All Publications

  • Hierarchical Modeling and Shrinkage for User Session Length Prediction in Media Streaming Dedieu, A., Mazumder, R., Zhu, Z., Vahabi, H., Cuzzocrea, A., Allan, J., Paton, N., Srivastava, D., Agrawal, R., Broder, A., Zaki, M., Candan, S., Labrinidis, A., Schuster, A., Wang, H. ASSOC COMPUTING MACHINERY. 2018: 607–16
  • Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Monajemi, H., Jafarpour, S., Gavish, M., Donoho, D. L. 2013; 110 (4): 1181-1186


    In compressed sensing, one takes samples of an N-dimensional vector using an matrix A, obtaining undersampled measurements Y = Ax(0). For random matrices with independent standard Gaussian entries, it is known that, when is k-sparse, there is a precisely determined phase transition: for a certain region in the (k/n,n/N)-phase diagram, convex optimization typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property--with the same phase transition location--holds for a wide range of non-Gaussian random matrix ensembles. We report extensive experiments showing that the Gaussian phase transition also describes numerous deterministic matrices, including Spikes and Sines, Spikes and Noiselets, Paley Frames, Delsarte-Goethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Namely, for each of these deterministic matrices in turn, for a typical k-sparse object, we observe that convex optimization is successful over a region of the phase diagram that coincides with the region known for Gaussian random matrices. Our experiments considered coefficients constrained to X(N) for four different sets X [symbol: see text]{[0, 1], R(=), R, C}, and the results establish our finding for each of the four associated phase transitions.

    View details for DOI 10.1073/pnas.1219540110

    View details for PubMedID 23277588