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Comparing Probabilistic Models for Melodic Sequences

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 6913)


Modelling the real world complexity of music is a challenge for machine learning. We address the task of modeling melodic sequences from the same music genre. We perform a comparative analysis of two probabilistic models; a Dirichlet Variable Length Markov Model (Dirichlet-VMM) and a Time Convolutional Restricted Boltzmann Machine (TC-RBM). We show that the TC-RBM learns descriptive music features, such as underlying chords and typical melody transitions and dynamics. We assess the models for future prediction and compare their performance to a VMM, which is the current state of the art in melody generation. We show that both models perform significantly better than the VMM, with the Dirichlet-VMM marginally outperforming the TC-RBM. Finally, we evaluate the short order statistics of the models, using the Kullback-Leibler divergence between test sequences and model samples, and show that our proposed methods match the statistics of the music genre significantly better than the VMM.


  • melody modeling
  • music feature extraction
  • time convolutional restricted Boltzmann machine
  • variable length Markov model
  • Dirichlet prior


  • Ackley, D.H., Hinton, G.E., Sejnowski, T.J.: A learning algorithm for Boltzmann machines. Cognitive Science 9(1), 147–169 (1985)

    CrossRef  Google Scholar 

  • Dubnov, S., Assayag, G., Lartillot, O., Bejerano, G.: Using machine-learning methods for musical style modeling. Computer 36(10), 73–80 (2003)

    CrossRef  Google Scholar 

  • Eck, D., Lapalme, J.: Learning musical structure directly from sequences of music. Technical report, Université de Montreal (2008)

    Google Scholar 

  • Eck, D., Schmidhuber, J.: Learning the long-term structure of the blues. In: Dorronsoro, J.R. (ed.) ICANN 2002. LNCS, vol. 2415, pp. 284–289. Springer, Heidelberg (2002)

    CrossRef  Google Scholar 

  • Eerola, T., Toiviainen, P.: MIDI Toolbox: MATLAB Tools for Music Research. University of Jyväskylä, Jyväskylä, Finland (2004),

  • Hinton, G.E.: Training products of experts by minimizing contrastive divergence. Neural Computation 14(8), 1771–1800 (2002)

    CrossRef  MATH  Google Scholar 

  • Hinton, G.E., Osindero, S., Teh, Y.W.: A fast learning algorithm for deep belief nets. Neural Computation 18(7), 1527–1554 (2006)

    CrossRef  MATH  MathSciNet  Google Scholar 

  • Lavrenko, V., Pickens, J.: Polyphonic music modeling with random fields. In: Rowe, L.A., Vin, H.M., Plagemann, T., Shenoy, P.J., Smith, J.R. (eds.) Proceedings of the Eleventh ACM International Conference on Multimedia, ACM Multimedia, pp. 120–129. ACM, New York (2003)

    CrossRef  Google Scholar 

  • Lee, H., Ekanadham, C., Ng, A.Y.: Sparse deep belief net model for visual area V2. In: Platt, J.C., Koller, D., Singer, Y., Roweis, S.T. (eds.) NIPS. Advances in NIPS, vol. 20. MIT Press, Cambridge (2008)

    Google Scholar 

  • Lee, H., Grosse, R., Ranganath, R., Ng, A.Y.: Convolutional deep belief networks for scalable unsupervised learning of hierarchical representations. In: Danyluk, A.P., Bottou, L., Littman, M.L. (eds.) ICML. ACM ICPS, vol. 382, p. 77. ACM, New York (2009)

    Google Scholar 

  • Lerdahl, F., Jackendoff, R.: A Generative Theory of Tonal Music. The MIT Press, Cambridge (1983)

    Google Scholar 

  • Norouzi, M., Ranjbar, M., Mori, G.: Stacks of convolutional restricted Boltzmann machines for shift-invariant feature learning. In: IEEE Computer Society Conference on CVPR, CVRP 2009, pp. 2735–2742. IEEE, Los Alamitos (2009)

    Google Scholar 

  • Paiement, J.-F.: Probabilistic Models for Music. PhD thesis, Ecole Polytechnique Fédérale de Lausanne (EPFL) (2008)

    Google Scholar 

  • Ron, D., Singer, Y., Tishby, N.: The power of amnesia. In: Cowan, J.D., Tesauro, G., Alspector, J. (eds.) NIPS. Advances in NIPS, vol. 6, pp. 176–183. Morgan Kaufmann, San Francisco (1994)

    Google Scholar 

  • Sutskever, I., Hinton, G.E.: Learning multilevel distributed representations for high-dimensional sequences. Journal of ML Research - Proceedings Track 2, 548–555 (2007)

    Google Scholar 

  • Taylor, G.W., Hinton, G.E.: Factored conditional restricted Boltzmann machines for modeling motion style. In: Danyluk, A.P., Bottou, L., Littman, M.L. (eds.) ICML. ACM ICPS, vol. 382, p. 129. ACM, New York (2009)

    Google Scholar 

  • Taylor, G.W., Hinton, G.E., Roweis, S.T.: Modeling human motion using binary latent variables. In: Schölkopf, B., Platt, J.C., Hoffman, T. (eds.) NIPS. Advances in NIPS, vol. 19, pp. 1345–1352. MIT Press, Cambridge (2007)

    Google Scholar 

  • Weiland, M., Smaill, A., Nelson, P.: Learning musical pitch structures with hierarchical hidden Markov models. Technical report, University of Edinburgh (2005)

    Google Scholar 

  • Welling, M., Rosen-Zvi, M., Hinton, G.E.: Exponential family harmoniums with an application to information retrieval. In: NIPS. Advances in NIPS, vol. 17 (2004)

    Google Scholar 

  • Wood, F., Archambeau, C., Gasthaus, J., James, L., Teh, Y.W.: A stochastic memoizer for sequence data. In: Danyluk, A.P., Bottou, L., Littman, M.L. (eds.) ICML. ACM ICPS, vol. 382, p. 142. ACM, New York (2009)

    Google Scholar 

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Spiliopoulou, A., Storkey, A. (2011). Comparing Probabilistic Models for Melodic Sequences. In: Gunopulos, D., Hofmann, T., Malerba, D., Vazirgiannis, M. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2011. Lecture Notes in Computer Science(), vol 6913. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23807-9

  • Online ISBN: 978-3-642-23808-6

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