We look at sequential classification and regression problems in which f\Sigma1g-labeled instances are given on-line, one at a time, and for each new instance, before seeing the label, the learning system must either predict the label, or estimate the probability that the label is +1. We look at the performance of Bayes method for this task, as measured by the total number of mistakes for the classification problem, and by the total log loss (or information gain) for the regression problem. Our results are given by comparing the performance of Bayes method to the performance of a hypothetical "omniscient scientist" who is able to use extra information about the labeling process that would not be available in the standard learning protocol. The results show that Bayes methods perform only slightly worse than the omniscient scientist in many cases. These results generalize previous results of Haussler, Kearns and Schapire, and Opper and Haussler. 1 Introduction Several recent papers in...

___________________________________ SUPERVISED COMPETITIVE LEARNING: A TECHNOLOGY FOR PEN-BASED ADAPTATION IN REAL TIME by Thomas H. Fuller, Jr. ___________________________________________________________ ADVISOR: Professor Takayuki Dan Kimura ___________________________________________________________ December, 1994 Saint Louis, Missouri ___________________________________________________________ The advent of affordable, pen-based computers promises wide application in educational and home settings. In such settings, systems will be regularly employed by a few users (children or students), and occasionally by other users (teachers or parents). The systems must adapt to the writing and gestures of regular users but not lose prior recognition ability. Furthermore, this adaptation must occur in real time not to frustrate or confuse the user, and not to interfere with the task at hand. It must also provide a reliable measure of the likelihood of correct recognition. Supervised Competitiv...