This paper presents predictive gain scheduling, a technique for simplify(cid:173) ing reinforcement learning problems by decomposition. Link admission control of self-similar call traffic is used to demonstrate the technique. The control problem is decomposed into on-line prediction of near-fu(cid:173) ture call arrival rates, and precomputation of policies for Poisson call ar(cid:173) rival processes. At decision time, the predictions are used to select among the policies. Simulations show that this technique results in sig(cid:173) nificantly faster learning without any performance loss, compared to a reinforcement learning controller that does not decompose the problem.

In this paper we introduce a new sparseness inducing prior which does not involve any (hy- per)parameters that need to be adjusted or estimated. Although other applications are possi- ble, we focus here on supervised learning problems: regression and classification. Experi- ments with several publicly available benchmark data sets show that the proposed approach yields state-of-the-art performance. In particular, our method outperforms support vector machines and performs competitively with the best alternative techniques, both in terms of error rates and sparseness, although it involves no tuning or adjusting of sparseness- controlling hyper-parameters.

Learning curves for Gaussian process regression are well understood when the'student' model happens to match the'teacher' (true data generation process). I derive approximations to the learning curves for the more generic case of mismatched models, and find very rich behaviour: For large input space dimensionality, where the results become exact, there are universal (student-independent) plateaux in the learning curve, with transitions in between that can exhibit arbitrarily many over-fitting maxima; over-fitting can occur even if the student estimates the teacher noise level correctly. In lower dimensions, plateaux also appear, and the learning curve remains dependent on the mismatch between student and teacher even in the asymptotic limit of a large number of training examples. Learn(cid:173) ing with excessively strong smoothness assumptions can be partic(cid:173) ularly dangerous: For example, a student with a standard radial basis function covariance function will learn a rougher teacher func(cid:173) tion only logarithmically slowly. All predictions are confirmed by simulations.

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. Moreover, unlike in batch learning where the -trick only applies to the -insensitive loss function we are able to derive gen- eral trimmed-mean types of estimators such as for Huber's robust loss.

Greedy approximation algorithms have been frequently used to obtain sparse solutions to learning problems. In this paper, we present a general greedy algorithm for solving a class of convex optimization problems. We derive a bound on the rate of approximation for this algorithm, and show that our algorithm includes a number of earlier studies as special cases.

We investigate the generalization performance of some learning prob- lems in Hilbert functional Spaces. We introduce a notion of convergence of the estimated functional predictor to the best underlying predictor, and obtain an estimate on the rate of the convergence. This estimate allows us to derive generalization bounds on some learning formulations.

We present a new approach to the supervised learning of lateral inter- actions for the competitive layer model (CLM) dynamic feature binding architecture. The method is based on consistency conditions, which were recently shown to characterize the attractor states of this linear threshold recurrent network. For a given set of training examples the learning prob- lem is formulated as a convex quadratic optimization problem in the lat- eral interaction weights. An efficient dimension reduction of the learning problem can be achieved by using a linear superposition of basis inter- actions. We show the successful application of the method to a medical image segmentation problem of fluorescence microscope cell images.

We study online learning in Boolean domains using kernels which cap- ture feature expansions equivalent to using conjunctions over basic fea- tures. We demonstrate a tradeoff between the computational efficiency with which these kernels can be computed and the generalization abil- ity of the resulting classifier. We first describe several kernel functions which capture either limited forms of conjunctions or all conjunctions. We show that these kernels can be used to efficiently run the Percep- tron algorithm over an exponential number of conjunctions; however we also prove that using such kernels the Perceptron algorithm can make an exponential number of mistakes even when learning simple func- tions. We also consider an analogous use of kernel functions to run the multiplicative-update Winnow algorithm over an expanded feature space of exponentially many conjunctions.

In this paper we show that on-line algorithms for classification and re- gression can be naturally used to obtain hypotheses with good data- dependent tail bounds on their risk. Our results are proven without re- quiring complicated concentration-of-measure arguments and they hold for arbitrary on-line learning algorithms. Furthermore, when applied to concrete on-line algorithms, our results yield tail bounds that in many cases are comparable or better than the best known bounds.

We consider the learning problem of finding a dependency between a general class of objects and another, possibly different, general class of objects. The objects can be for example: vectors, images, strings, trees or graphs. Such a task is made possible by employing similarity measures in both input and output spaces using ker(cid:173) nel functions, thus embedding the objects into vector spaces.