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Random networks of nonlinear functions have a long history of empirical success in function fitting but few theoretical guarantees. In this paper, using techniques from probability on Banach Spaces, we analyze a specific architecture of random nonlinearities, provide L<sub>infin</sub> and L<sub>2</sub> error bounds for approximating functions in Reproducing(More)
In this paper, we focus on compressed sensing and recovery schemes for low-rank matrices, asking under what conditions a low-rank matrix can be sensed and recovered from incomplete, inaccurate, and noisy observations. We consider three schemes, one based on a certain Restricted Isometry Property and two based on directly sensing the row and column space of(More)
Suppose that one observes an incomplete subset of entries selected uniformly at random from a low-rank matrix. When is it possible to complete the matrix and recover the entries that have not been seen? We show that in very general settings, one can perfectly recover all of the missing entries from a sufficiently large random subset by solving a convex(More)
This document contains a list of open problems and research directions that have been suggested by participants at the Bertinoro Workshop on Sublinear Algorithms (May 2011) and IITK Workshop on Algorithms for Processing Massive Data Sets (December 2009). Many of the questions were discussed at the workshop or were posed during presentations. Further details(More)
Pursuing a line of work begun by Whitney, Nash showed that every C manifold of dimension d can be embedded in R in such a manner that the local structure at each point is preserved isometrically. We provide an analog of this result for discrete subsets of Euclidean space. For perfect preservation of infinitesimal neighborhoods we substitute near-isometric(More)
Despite recent developments in improved acquisition, seismic data often remains undersampled along source and receiver coordinates, resulting in incomplete data for key applications such as migration and multiple prediction. We interpret the missing-trace interpolation problem in the context of matrix completion and outline three practical principles for(More)