In this paper we show that online algorithms for classification and regression canbe naturally used to obtain hypotheses with good datadependent tailbounds on their risk. Our results are proven without requiring complicated concentration-of-measure arguments and they hold for arbitrary online learning algorithms. Furthermore, when applied to concrete online algorithms, our results yield tail bounds that in many cases are comparable or better than the best known bounds.

We consider online learning in a Reproducing Kernel Hilbert Space. Our method is computationally efficient and leads to simple algorithms. In particular we derive update equations for classification, regression, and novelty detection. The inclusion of the -trick allows us to give a robust parameterization.

We present a method for determining the globally optimal online learning rule for a soft committee machine under a statistical mechanics framework. This work complements previous results on locally optimal rules, where only the rate of change in generalization error was considered. We maximize the total reduction in generalization error over the whole learning process and show how the resulting rule can significantly outperform the locally optimal rule. 1 Introduction We consider a learning scenario in which a feed-forward neural network model (the student) emulates an unknown mapping (the teacher), given a set of training examples produced by the teacher. The performance of the student network is typically measured by its generalization error, which is the expected error on an unseen example. The aim of training is to reduce the generalization error by adapting the student network's parameters appropriately. A common form of training is online learning, where training patterns are presented sequentially and independently to the network at each learning step.

Online learning is one of the most common forms of neural network training. We present an analysis of online learning from finite training sets for nonlinear networks (namely, soft-committee machines), advancing the theory to more realistic learning scenarios. Dynamical equations are derived for an appropriate set of order parameters; these are exact in the limiting case of either linear networks or infinite training sets. Preliminary comparisons with simulations suggest that the theory captures some effects of finite training sets, but may not yet account correctly for the presence of local minima.

Online learning is one of the most common forms of neural network training. We present an analysis of online learning from finite training sets for nonlinear networks (namely, soft-committee machines), advancing the theory to more realistic learning scenarios. Dynamical equations are derived for an appropriate set of order parameters; these are exact in the limiting case of either linear networks or infinite training sets. Preliminary comparisons with simulations suggest that the theory captures some effects of finite training sets, but may not yet account correctly for the presence of local minima.

We present a method for determining the globally optimal online learning rule for a soft committee machine under a statistical mechanics framework. This work complements previous results on locally optimal rules, where only the rate of change in generalization error was considered. We maximize the total reduction in generalization error over the whole learning process and show how the resulting rule can significantly outperform the locally optimal rule. 1 Introduction We consider a learning scenario in which a feed-forward neural network model (the student) emulates an unknown mapping (the teacher), given a set of training examples produced by the teacher. The performance of the student network is typically measured by its generalization error, which is the expected error on an unseen example. The aim of training is to reduce the generalization error by adapting the student network's parameters appropriately. A common form of training is online learning, where training patterns are presented sequentially and independently to the network at each learning step.

We present a method for determining the globally optimal online learning rule for a soft committee machine under a statistical mechanics framework. This work complements previous results on locally optimal rules, where only the rate of change in generalization the total reduction inerror was considered. We maximize the whole learning process and show howgeneralization error over the resulting rule can significantly outperform the locally optimal rule. 1 Introduction We consider a learning scenario in which a feed-forward neural network model (the an unknown mapping (the teacher), given a set of training examplesstudent) emulates The performance of the student network is typicallyproduced by the teacher. A common form of training is online learning, where training patterns are presented sequentially and independently to the network at each learning step. This form of training can be beneficial in terms of both storage and computation time, especially for large systems.

Online learning is one of the most common forms of neural network training.We present an analysis of online learning from finite training sets for nonlinear networks (namely, soft-committee machines), advancingthe theory to more realistic learning scenarios. Dynamical equations are derived for an appropriate set of order parameters; these are exact in the limiting case of either linear networks or infinite training sets. Preliminary comparisons with simulations suggest that the theory captures some effects of finite training sets, but may not yet account correctly for the presence of local minima.

By an extension of statistical mechanics methods, we obtain exact results for the time-dependent generalization error of a linear network with a large number of weights N. We find, for example, that for small training sets of size p N, larger learning rates can be used without compromising asymptotic generalization performance or convergence speed. Encouragingly, for optimal settings of TJ (and, less importantly, weight decay,\) at given final learning time, the generalization performance of online learning is essentially as good as that of offline learning.

An adaptive online algorithm extending the learning of learning idea is proposed and theoretically motivated. Relying only on gradient flow information it can be applied to learning continuous functions or distributions, even when no explicit loss function is given and the Hessian is not available. Its efficiency is demonstrated for a non-stationary blind separation task of acoustic signals.