Complexity versus Agreement for Many Views
Odalric-Ambrym Maillard and Nicolas Vayatis
Algorithmic Learning Theory, 20th International Conference
Lecture Notes in Computer Science
, Porto, Portugal
The paper considers the problem of semi-supervised multi-view classification, where each view corresponds to a Reproducing Kernel Hilbert Space. An algorithm based on co-regularization methods with extra penalty terms reflecting smoothness and general agreement properties is proposed. We first provide explicit tight control on the Rademacher (L 1) complexity of the corresponding class of learners for arbitrary many views, then give the asymptotic behavior of the bounds when the co-regularization term increases, making explicit the relation between consistency of the views and reduction of the search space. Since many views involve many parameters, we third provide a parameter selection procedure, based on the stability approach with clustering and localization arguments. To this aim, we give an explicit bound on the variance (L 2-diameter) of the class of functions. Finally we illustrate the algorithm through simulations on toy examples.