Abstract. In many fields, such as bioinformatics or multimedia, data may be described using different sets of features (or views) which carry either global or local information. Some learning tasks make use of these several views in order to improve overall predictive power of classifiers through fusion-based methods. Usually, these approaches rely on a weighted combination of classifiers (or selected descriptions), where classifiers are learned independently. One drawback of these methods is that the classifier learned on one view does not communicate its failures within the other views. This paper deals with a novel approach to integrate multiview information. The proposed algorithm, named Mumbo, is based on boosting. Within the boosting scheme, Mumbo maintains one distribution of examples on each view, and at each round, it learns one weak classifier on each view. Within a view, the distribution of examples evolves both with the ability of the dedicated classifier to deal with examples of the corresponding features space, and with the ability of classifiers in other views to process the same examples within their own description spaces. Hence, the principle is to slightly remove the hard examples from the learning space of one view, while their weights get higher in the other views. This way, we expect that examples are urged to be processed by the most appropriate views, when possible. At the end of the iterative learning process, a final classifier is computed by a weighted combination of selected weak classifiers.This paper provides the Mumbo algorithm in a multiclass and multiview setting, based on recent theoretical advances in boosting. The boosting properties of Mumbo are proved, as well as some results on its generalization capabilities. Several experimental results are reported which point out that complementary views may actually cooperate under some assumptions.

Several sparsity-constrained algorithms, such as orthogonal matching pursuit (OMP) or the Frank-Wolfe (FW) algorithm, with sparsity constraints work by iteratively selecting a novel atom to add to the current nonzero set of variables. This selection step is usually performed by computing the gradient and then by looking for the gradient component with maximal absolute entry. This step can be computationally expensive especially for large-scale and high-dimensional data. In this paper, we aim at accelerating these sparsity-constrained optimization algorithms by exploiting the key observation that, for these algorithms to work, one only needs the coordinate of the gradient's top entry. Hence, we introduce algorithms based on greedy methods and randomization approaches that aim at cheaply estimating the gradient and its top entry. Another of our contribution is to cast the problem of finding the best gradient entry as a best-arm identification in a multiarmed bandit problem. Owing to this novel insight, we are able to provide a bandit-based algorithm that directly estimates the top entry in a very efficient way. Theoretical observations stating that the resulting inexact FW or OMP algorithms act, with high probability, similar to their exact versions are also given. We have carried out several experiments showing that the greedy deterministic and the bandit approaches we propose can achieve an acceleration of an order of magnitude while being as efficient as the exact gradient when used in algorithms, such as OMP, FW, or CoSaMP.

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