Given a graph between N high-dimensional nodes, can we faithfully visualize it in just a few dimensions? We present an algorithm that improves the state-of-the art in dimensionality reduction by extending the Maximum Variance Unfolding method. Visualizations are shown for social networks, species trees, image datasets and human activity. If we are only given a dataset of N samples, how should we link the samples to build a graph? The space to explore is daunting with 2^(N2) choices but two interesting subfamilies are tractable: matchings and b-matchings. We place distributions over these families and recover the optimal graph or perform Bayesian inference over graphs efficiently using belief propagation algorithms. Higher order distributions over matchings can also be handled efficiently via fast Fourier algorithms. Applications are shown in tracking, network reconstruction, classification, and clustering. Biography 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. Jebara is also co-founder and head of the advisory board at Sense Networks. He has published over 50 peer-reviewed papers in conferences and journals including NIPS, ICML, UAI, COLT, JMLR, CVPR, ICCV, and AISTAT. He is the author of the book Machine Learning: Discriminative and Generative (Kluwer). Jebara 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 from the Pattern Recognition Society. He has served as chair and program committee member for many learning conferences. Jebara'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. Jebara's lab is supported in part by the Central Intelligence Agency, the National Science Foundation, the Office of Naval Research, the National Security Agency, and Microsoft.