Skip to main content

2017 | OriginalPaper | Buchkapitel

PAC-Bayesian Analysis for a Two-Step Hierarchical Multiview Learning Approach

verfasst von : Anil Goyal, Emilie Morvant, Pascal Germain, Massih-Reza Amini

Erschienen in: Machine Learning and Knowledge Discovery in Databases

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We study a two-level multiview learning with more than two views under the PAC-Bayesian framework. This approach, sometimes referred as late fusion, consists in learning sequentially multiple view-specific classifiers at the first level, and then combining these view-specific classifiers at the second level. Our main theoretical result is a generalization bound on the risk of the majority vote which exhibits a term of diversity in the predictions of the view-specific classifiers. From this result it comes out that controlling the trade-off between diversity and accuracy is a key element for multiview learning, which complements other results in multiview learning. Finally, we experiment our principle on multiview datasets extracted from the Reuters RCV1/RCV2 collection.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Anhänge
Nur mit Berechtigung zugänglich
Fußnoten
1
The fusion of descriptions, resp. of models, is sometimes called Early Fusion, resp. Late Fusion.
 
2
Our notion of hyper-prior and hyper-posterior distributions is different than the one proposed for lifelong learning [25], where they basically consider hyper-prior and hyper-posterior over the set of possible priors: The prior distribution P over the voters’ set is viewed as a random variable.
 
4
We use linear SVM model as it is usually done for text classification tasks [e.g., 12].
 
Literatur
1.
Zurück zum Zitat Amini, M.-R., Usunier, N., Goutte, C.: Learning from multiple partially observed views - an application to multilingual text categorization. In: NIPS, pp. 28–36 (2009) Amini, M.-R., Usunier, N., Goutte, C.: Learning from multiple partially observed views - an application to multilingual text categorization. In: NIPS, pp. 28–36 (2009)
2.
Zurück zum Zitat Atrey, P.K., Hossain, M.A., El-Saddik, A., Kankanhalli, M.S.: Multimodal fusion for multimedia analysis: a survey. Multimedia Syst. 16(6), 345–379 (2010)CrossRef Atrey, P.K., Hossain, M.A., El-Saddik, A., Kankanhalli, M.S.: Multimodal fusion for multimedia analysis: a survey. Multimedia Syst. 16(6), 345–379 (2010)CrossRef
3.
Zurück zum Zitat Bégin, L., Germain, P., Laviolette, F., Roy, J.-F.: PAC-Bayesian bounds based on the Rényi divergence. In: AISTATS, pp. 435–444 (2016) Bégin, L., Germain, P., Laviolette, F., Roy, J.-F.: PAC-Bayesian bounds based on the Rényi divergence. In: AISTATS, pp. 435–444 (2016)
4.
Zurück zum Zitat Blum, A., Mitchell, T.M.: Combining Labeled and Unlabeled Data with Co-training. In: COLT, pp. 92–100 (1998) Blum, A., Mitchell, T.M.: Combining Labeled and Unlabeled Data with Co-training. In: COLT, pp. 92–100 (1998)
5.
Zurück zum Zitat Catoni, O.: PAC-Bayesian Supervised Classification: The Thermodynamics of Statistical Learning, vol. 56. Institute of Mathematical Statistic, Shaker Heights (2007)MATH Catoni, O.: PAC-Bayesian Supervised Classification: The Thermodynamics of Statistical Learning, vol. 56. Institute of Mathematical Statistic, Shaker Heights (2007)MATH
6.
Zurück zum Zitat Chapelle, O., Schlkopf, B., Zien, A.: Semi-Supervised Learning, 1st edn. The MIT Press, Cambridge (2010). ISBN 0262514125, 9780262514125 Chapelle, O., Schlkopf, B., Zien, A.: Semi-Supervised Learning, 1st edn. The MIT Press, Cambridge (2010). ISBN 0262514125, 9780262514125
7.
Zurück zum Zitat Cortes, C., Vapnik, V.: Support-vector networks. Mach. Learn. 20(3), 273–297 (1995)MATH Cortes, C., Vapnik, V.: Support-vector networks. Mach. Learn. 20(3), 273–297 (1995)MATH
8.
Zurück zum Zitat Donsker, M.D., Varadhan, S.S.: Asymptotic evaluation of certain markov process expectations for large time, I. Commun. Pure Appl. Math. 28(1), 1–47 (1975)MathSciNetCrossRefMATH Donsker, M.D., Varadhan, S.S.: Asymptotic evaluation of certain markov process expectations for large time, I. Commun. Pure Appl. Math. 28(1), 1–47 (1975)MathSciNetCrossRefMATH
9.
Zurück zum Zitat Germain, P., Lacasse, A., Laviolette, F., Marchand, M.: PAC-Bayesian learning of linear classifiers. In: ICML, pp. 353–360 (2009) Germain, P., Lacasse, A., Laviolette, F., Marchand, M.: PAC-Bayesian learning of linear classifiers. In: ICML, pp. 353–360 (2009)
10.
Zurück zum Zitat Germain, P., Lacasse, A., Laviolette, F., Marchand, M., Roy, J.: Risk bounds for the majority vote: from a PAC-Bayesian analysis to a learning algorithm. JMLR 16, 787–860 (2015)MathSciNetMATH Germain, P., Lacasse, A., Laviolette, F., Marchand, M., Roy, J.: Risk bounds for the majority vote: from a PAC-Bayesian analysis to a learning algorithm. JMLR 16, 787–860 (2015)MathSciNetMATH
11.
Zurück zum Zitat Goyal, A., Morvant, E., Germain, P., Amini, M.-R.: PAC-Bayesian analysis for a two-step hierarchical multiview learning approach. arXiv preprint arXiv:1606.07240 (2016) Goyal, A., Morvant, E., Germain, P., Amini, M.-R.: PAC-Bayesian analysis for a two-step hierarchical multiview learning approach. arXiv preprint arXiv:​1606.​07240 (2016)
12.
13.
Zurück zum Zitat Kuncheva, L.I.: Combining Pattern Classifiers: Methods and Algorithms. Wiley-Interscience, Hoboken (2004). ISBN 0471210781CrossRefMATH Kuncheva, L.I.: Combining Pattern Classifiers: Methods and Algorithms. Wiley-Interscience, Hoboken (2004). ISBN 0471210781CrossRefMATH
14.
Zurück zum Zitat Lacasse, A., Laviolette, F., Marchand, M., Germain, P., Usunier, N.: PAC-Bayes bounds for the risk of the majority vote and the variance of the Gibbs classifier. In: NIPS, pp. 769–776 (2006) Lacasse, A., Laviolette, F., Marchand, M., Germain, P., Usunier, N.: PAC-Bayes bounds for the risk of the majority vote and the variance of the Gibbs classifier. In: NIPS, pp. 769–776 (2006)
15.
Zurück zum Zitat Langford, J.: Tutorial on practical prediction theory for classification. JMLR 6, 273–306 (2005)MathSciNetMATH Langford, J.: Tutorial on practical prediction theory for classification. JMLR 6, 273–306 (2005)MathSciNetMATH
16.
Zurück zum Zitat Langford, J., Shawe-Taylor, J.: PAC-Bayes & margins. In: NIPS, pp. 423–430. MIT Press (2002) Langford, J., Shawe-Taylor, J.: PAC-Bayes & margins. In: NIPS, pp. 423–430. MIT Press (2002)
17.
Zurück zum Zitat Laviolette, F., Marchand, M., Roy, J.-F.: From PAC-Bayes bounds to quadratic programs for majority votes. In: ICML (2011) Laviolette, F., Marchand, M., Roy, J.-F.: From PAC-Bayes bounds to quadratic programs for majority votes. In: ICML (2011)
19.
Zurück zum Zitat Lehmann, E.: Nonparametric Statistical Methods Based on Ranks. McGraw-Hill, New York (1975)MATH Lehmann, E.: Nonparametric Statistical Methods Based on Ranks. McGraw-Hill, New York (1975)MATH
21.
22.
Zurück zum Zitat McAllester, D.A.: PAC-Bayesian stochastic model selection. Mach. Learn. 51, 5–21 (2003)CrossRefMATH McAllester, D.A.: PAC-Bayesian stochastic model selection. Mach. Learn. 51, 5–21 (2003)CrossRefMATH
23.
24.
Zurück zum Zitat Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., Duchesnay, E.: Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011)MathSciNetMATH Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., Duchesnay, E.: Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011)MathSciNetMATH
25.
Zurück zum Zitat Pentina, A., Lampert, C.H.: A PAC-Bayesian bound for lifelong learning. In: ICML, pp. 991–999 (2014) Pentina, A., Lampert, C.H.: A PAC-Bayesian bound for lifelong learning. In: ICML, pp. 991–999 (2014)
26.
Zurück zum Zitat Roy, J.-F., Marchand, M., Laviolette, F.: A column generation bound minimization approach with PAC-Bayesian generalization guarantees. In: Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, pp. 1241–1249 (2016) Roy, J.-F., Marchand, M., Laviolette, F.: A column generation bound minimization approach with PAC-Bayesian generalization guarantees. In: Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, pp. 1241–1249 (2016)
27.
28.
Zurück zum Zitat Snoek, C., Worring, M., Smeulders, A.W.M.: Early versus late fusion in semantic video analysis. In: ACM Multimedia, pp. 399–402 (2005) Snoek, C., Worring, M., Smeulders, A.W.M.: Early versus late fusion in semantic video analysis. In: ACM Multimedia, pp. 399–402 (2005)
29.
Zurück zum Zitat Sun, S., Shawe-Taylor, J., Mao, L.: PAC-Bayes analysis of multi-view learning. CoRR, abs/1406.5614 (2016) Sun, S., Shawe-Taylor, J., Mao, L.: PAC-Bayes analysis of multi-view learning. CoRR, abs/1406.5614 (2016)
30.
Zurück zum Zitat Wolpert, D.H.: Stacked generalization. Neural Netw. 5(2), 241–259 (1992)CrossRef Wolpert, D.H.: Stacked generalization. Neural Netw. 5(2), 241–259 (1992)CrossRef
Metadaten
Titel
PAC-Bayesian Analysis for a Two-Step Hierarchical Multiview Learning Approach
verfasst von
Anil Goyal
Emilie Morvant
Pascal Germain
Massih-Reza Amini
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-71246-8_13