For a dichotomy, concept drift means that the classification function changes over time. We want to extend the theoretical analyses of learning to include time-varying concepts; to explore the behavior of current learning algorithms in the face of concept drift; and to devise tracking algorithms to better handle concept drift. In this paper, we briefly describe our theoretical model and then present the results of simulations *kuh@wiliki.eng.hawaii.edu

For a dichotomy, concept drift means that the classification function changes over time. We want to extend the theoretical analyses of learning to include time-varying concepts; to explore the behavior of current learning algorithms in the face of concept drift; and to devise tracking algorithms to better handle concept drift. In this paper, we briefly describe our theoretical model and then present the results of simulations *kuh@wiliki.eng.hawaii.edu

This work extends computational learning theory to situations in which concepts vary over time, e.g., system identification of a time-varying plant. We have extended formal definitions of concepts and learning to provide a framework in which an algorithm can track a concept as it evolves over time. Given this framework and focusing on memory-based algorithms, we have derived some PACstyle sample complexity results that determine, for example, when tracking is feasible. We have also used a similar framework and focused on incremental tracking algorithms for which we have derived some bounds on the mistake or error rates for some specific concept classes. 1 INTRODUCTION The goal of our ongoing research is to extend computational learning theory to include concepts that can change or evolve over time. For example, face recognition is complicated by the fact that a persons face changes slowly with age and more quickly with changes in make up, hairstyle, or facial hair.

This work extends computational learning theory to situations in which concepts vary over time, e.g., system identification of a time-varying plant. We have extended formal definitions of concepts and learning to provide a framework in which an algorithm can track a concept as it evolves over time. Given this framework and focusing on memory-based algorithms, we have derived some PACstyle sample complexity results that determine, for example, when tracking is feasible. We have also used a similar framework and focused on incremental tracking algorithms for which we have derived some bounds on the mistake or error rates for some specific concept classes. 1 INTRODUCTION The goal of our ongoing research is to extend computational learning theory to include concepts that can change or evolve over time. For example, face recognition is complicated by the fact that a persons face changes slowly with age and more quickly with changes in make up, hairstyle, or facial hair.

This work extends computational learning theory to situations in which concepts vary over time, e.g., system identification of a time-varying plant. We have extended formal definitions of concepts and learning to provide a framework in which an algorithm can track a concept as it evolves over time. Given this framework and focusing on memory-based algorithms, we have derived some PACstyle sample complexity results that determine, for example, when tracking is feasible. We have also used a similar framework and focused on incremental tracking algorithms for which we have derived some bounds on the mistake or error rates for some specific concept classes. 1 INTRODUCTION The goal of our ongoing research is to extend computational learning theory to include concepts that can change or evolve over time. For example, face recognition is complicated bythe fact that a persons face changes slowly with age and more quickly with changes in make up, hairstyle, or facial hair.

We consider a 2-layer, 3-node, n-input neural network whose nodes compute linear threshold functions of their inputs. We show that it is NPcomplete to decide whether there exist weights and thresholds for the three nodes of this network so that it will produce output consistent witha given set of training examples. We extend the result to other simple networks. This result suggests that those looking for perfect training algorithms cannot escape inherent computational difficulties just by considering only simple or very regular networks. It also suggests the importance, given a training problem, of finding an appropriate network and input encoding for that problem. It is left as an open problem to extend our result to nodes with nonlinear functions such as sigmoids.

We consider a 2-layer, 3-node, n-input neural network whose nodes compute linear threshold functions of their inputs. We show that it is NPcomplete to decide whether there exist weights and thresholds for the three nodes of this network so that it will produce output consistent with a given set of training examples. We extend the result to other simple networks. This result suggests that those looking for perfect training algorithms cannot escape inherent computational difficulties just by considering only simple or very regular networks. It also suggests the importance, given a training problem, of finding an appropriate network and input encoding for that problem. It is left as an open problem to extend our result to nodes with nonlinear functions such as sigmoids.