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This paper generalizes an important result from the PAC-Bayesian literature for binary classification to the case of ensemble methods for structured outputs. We prove a generic version of the Cbound, an upper bound over the risk of models expressed as a weighted majority vote that is based on the first and second statistical moments of the votes margin. This bound may advantageously $(i)$ be applied on more complex outputs such as multiclass labels and multilabel, and $(ii)$ allow to consider margin relaxations. These results open the way to develop new ensemble methods for structured output prediction with PAC-Bayesian guarantees.
The C-bound, introduced in Lacasse et al., gives a tight upper bound on the risk of a binary majority vote classifier. In this work, we present a first step towards extending this work to more complex outputs, by providing generalizations of the C-bound to the multiclass and multi-label settings.
In machine learning we often encounter structured output prediction problems (SOPPs), i.e. problems where the output space admits a rich internal structure. Application domains where SOPPs naturally occur include natural language processing, speech r
This paper introduces a generalization of Convolutional Neural Networks (CNNs) from low-dimensional grid data, such as images, to graph-structured data. We propose a novel spatial convolution utilizing a random walk to uncover the relations within th
Several real problems ranging from text classification to computational biology are characterized by hierarchical multi-label classification tasks. Most of the methods presented in literature focused on tree-structured taxonomies, but only few on tax
Over-parameterization and adaptive methods have played a crucial role in the success of deep learning in the last decade. The widespread use of over-parameterization has forced us to rethink generalization by bringing forth new phenomena, such as imp