We explore methods for incorporating prior knowledge about a problem at hand in Support Vector learning machines. We show that both invariances undergroup transfonnations and prior knowledge about locality in images can be incorporated by constructing appropriate kernel functions.

This idea has been extended compute the relative Hessian by (Pham, 1996).

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.

Peter Dayan E25-210, MIT Cambridge, MA 02139 We provide a model of the standard watermaze task, and of a more challenging task involving novel platform locations, in which rats exhibit one-trial learning after a few days of training. The model uses hippocampal place cells to support reinforcement learning, and also, in an integrated manner, to build and use allocentric coordinates. 1 INTRODUCTION

It is known that humans can make finer discriminations between familiar sounds (e.g.

A new algorithm is presented which approximates the perceived visual similarity between images. The images are initially transformed intoa feature space which captures visual structure, texture and color using a tree of filters. Similarity is the inverse of the distance in this perceptual feature space. Using this algorithm we have constructed an image database system which can perform example based retrieval on large image databases. Using carefully constructed target sets, which limit variation to only a single visual characteristic, retrieval rates are quantitatively compared to those of standard methods. 1 Introduction Without supplementary information, there exists no way to directly measure the similarity between the content of images.

The generalization ability of a neural network can sometimes be improved dramatically by regularization. To analyze the improvement oneneeds more refined results than the asymptotic distribution ofthe weight vector. Here we study the simple case of one-dimensional linear regression under quadratic regularization, i.e., ridge regression. We study the random design, misspecified case, where we derive expansions for the optimal regularization parameter andthe ensuing improvement. It is possible to construct examples where it is best to use no regularization.

Sleep staging is usually based on rules defined by Rechtschaffen and Kales (see [8]). Rechtschaffen and Kales rules define 4 sleep stages, stage one to four, as well as rapid eye movement (REM) and wakefulness. In [1] J. Bentrup and S. Ray report that every year nearly one million US citizens consulted their physicians concerning their sleep. Since sleep staging is a tedious task (one all night recording on average takes abou t 3 hours to score manually), much effort was spent in designing automatic sleep stagers. Sleep staging is a classification problem which was solved using classical statistical t.echniques or techniques emerged from the field of artificial intelligence (AI) .

An adaptive online algorithm is proposed to estimate hierarchical data structures for non-stationary data sources. The approach is based on the principle of minimum cross entropy to derive a decision tree for data clustering and it employs a metalearning idea (learning to learn) to adapt to changes in data characteristics. Its efficiency is demonstrated by grouping non-stationary artifical data and by hierarchical segmentation of LANDSAT images. 1 Introduction Unsupervised learning addresses the problem to detect structure inherent in unlabeled andunclassified data. N. The encoding usually is represented by an assignment matrix M (Mia), where Mia 1 if and only if Xi belongs to cluster L: 1 MiaV (Xi, Ya) measures the quality of a data partition, Le., optimal assignments and prototypes (M,y)OPt argminM,y1i (M,Y) minimize the inhomogeneity of clusters w.r.t. a given distance measure V. For reasons of simplicity we restrict the presentation to the ' sum-of-squared-error criterion V(x, y) To facilitate this minimization a deterministic annealing approach was proposed in [5] which maps the discrete optimization problem, i.e. how to determine the data assignments, viathe Maximum Entropy Principle [2] to a continuous parameter es- Unsupervised Online Learning ofDecision Trees for Data Analysis 515 timation problem.

Most previous work in inductive learning has concentrated on learning to classify. However, there are many applications in which it is desirable to order rather than classify instances. An example might be a personalized email filter that gives a priority ordering to unread mail. Here we will consider the problem of learning how to construct such orderings, given feedback in the form of preference judgments, i.e., statements that one instance should be ranked ahead of another. Such orderings could be constructed based on a learned classifier or regression model, and in fact often are.