derived from [15] that put useful constraints on melodies based on musico... |

30 |
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Citation Context ...cal models that capture melodic structures in a given musical style using as evidence a limited amount of symbolic MIDI 1 data. A few generative models have already been proposed for music in general =-=[7, 18]-=-. While these models generate impressive musical results, we are not aware of proper quantitative comparisons between generative models of music, that is for instance in terms of out-of-sample predict... |

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Citation Context ...s. For instance, a good music model could help improve the poor performance of state-of-the-art transcription systems; it could as well be included in genre classifiers, automatic composition systems =-=[9]-=-, or algorithms for music information retrieval [10]. 2 Rhythm Model We want to model rhythms in a dataset X consisting of rhythms of the same musical genre. We first quantize the database by segmenti... |

29 |
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Citation Context ...ed in Section 5. 4.2 Narmour Features In this section, we introduce melodic features that will prove to be useful for melodic prediction. The Implication-Realization (I-R) model has been developed by =-=[15, 16]-=- as a theory of musical expectation. This fairly complex musicological model was then simplified and implemented by [24], who proposed a formal analysis of each sequence of three consecutive notes, ac... |

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Citation Context ...sing particular notes in other music components, such as melodies or accompaniments. Chord changes occur at fixed time intervals in most of the musical genres, which makes them much simpler to detect =-=[14]-=- than beginnings and endings of musical notes, which can happen almost everywhere in music signal. Thus, knowing the relations between such chords and actual notes would certainly help to discover lon... |

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Citation Context ...h a model is shown in Section 5 to have much better prediction accuracy than using a simpler IOHMM model alone. Unsupervised probabilistic models can be sampled to generate genuine chord progressions =-=[20]-=-. The melodic model described here is able to generate realistic melodies given these chord progressions and beginning of melodies. This system can be used as a tool to ease music composition. Audio f... |

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Citation Context ...Naively trying all possible subsequences to maximize (9) leads to O(|A| (m−s+1) ) computations. Instead, we propose to search the space of sequences using a variant of the Greedy Max Cut (GMC) method =-=[22]-=- that has proven to be optimal in terms of running time and performance for binary MDS optimization. The subsequence ˆxs,..., ˆxm can be simply initialized with (ˆxs,..., ˆxm) = max pHMM(˜xs,..., ˜xm|... |

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Citation Context ...nd actual notes would certainly help to discover long-term musical structures in tonal music. It is fairly easy to generate interesting chord progressions given melodies in a particular musical genre =-=[1, 19]-=-. However, the dual problem that we address in this paper is much more difficult. In Section 4.2, we describe melodic features derived from [15] that put useful constraints on melodies based on musico... |

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(Show Context)
Citation Context ...ove the poor performance of state-of-the-art transcription systems; it could as well be included in genre classifiers, automatic composition systems [9], or algorithms for music information retrieval =-=[10]-=-. 2 Rhythm Model We want to model rhythms in a dataset X consisting of rhythms of the same musical genre. We first quantize the database by segmenting each song in m time steps and associate each note... |

4 |
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(Show Context)
Citation Context ...c prediction. The Implication-Realization (I-R) model has been developed by [15, 16] as a theory of musical expectation. This fairly complex musicological model was then simplified and implemented by =-=[24]-=-, who proposed a formal analysis of each sequence of three consecutive notes, according to five perceptual items: registral direction, intervallic difference, registral return, proximity, and closure,... |