Anil Goyal - Learning a Multiview Weighted Majority Vote Classifier: Using PAC-Bayesian Theory and Boosting

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Anil Goyal
Anil Goyal
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PhD defense will be in room D03 at Institut d’Optique Graduate School, 18 Rue du Professeur Benoît Lauras, 42000 Saint-Etienne.


  • Prof. Jean-Christophe Janodet, Université d’Évry, Évry (Rapporteur)
  • Dr Cécile Capponi, Aix-Marseille Université, Marseille  (Rapportrice)
  • Prof. Amaury Habrard, Université Jean Monnet, Saint-Etienne (Examinateur)
  • Prof. Massih-Reza Amini, Université de Grenoble-Alpes, Grenoble (Directeur)
  • Dr Emilie Morvant, Université Jean Monnet, Saint-Etienne (Co-directrice)



With tremendous generation of data, we have data collected from different information sources having heterogeneous properties, thus it is important to consider these representations or views of the data. This problem of machine learning is referred as multiview learning. It has many applications in other domains for e.g. in medical imaging, we can represent human brain with different set of features for example MRI, t-fMRI, EEG, etc. In this thesis, we focus on supervised multiview learning, where we see multiview learning as combination of different view-specific classifiers or views. Therefore, according to our point of view, it is interesting to tackle multiview learning issue through PAC-Bayesian framework. It is an interesting theoretical tool to understand this setting as it allows to directly capture the trade-off between accuracy and diversity between voters. In consequence, we have extended the single-view PAC-Bayesian analysis to multiview learning with more than two views. We considered a two-level hierarchy of distributions over the view-specific voters and the views. Based on this strategy, we derived PAC-Bayesian generalization bounds (both probabilistic and expected risk bounds) for multiview learning. From practical point of view, we designed two multiview learning algorithms based on our two-level PAC-Bayesian strategy. The first algorithm is a one-step boosting based multiview learning algorithm called as PB-MVBoost. It iteratively learns the weights over the views by optimizing the multiview C-Bound which controls the trade-off between the accuracy and the diversity between the views. The second algorithm is based on late fusion approach where we combine the predictions of view-specific classifiers using the PAC-Bayesian algorithm CqBoost which controls the trade-off between the accuracy and the diversity between the view-specific classifiers. Finally, we show that minimization of classification error for multiview weighted majority vote is equivalent to the minimization of Bregman divergences. This allowed us to derive a parallel update optimization algorithm (referred as MωMvC2) to learn our multiview weighted majority vote.