Inference of ω-languages from prefixes

Büchi automata are used to recognize languages of infinite strings. Such languages have been introduced to describe the behavior of real-time systems or infinite games. The question of inferring them from infinite examples has already been studied, but it may seem more reasonable to believe that the data from which we want to learn is a set of finite strings, namely the prefixes of accepted or rejected infinite strings. We describe the problems of identification in the limit and polynomial identification in the limit from given data associated to different interpretations of these prefixes: a positive prefix is universal (respectively existential) when all the infinite strings of which it is a prefix are in the language (respectively when at least one is); the same applies to the negative prefixes. We prove that the classes of regular ω-languages (those recognized by Büchi automata) and of deterministic ω-languages (those recognized by deterministic Büchi automata) are not identifiable in the limit, whatever interpretation for the prefixes is taken. We give a polynomial algorithm that identifies the class of safe languages from positive existential prefixes and negative universal prefixes. We show that this class is maximal for polynomial identification in the limit from given data, in the sense that no superclass can even be identified in the limit

A boosting approach to multiview classification with cooperation

International audienceNowadays in numerous fields such as bioinformatics or multimedia, data may be described using many different sets of features (or views) which carry either global or local information. Many learning tasks make use of these competitive 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 learnt independently the ones from the others. One drawback of these methods is that the classifier learnt on one view does not communicate its lack to the other views. In other words, learning algorithms do not cooperate although they are trained on the same objects. This paper deals with a novel approach to integrate multiview information within an iterative learning scheme, where the classifier learnt on one view is allowed to somehow communicate its performances to the other views. 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. Such an approach is merely useful when some examples detected as outliers in a view -- for instance because of noise -- are quite probabilisticaly regular hence informative within some other view. This paper provides the Mumbo algorithm in a multiclass and multiview setting, based on recent advances in theoretical boosting. The boosting properties of Mumbo are proven, as well as a some results on its generalization capabilities. Several experimental results are reported which point out that complementary views may actually cooperate under some assumptions

Multiview Learning of Weighted Majority Vote by Bregman Divergence Minimization

International audienceWe tackle the issue of classifier combinations when observations have multiple views. Our method jointly learns view-specific weighted majority vote classifiers (i.e. for each view) over a set of base voters, and a second weighted majority vote classifier over the set of these view-specific weighted majority vote classifiers. We show that the empirical risk minimization of the final majority vote given a multiview training set can be cast as the minimization of Bregman divergences. This allows us to derive a parallel-update optimization algorithm for learning our multiview model. We empirically study our algorithm with a particular focus on the impact of the training set size on the multiview learning results. The experiments show that our approach is able to overcome the lack of labeled information

Experiment for Regional Sources and Sinks of Oxidants (EXPRESSO): An overview

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