We consider the hypothesis that systems learning aspects of visual perception may benefit from the use of suitably designed developmental progressions during training. Four models were trained to estimate motion velocities in sequences of visual images. Three of the models were "developmental models" in the sense that the nature of their input changed during the course of training. They received a relatively impoverished visual input early in training, and the quality of this input improved as training progressed. One model used a coarse-to-multiscale developmental progression (i.e. it received coarse-scale motion features early in training and finer-scale features were added to its input as training progressed), another model used a fine-to-multiscale progression, and the third model used a random progression.

Dimensionality reduction techniques such as principal component analysis and factor analysis are used to discover a linear mapping between high dimensional data samples and points in a lower dimensional subspace. In [6], Jojic and Frey introduced mixture of transformation-invariant component analyzers (MTCA) that can account for global transformations such as translations and rotations, perform clustering and learn local appearance deformations by dimensionality reduction.

The problem of super-resolution involves generating feasible higher resolution images, which are pleasing to the eye and realistic, from a given low resolution image. This might be attempted by using simplefilters for smoothing out the high resolution blocks or through applications where substantial prior information is used to imply the textures and shapes which will occur in the images. In this paper we describe an approach which lies between the two extremes. It is a generic unsupervised method which is usable in all domains, but goes beyond simple smoothing methods in what it achieves. We use a dynamic treelike architecture to model the high resolution data. Approximate conditioning on the low resolution image is achieved through a mean field approach.

We apply the replica method of Statistical Physics combined with a variational methodto the approximate analytical computation of bootstrap averages for estimating the generalization error. We demonstrate our approach onregression with Gaussian processes and compare our results with averages obtained by Monte-Carlo sampling.

Many control problems take place in continuous state-action spaces, e.g., as in manipulator robotics, where the control objective is often definedas finding a desired trajectory that reaches a particular goal state. While reinforcement learning offers a theoretical framework tolearn such control policies from scratch, its applicability to higher dimensional continuous state-action spaces remains rather limited to date. Instead of learning from scratch, in this paper we suggest to learn a desired complex control policy by transforming an existing simple canonical control policy. For this purpose, we represent canonical policies in terms of differential equations with well-defined attractor properties. By nonlinearly transforming the canonical attractor dynamics using techniques from nonparametric regression, almost arbitrary new nonlinear policies can be generated withoutlosing the stability properties of the canonical system.

Echo state networks (ESN) are a novel approach to recurrent neural network training. An ESN consists of a large, fixed, recurrent "reservoir" network, from which the desired output is obtained by training suitable output connection weights. Determination of optimal output weights becomes a linear, uniquely solvable task of MSE minimization. This article reviews the basic ideas and describes an online adaptation scheme based on the RLS algorithm known from adaptive linear systems. As an example, a 10th order NARMA system is adaptively identified.

In the Bayesian approach, regularization is achieved by specifying a prior distribution over the parameters and subsequently averaging over the posterior distribution. This regularization provides not only smoother estimates of the parameters compared to maximum likelihood but also guides the selection of model structures. It was pointed out in [6] that a very large scale parameter of the Dirichlet prior can degrade predictive accuracy due to severe regularization of the parameter estimates. We complement this discussion here and show that a very small scale parameter can lead to poor over-regularized structures when a product of (conjugate) Dirichlet priors is used over multinomial conditional distributions (Section 3). Section 4 demonstrates the effect of the scale parameter and how it can be calibrated. We focus on the class of Bayesian network models throughout this paper.

One of the first semi-supervised algorithms [1] was applied to web page classification. This is a typical example where the number of unlabeled examples can be made as large as possible since there are billions of web page, but labeling is expensive since it requires human intervention. Since then, there has been a lot of interest for this paradigm in the machine learning community; an extensive review of existing techniques can be found in [10]. It has been shown experimentally that under certain conditions, the decision function can be estimated more accurately, yielding lower generalization error [1, 4, 6]. However, in a discriminative framework, it is not obvious to determine how unlabeled data or even the perfect knowledge of the input distribution P(x) can help in the estimation of the decision function.

We introduce a novel learning algorithm for binary classification with hyperplane discriminants based on pairs of training points from opposite classes (dyadic hypercuts). This algorithm is further extended to nonlinear discriminants using kernel functions satisfying Mercer's conditions. An ensemble of simple dyadic hypercuts is learned incrementally by means of a confidence-rated version of AdaBoost, which provides a sound strategy for searching through the finite set of hypercut hypotheses. In experiments with real-world datasets from the UCI repository, the generalization performance of the hypercut classifiers was found to be comparable to that of SVMs and k-NN classifiers. Furthermore, the computational cost of classification (at run time) was found to be similar to, or better than, that of SVM. Similarly to SVMs, boosted dyadic kernel discriminants tend to maximize the margin (via AdaBoost). In contrast to SVMs, however, we offer an online and incremental learning machine for building kernel discriminants whose complexity (number of kernel evaluations) can be directly controlled (traded off for accuracy).

There are several reinforcement learning algorithms that yield approximate solutions for the problem of policy evaluation when the value function is represented with a linear function approximator. In this paper we show that each of the solutions is optimal with respect to a specific objective function.