Representation Discovery using Harmonic Analysis

Representations are at the heart of artificial intelligence (AI). This book is devoted to the problem of representation discovery: how can an intelligent system construct representations from its experience? Representation discovery re-parameterizes the state space - prior to the application of information retrieval, machine learning, or optimization techniques - facilitating later inference processes by constructing new task-specific bases adapted to the state space geometry. This book presents a general approach to representation discovery using the framework of harmonic analysis, in particular Fourier and wavelet analysis. Biometric compression methods, the compact disc, the computerized axial tomography (CAT) scanner in medicine, JPEG compression, and spectral analysis of time-series data are among the many applications of classical Fourier and wavelet analysis. A central goal of this book is to show that these analytical tools can be generalized from their usual setting in (infinite-dimensional) Euclidean spaces to discrete (finite-dimensional) spaces typically studied in many subfields of AI. Generalizing harmonic analysis to discrete spaces poses many challenges: a discrete representation of the space must be adaptively acquired; basis functions are not pre-defined, but rather must be constructed. Algorithms for efficiently computing and representing bases require dealing with the curse of dimensionality. However, the benefits can outweigh the costs, since the extracted basis functions outperform parametric bases as they often reflect the irregular shape of a particular state space. Case studies from computer graphics, information retrieval, machine learning, and state space planning are used to illustrate the benefits of the proposed framework, and the challenges that remain to be addressed. Representation discovery is an actively developing field, and the author hopes this book will encourage other researchers to explore this exciting area of research. Table of Contents: Overview / Vector Spaces / Fourier Bases on Graphs / Multiscale Bases on Graphs / Scaling to Large Spaces / Case Study: State-Space Planning / Case Study: Computer Graphics / Case Study: Natural Language / Future Directions

Overview.- Vector Spaces.- Fourier Bases on Graphs.- Multiscale Bases on Graphs.- Scaling to Large Spaces.- Case Study: State-Space Planning.- Case Study: Computer Graphics.- Case Study: Natural Language.- Future Directions.

Dr. Sridhar Mahadevan is an Associate Professor in the Department of Computer Science at the University of Massachusetts, Amherst. He received his PhD from Rutgers University in 1990. Professor Mahadevan's research interests span several subfields of artificial intelligence and computer science, including machine learning, multi-agent systems, planning, perception, and robotics. His PhD thesis introduced the learning apprentice model of knowledge acquisition from experts, as well as a rigorous study of concept learning with prior determination knowledge using the framework of Probably Approximately Correct (PAC) learning. In 1993, he co-edited (with Jonathan Connell) the book Robot Learning published by Kluwer Academic Press, one of the first books on the application of machine learning to robotics. Over the past decade, his research has centered around Markov decision processes and reinforcement learning, where his papers are among the most cited in the field. His recent work on spectral and wavelet methods for Markov decision processes has generated much attention, leading to a unified framework for learning representation and behavior. Professor Mahadevan is an Associate Editor for the Journal of Machine Learning Research. Previously, he served for many years as an Associate Editor for Journal of AI Research and the Machine Learning Journal. He has been on numerous program committees for AAAI, ICML, IJCAI, NIPS, ICRA, and IROS conferences, including area chair for at AAAI, ICML, and NIPS conferences. In 2001, he co-authored a paper with his students Rajbala Makar and Mohammad Ghavamzadeh that received the best student paper award in the 5th International Conference on Autonomous Agents. In 1999, he co-authored a paper with Gang Wang that received the best paper award (runner-up) at the 16th International Conference on Machine Learning. He was an invited tutorial speaker at ICML 2006, IJCAI 2007, and AAAI 2007.