Benjamin Weitz

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Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is incoherent and the subsample is drawn uniformly at random. Are these assumptions necessary? It is well known that(More)
We give constructions of n k × n k × n tensors of rank at least 2n k − O(n k−1). As a corollary we obtain an [n] r shaped tensor with rank at least 2n ⌊r/2⌋ − O(n ⌊r/2⌋−1) when r is odd. The tensors are constructed from a simple recursive pattern, and the lower bounds are proven using a partitioning theorem developed by Brockett and Dobkin. These two bounds(More)
We describe how paperXML, a logical document structure markup for scholarly articles, is generated on the basis of OCR tool outputs. PaperXML has been initially developed for the ACL Anthology Searchbench. The main purpose was to robustly provide uniform access to sentences in ACL Anthology papers from the past 46 years, ranging from scanned,(More)
Yannakakis showed that the matching problem does not have a small symmetric linear program. Rothvoß recently proved that any, not necessarily symmetric, linear program also has exponential size. It is natural to ask whether the matching problem can be expressed compactly in a framework such as semidefinite programming (SDP) that is more powerful than linear(More)
We give an algorithm for the adversarial matrix completion problem, in which we wish to recover a low rank matrix when adversarially chosen entries are hidden. We show that, so long as the number of missing entries in any row or column is bounded by a function of the dimension, rank, and incoherence of the matrix, nuclear norm minimization recovers the(More)
We introduce an offline dynamic Steiner network problem in which a directed graph, as well as changes to its vertices and edges over a set of discrete times, are given as input; the goal is to find a minimal sub-graph satisfying a set of k time-sensitive connectivity demands. This problem is motivated by our work in computational biology, and naturally(More)
We give an algorithm for completing an order-m symmetric low-rank tensor from its mul-tilinear entries in time roughly proportional to the number of tensor entries. We apply our tensor completion algorithm to the problem of learning mixtures of product distributions over the hypercube, obtaining new algorithmic results. If the centers of the product(More)
Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is incoherent and the subsample is drawn uniformly at random. Are these assumptions necessary? It is well known that(More)
In this paper we investigate the problem of extracting information about chemical reactions involving multiple species from the time history of the concentration of each species. The mathematical model of the kinetic system leads to a system of ordinary differential equations. Our focus is to examine whether the species' concentrations as functions of time(More)
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