| Abstract: |
Many machine learning problems on data can naturally be formulated as problems on graphs. For example, dimensionality reduction and visualization are related to graph embedding. Given a sparse graph between N high-dimensional data nodes, how do we faithfully embed it in low dimension? We present an algorithm that improves dimensionality reduction by extending the Maximum Variance Unfolding method. But, given only a dataset of N samples, how do we construct a sparse graph in the first place? The space to explore is daunting with 2^(N2) graphs to choose from yet two interesting subfamilies are tractable: matchings and b-matchings. By placing distributions over matchings and using loopy belief propagation, we efficiently infer the optimal graph. Higher order inference over matchings is also efficient via fast Fourier algorithms. Matching not only has intriguing algebraic properties, it also leads to improvements in graph reconstruction, graph embedding, graph labeling, and graph partitioning. We show results on text, network and image data. Time permitting, we will show results on location data from millions of tracked mobile phone users which lets us discover patterns of human behavior, networks of places and networks of people. |
| Speaker Bio: |
Tony Jebara is Associate Professor of Computer Science at Columbia University and director of the Columbia Machine Learning Laboratory. His research intersects computer science and statistics to develop new frameworks for learning from data with applications in vision, networks, spatio-temporal data, and text. Tony is also co-founder of Sense Networks. He has published over 50 peer-reviewed papers in conferences and journals including NIPS, ICML, UAI, COLT, JMLR, Science, CVPR, ICCV, and AISTAT. He is the author of the book Machine Learning: Discriminative and Generative. Tony is the recipient of the Career award from the National Science Foundation and has also received honors for his papers from the International Conference on Machine Learning and the Pattern Recognition Society. Tony's research has been featured on television (ABC, BBC, New York One, TechTV, etc.) as well as in the popular press (New York Times, Slash Dot, Wired, Scientific American, Newsweek, etc.). He obtained his PhD in 2002 from MIT. Recently, Esquire magazine named him one of their Best and Brightest of 2008. Tony's lab is supported in part by the NSF, CIA, NSA, DHS, and ONR . |