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DOI: 10.4230/LIPIcs.ITCS.2018.7

Non-Negative Sparse Regression and Column Subset Selection with L1 Error

Authors: Aditya Bhaskara and Silvio Lattanzi

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract

We consider the problems of sparse regression and column subset selection under L1 error. For both problems, we show that in the non-negative setting it is possible to obtain tight and efficient approximations, without any additional structural assumptions (such as restricted isometry, incoherence, expansion, etc.). For sparse regression, given a matrix A and a vector b with non-negative entries, we give an efficient algorithm to output a vector x of sparsity O(k), for which |Ax - b|_1 is comparable to the smallest error possible using non-negative k-sparse x. We then use this technique to obtain our main result: an efficient algorithm for column subset selection under L1 error for non-negative matrices.

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Aditya Bhaskara and Silvio Lattanzi. Non-Negative Sparse Regression and Column Subset Selection with L1 Error. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bhaskara_et_al:LIPIcs.ITCS.2018.7,
  author =	{Bhaskara, Aditya and Lattanzi, Silvio},
  title =	{{Non-Negative Sparse Regression and Column Subset Selection with L1 Error}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.7},
  URN =		{urn:nbn:de:0030-drops-83548},
  doi =		{10.4230/LIPIcs.ITCS.2018.7},
  annote =	{Keywords: Sparse regression, L1 error optimization, Column subset selection}
}

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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.604

On Reconstructing a Hidden Permutation

Authors: Flavio Chierichetti, Anirban Dasgupta, Ravi Kumar, and Silvio Lattanzi

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

Abstract

The Mallows model is a classical model for generating noisy perturbations of a hidden permutation, where the magnitude of the perturbations is determined by a single parameter. In this work we consider the following reconstruction problem: given several perturbations of a hidden permutation that are generated according to the Mallows model, each with its own parameter, how to recover the hidden permutation? When the parameters are approximately known and satisfy certain conditions, we obtain a simple algorithm for reconstructing the hidden permutation; we also show that these conditions are nearly inevitable for reconstruction. We then provide an algorithm to estimate the parameters themselves. En route we obtain a precise characterization of the swapping probability in the Mallows model.

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Flavio Chierichetti, Anirban Dasgupta, Ravi Kumar, and Silvio Lattanzi. On Reconstructing a Hidden Permutation. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 604-617, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{chierichetti_et_al:LIPIcs.APPROX-RANDOM.2014.604,
  author =	{Chierichetti, Flavio and Dasgupta, Anirban and Kumar, Ravi and Lattanzi, Silvio},
  title =	{{On Reconstructing a Hidden Permutation}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{604--617},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.604},
  URN =		{urn:nbn:de:0030-drops-47251},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.604},
  annote =	{Keywords: Mallows model; Rank aggregation; Reconstruction}
}

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Documents authored by Lattanzi, Silvio

Non-Negative Sparse Regression and Column Subset Selection with L1 Error

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On Reconstructing a Hidden Permutation

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