Can matrix coherence be efficiently and accurately estimated?

Mehryar Mohri, Ameet Talwalkar

Research output: Contribution to journalArticle

Abstract

Matrix coherence has recently been used to characterize the ability to extract global information from a subset of matrix entries in the context of low-rank approximations and other sampling-based algorithms. The significance of these results crucially hinges upon the possibility of efficiently and accurately testing this coherence assumption. This paper precisely addresses this issue. We introduce a novel sampling-based algorithm for estimating coherence, present associated estimation guarantees and report the results of extensive experiments for coherence estimation. The quality of the estimation guarantees we present depends on the coherence value to estimate itself, but this turns out to be an inherent property of samplingbased coherence estimation, as shown by our lower bound. In practice, however, we find that these theoretically unfavorable scenarios rarely appear, as our algorithm efficiently and accurately estimates coherence across a wide range of datasets, and these estimates are excellent predictors of the effectiveness of sampling-based matrix approximation on a case-by-case basis. These results are significant as they reveal the extent to which coherence assumptions made in a number of recent machine learning publications are testable.

Original languageEnglish (US)
Pages (from-to)534-542
Number of pages9
JournalJournal of Machine Learning Research
Volume15
StatePublished - 2011

Fingerprint

Sampling
Estimate
Matrix Approximation
Low-rank Approximation
Hinges
Learning systems
Predictors
Machine Learning
Lower bound
Scenarios
Testing
Subset
Range of data
Experiment
Experiments
Context

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability

Cite this

Can matrix coherence be efficiently and accurately estimated? / Mohri, Mehryar; Talwalkar, Ameet.

In: Journal of Machine Learning Research, Vol. 15, 2011, p. 534-542.

Research output: Contribution to journalArticle

@article{a210ea25ec2143dda6b4d26208ffddf0,
title = "Can matrix coherence be efficiently and accurately estimated?",
abstract = "Matrix coherence has recently been used to characterize the ability to extract global information from a subset of matrix entries in the context of low-rank approximations and other sampling-based algorithms. The significance of these results crucially hinges upon the possibility of efficiently and accurately testing this coherence assumption. This paper precisely addresses this issue. We introduce a novel sampling-based algorithm for estimating coherence, present associated estimation guarantees and report the results of extensive experiments for coherence estimation. The quality of the estimation guarantees we present depends on the coherence value to estimate itself, but this turns out to be an inherent property of samplingbased coherence estimation, as shown by our lower bound. In practice, however, we find that these theoretically unfavorable scenarios rarely appear, as our algorithm efficiently and accurately estimates coherence across a wide range of datasets, and these estimates are excellent predictors of the effectiveness of sampling-based matrix approximation on a case-by-case basis. These results are significant as they reveal the extent to which coherence assumptions made in a number of recent machine learning publications are testable.",
author = "Mehryar Mohri and Ameet Talwalkar",
year = "2011",
language = "English (US)",
volume = "15",
pages = "534--542",
journal = "Journal of Machine Learning Research",
issn = "1532-4435",
publisher = "Microtome Publishing",

}

TY - JOUR

T1 - Can matrix coherence be efficiently and accurately estimated?

AU - Mohri, Mehryar

AU - Talwalkar, Ameet

PY - 2011

Y1 - 2011

N2 - Matrix coherence has recently been used to characterize the ability to extract global information from a subset of matrix entries in the context of low-rank approximations and other sampling-based algorithms. The significance of these results crucially hinges upon the possibility of efficiently and accurately testing this coherence assumption. This paper precisely addresses this issue. We introduce a novel sampling-based algorithm for estimating coherence, present associated estimation guarantees and report the results of extensive experiments for coherence estimation. The quality of the estimation guarantees we present depends on the coherence value to estimate itself, but this turns out to be an inherent property of samplingbased coherence estimation, as shown by our lower bound. In practice, however, we find that these theoretically unfavorable scenarios rarely appear, as our algorithm efficiently and accurately estimates coherence across a wide range of datasets, and these estimates are excellent predictors of the effectiveness of sampling-based matrix approximation on a case-by-case basis. These results are significant as they reveal the extent to which coherence assumptions made in a number of recent machine learning publications are testable.

AB - Matrix coherence has recently been used to characterize the ability to extract global information from a subset of matrix entries in the context of low-rank approximations and other sampling-based algorithms. The significance of these results crucially hinges upon the possibility of efficiently and accurately testing this coherence assumption. This paper precisely addresses this issue. We introduce a novel sampling-based algorithm for estimating coherence, present associated estimation guarantees and report the results of extensive experiments for coherence estimation. The quality of the estimation guarantees we present depends on the coherence value to estimate itself, but this turns out to be an inherent property of samplingbased coherence estimation, as shown by our lower bound. In practice, however, we find that these theoretically unfavorable scenarios rarely appear, as our algorithm efficiently and accurately estimates coherence across a wide range of datasets, and these estimates are excellent predictors of the effectiveness of sampling-based matrix approximation on a case-by-case basis. These results are significant as they reveal the extent to which coherence assumptions made in a number of recent machine learning publications are testable.

UR - http://www.scopus.com/inward/record.url?scp=84862273806&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862273806&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84862273806

VL - 15

SP - 534

EP - 542

JO - Journal of Machine Learning Research

JF - Journal of Machine Learning Research

SN - 1532-4435

ER -