Researchers in many disciplines now face the formidable task of processing massive amounts of high-dimensional and highly structured data. Advances in data collection and information technologies have coupled with innovations in computing to make commonplace the task of learning from complex data. As a result, fundamental statistical research is being undertaken in a variety of different fields. Driven by the difficulty of these new problems, and fueled by the explosion of available computer power, highly adaptive, non-linear procedures are now essential components of modern ¿data analysis,¿ a term that we liberally interpret to include speech and pattern recognition, classification, data compression and image processing. The development of new, flexible methods combines advances from many sources, including approximation theory, numerical analysis, machine learning, signal processing and statistics. This volume collects 31 papers from a unique workshop designed to promote communication between these different disciplines. Held in the spring of 2001 at the Mathematical Sciences Research Institute in Berkeley, CA, the meeting brought together eminent experts from machine learning, artificial intelligence, applied mathematics, image analysis, signal processing, information theory, and optimization. In addition to presentations on fundamental methodological work, there were talks on complex applications like environmental modeling, network analysis, and bioinformatics. Statistics