Institute for Computational and Mathematical Engineering (ICME)

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  • Benjamin Van Roy

    Benjamin Van Roy

    Professor of Electrical Engineering, of Management Science and Engineering and, by courtesy, of Computer Science

    BioBenjamin Van Roy is a Professor of Electrical Engineering, Management Science and Engineering, and, by courtesy, Computer Science, at Stanford University, where he has served on the faculty since 1998. His research focuses on understanding how an agent interacting with a poorly understood environment can learn over time to make effective decisions. He is interested in questions concerning what is possible or impossible as well as how to design efficient learning algorithms that achieve the possible. His research contributes to the fields of reinforcement learning, online optimization, and approximate dynamic programming, and offers means to addressing central problems of artificial intelligence.

    He has graduated fifteen doctoral students, published over forty articles in peer-reviewed journals, and been listed as an inventor in over a dozen patents. He has served on the editorial boards of Machine Learning, Mathematics of Operations Research, and Operations Research, for which he has also served as editor of the Financial Engineering Area. He has also founded and/or led research programs at several technology companies, including Unica (acquired by IBM), Enuvis (acquired by SiRF), and Morgan Stanley.

    He received the SB in Computer Science and Engineering and the SM and PhD in Electrical Engineering and Computer Science, all from MIT. He has been a recipient of the MIT George C. Newton Undergraduate Laboratory Project Award, the MIT Morris J. Levin Memorial Master's Thesis Award, the MIT George M. Sprowls Doctoral Dissertation Award, the National Science Foundation CAREER Award, the Stanford Tau Beta Pi Award for Excellence in Undergraduate Teaching, and the Management Science and Engineering Department's Graduate Teaching Award. He is an INFORMS Fellow and has been a Frederick E. Terman Fellow and a David Morgenthaler II Faculty Scholar. He has held visiting positions as the Wolfgang and Helga Gaul Visiting Professor at the University of Karlsruhe and as the Chin Sophonpanich Foundation Professor and the InTouch Professor at Chulalongkorn University.

  • Varun Vasudevan

    Varun Vasudevan

    Ph.D. Student in Computational and Mathematical Engineering, admitted Autumn 2016

    Current Research and Scholarly InterestsMaster's Thesis

    Title: Best rank-1 approximations without orthogonal invariance for the 1-norm.

    Abstract: Data measured in the real-world is often composed of both a true signal, such as an image or experimental response, and a perturbation, such as noise or weak secondary effects. Low-rank matrix approximation is one commonly used technique to extract the true signal from the data. Given a matrix representation of the data, this method seeks the nearest low-rank matrix where the distance is measured using a matrix norm.

    The classic Eckart-Young-Mirsky theorem tells us how to use the Singular Value Decomposition (SVD) to compute a best low-rank approximation of a matrix for any orthogonally invariant norm. This leaves as an open question how to compute a best low-rank approximation for norms that are not orthogonally invariant, like the 1-norm.

    In this thesis, we present how to calculate the best rank-1 approximations for 2-by-n and n-by-2 matrices in the 1-norm. We consider both the operator induced 1-norm (maximum column 1-norm) and the Frobenius 1-norm (sum of absolute values over the matrix). We present some thoughts on how to extend the arguments to larger matrices.