From macglashan at tti-c.org Mon Oct 5 11:46:13 2009 From: macglashan at tti-c.org (Julia MacGlashan) Date: Mon Oct 5 11:46:41 2009 Subject: [TTIC Colloquium] TTI-C Colloquium: Konstantin Makarychev, IBM Message-ID: <033A23E71CB84DEC80313ED99DA9D4EE@jmacglDPLFYD1> REMINDER When: TODAY- Monday, Oct 5 @ 1:00pm Where: TTI-C Conference Room #526, 6045 S Kenwood Ave, 5th Floor Who: Konstantin Makarychev (IBM T.J. Watson Research Center) Title: Sparse Rectangular Representations of Matrix Data Given a matrix of integers, how compactly can we exactly represent the matrix as a sum of weighted rectangles? More precisely, given a set of allowable rectangles, using a linear combination of how few allowed rectangles can we represent the matrix? We study two variants. Motivated by database applications, the first case allows rectangles given by the cross product of two trees. Specifically, we are given one tree whose leaves are the rows and another whose leaves are the columns. A rectangle is allowed if and only if it is the cross product between the leaf descendants of a node in the first tree and the leaf descendants of a node in the second tree. The second variant of the problem allows all rectangles. For the database application, we give a 2-approximation algorithm and prove the problem NP-hard. We give a 2.56-approximation algorithm for second variant of the problem and prove it NP-Hard. To our knowledge these are the first results for the problem of sparsely and exactly representing matrices by weighted rectangles. Joint work with Howard Karloff, Flip Korn, and Yuval Rabani. Contact: Yury Makarychev, yury@tti-c.org -------------- next part -------------- An HTML attachment was scrubbed... URL: http://ttic.uchicago.edu/pipermail/colloquium/attachments/20091005/5faace96/attachment-0001.htm From macglashan at tti-c.org Tue Oct 20 10:39:04 2009 From: macglashan at tti-c.org (Julia MacGlashan) Date: Tue Oct 20 10:39:09 2009 Subject: [TTIC Colloquium] TTI-C Colloquium: Ben Recht, University of Wisconsin- Madison Message-ID: When: *Monday, Oct 26 @ 1:00pm* Where: * TTI-C Conference Room #526*, 6045 S Kenwood Ave Who: *Ben Recht*, University of Wisconsin-Madison Title: * A simpler approach to matrix completion* Matrix completion?where one seeks to recover a low rank matrix from a given subset of its entries?is a recurring problem in collaborative filtering, dimensionality reduction, and multi-class learning. While the general problem of finding the lowest rank matrix satisfying a set of equality constraints is NP-hard, in this talk I will discuss very general settings under which one can perfectly recover all of the missing entries of a low-rank matrix by solving a convex optimization problem. I will show that this convex programming heuristic can reconstruct most n x n matrices of rank r from most collections of entries, provided that the number of entries exceeds C n r log^2 n for some small, positive numerical constant C. These results improve on prior work by Candes and Recht, Candes and Tao, and Keshavan, Montanari, and Oh and build upon geometric ideas from the literature on "Compressed Sensing." The proof of bound on the number entries is short, self-contained, and uses very elementary analysis based on recent developments in quantum information theory. I will conclude by discussing how these results illustrate a general program for perfectly reconstructing geometric objects from very limited information. Bio: Benjamin Recht is an Assistant Professor of Computer Sciences at the University of Wisconsin-Madison. His research focuses on scalable computational tools based on convex optimization and randomized algorithms for large-scale data analysis, system identification, machine learning, and mathematical physiology. He was previously senior postdoctoral fellow at Center for the Mathematics of Information--a multidisciplinary research center established to promote information science and technology at Caltech. Recht received his B.S. with honors in Mathematics from the University of Chicago in 2000, and received a M.S. in 2002 and Ph.D. in 2006 from the MIT Media Laboratory. Contact: Nati Srebro, TTI-C nati@tti-c.org 834-7493 Speaker Schedule: http://www.tti-c.org/colloquium.php -------------- next part -------------- An HTML attachment was scrubbed... URL: http://ttic.uchicago.edu/pipermail/colloquium/attachments/20091020/c59904ee/attachment.htm From macglashan at tti-c.org Mon Oct 26 08:26:14 2009 From: macglashan at tti-c.org (Julia MacGlashan) Date: Mon Oct 26 08:26:35 2009 Subject: [TTIC Colloquium] TTI-C Colloquium: Ben Recht, University of Wisconsin- Madison Message-ID: *Reminder* When: *Monday, Oct 26 @ 1:00pm* Where: * TTI-C Conference Room #526*, 6045 S Kenwood Ave Who: *Ben Recht*, University of Wisconsin-Madison Title: * A simpler approach to matrix completion* Matrix completion?where one seeks to recover a low rank matrix from a given subset of its entries?is a recurring problem in collaborative filtering, dimensionality reduction, and multi-class learning. While the general problem of finding the lowest rank matrix satisfying a set of equality constraints is NP-hard, in this talk I will discuss very general settings under which one can perfectly recover all of the missing entries of a low-rank matrix by solving a convex optimization problem. I will show that this convex programming heuristic can reconstruct most n x n matrices of rank r from most collections of entries, provided that the number of entries exceeds C n r log^2 n for some small, positive numerical constant C. These results improve on prior work by Candes and Recht, Candes and Tao, and Keshavan, Montanari, and Oh and build upon geometric ideas from the literature on "Compressed Sensing." The proof of bound on the number entries is short, self-contained, and uses very elementary analysis based on recent developments in quantum information theory. I will conclude by discussing how these results illustrate a general program for perfectly reconstructing geometric objects from very limited information. Bio: Benjamin Recht is an Assistant Professor of Computer Sciences at the University of Wisconsin-Madison. His research focuses on scalable computational tools based on convex optimization and randomized algorithms for large-scale data analysis, system identification, machine learning, and mathematical physiology. He was previously senior postdoctoral fellow at Center for the Mathematics of Information--a multidisciplinary research center established to promote information science and technology at Caltech. Recht received his B.S. with honors in Mathematics from the University of Chicago in 2000, and received a M.S. in 2002 and Ph.D. in 2006 from the MIT Media Laboratory. Contact: Nati Srebro, TTI-C nati@tti-c.org 834-7493 Speaker Schedule: http://www.tti-c.org/colloquium.php -------------- next part -------------- An HTML attachment was scrubbed... URL: http://ttic.uchicago.edu/pipermail/colloquium/attachments/20091026/a2a5e088/attachment.htm From macglashan at tti-c.org Mon Oct 26 13:57:58 2009 From: macglashan at tti-c.org (Julia MacGlashan) Date: Mon Oct 26 13:58:14 2009 Subject: [TTIC Colloquium] TTI-C Colloquium: S V N Vishwanathan, Purdue Message-ID: When: *Monday, Nov 2 @ 1:00pm* Where: * TTI-C Conference Room #526*, 6045 S Kenwood Ave Who: *S V N Vishwanathan*, Purdue ( http://www.stat.purdue.edu/~vishy ) Title: * **A Quasi-Newton Approach to Nonsmooth Convex Optimization* Regularized risk minimization is at the heart of many machine learning algorithms. The underlying objective function to be minimized is convex, and often non-smooth. Classical optimization algorithms cannot handle this efficiently. In this talk we present our work on extending the well known BFGS quasi-Newton algorithm to handle non-smooth functions. Our extensions are justified both theoretically and experimentally. Joint work with Simon Guenter, Nic Schraudolph, Choon-Hui Teo and Jin Yu. Speaker Schedule: http://www.tti-c.org/colloquium.php Contact: Nati Srebro, TTI-C nati@tti-c.org 834-7493 -------------- next part -------------- An HTML attachment was scrubbed... URL: http://ttic.uchicago.edu/pipermail/colloquium/attachments/20091026/841ded20/attachment.htm