With the recent phenomenal growth of the availability and connectivity of computing resources and the advent of e-commerce, more valuable and private data is being stored online than ever before. But with greater value and availability comes greater threat. In this talk we examine the information security problem of anomaly detection --- recognizing the occurrence of ``out of the ordinary'' events which may prove to be hazardous. We evaluate this problem as a machine learning task and describe the application of two machine learning techniques: instance-based learning (IBL) and hidden Markov models (HMMs). This work focuses on anomaly detection at the user level (as opposed to the network or system call level), which introduces a number of interesting and complex issues from a machine learning standpoint. In particular, we explore privacy, resource constraints, non-stationarity (a.k.a. concept drift), and performance issues and give empirical analyses based on real user data. We close with some thoughts on extensions to this work and on other areas of application.