Researchers in many disciplines face the formidable task of analyzing massive amounts of high-dimensional and highly-structured data. This is due in part to recent advances in data collection and computing technologies. As a result, fundamental statistical research is being undertaken in a variety of different fields. Driven by the complexity 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 signal processing. The development of new, flexible methods combines advances from many sources, including approximation theory, numerical analysis, machine learning, signal processing and statistics. The proposed workshop intends to bring together eminent experts from these fields in order to exchange ideas and forge directions for the future.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 newproblems, 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 compressionand 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 differeló²