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We analyze a class of norms defined via an optimal interpolation problem involving the composition of norms and a linear operator. This construction, known as infimal postcomposition in convex analysis, is shown to encompass various norms which have been used as regularizers in machine learning, signal processing, and statistics. In particular, these include the latent group lasso, the overlapping group lasso, and certain norms used for learning tensors. We establish basic properties of this class of norms and we provide dual norms. The extension to more general classes of convex functions is also discussed. A stochastic block-coordinate version of the Douglas-Rachford algorithm is devised to solve minimization problems involving these regularizers. A prominent feature of the algorithm is that it yields iterates that converge to a solution in the case of nonsmooth losses and random block updates. Finally, we present numerical experiments with problems employing the latent group lasso penalty.

Disturbance of primary prospective motor control has been proposed to contribute to faults in higher mind functions of individuals with autism spectrum disorder, but little research has been conducted to characterize prospective control strategies in autism. In the current study, we applied pattern-classification analyses to kinematic features to verify whether children with autism spectrum disorder (ASD) and typically developing (TD) children altered their initial grasp in anticipation of self- and other-actions. Results indicate that children with autism adjusted their behavior to accommodate onward actions. The way they did so, however, varied idiosyncratically from one individual to another, which suggests that previous characterizations of general lack of prospective control strategies may be overly simplistic. These findings link abnormalities in anticipatory control with increased variability and offer insights into the difficulties that individuals with ASD may experience in social interaction.

This paper considers the least-square online gradient descent algorithm in a reproducing kernel Hilbert space (RKHS) without an explicit regularization term. We present a novel capacity independent approach to derive error bounds and convergence results for this algorithm. The essential element in our analysis is the interplay between the generalization error and a weighted cumulative error which we define in the paper. We show that, although the algorithm does not involve an explicit RKHS regularization term, choosing the step sizes appropriately can yield competitive error rates with those in the literature.

In this paper, we continue our study of learning an optimal kernel in a prescribed convex set of kernels (Micchelli & Pontil, 2005) . We present a reformulation of this problem within a feature space environment. This leads us to study regularization in the dual space of all continuous functions on a compact domain with values in a Hilbert space with a mix norm. We also relate this problem in a special case to $${\cal L}^p$$ regularization.

In this paper we first overview the main concepts of Statistical Learning Theory, a framework in which learning from examples can be studied in a principled way. We then briefly discuss well known as well as emerging learning techniques such as Regularization Networks and Support Vector Machines which can be justified in term of the same induction principle.

Regularization Networks and Support Vector Machines are techniques for solving certain problems of learning from examples – in particular, the regression problem of approximating a multivariate function from sparse data. Radial Basis Functions, for example, are a special case of both regularization and Support Vector Machines. We review both formulations in the context of Vapnik's theory of statistical learning which provides a general foundation for the learning problem, combining functional analysis and statistics. The emphasis is on regression: classification is treated as a special case.