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Coresets for the Average Case Error for Finite Query Sets.

Alaa Maalouf1, Ibrahim Jubran1, Murad Tukan1

  • 1Robotics & Big Data Labs, University of Haifa, Haifa 3498838, Israel.

Sensors (Basel, Switzerland)
|October 13, 2021
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Summary
This summary is machine-generated.

This study introduces average-case coresets, a novel approach to data approximation. These coresets offer a smaller, more efficient way to represent large datasets, improving computational tasks like principal component analysis.

Keywords:
approximation algorithmsaverage case analysisbig datacoresetdimensionality reductionsparsification

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Area of Science:

  • Machine Learning
  • Computational Theory

Background:

  • Coresets are weighted subsets approximating data loss functions for query sets.
  • Existing methods focus on worst-case error, leading to potentially large coreset sizes.
  • The Vapnik-Chervonenkis (VC) dimension often influences coreset size in worst-case scenarios.

Purpose of the Study:

  • To introduce and develop algorithms for average-case coresets, relaxing the worst-case error bound.
  • To achieve coresets whose size is independent of input size and VC dimension.
  • To improve computational efficiency in data approximation tasks.

Main Methods:

  • Developed deterministic and randomized algorithms for computing average-case coresets.
  • Reduced the average-case coreset problem to the vector summarization problem.
  • Proposed a linear-time algorithm for computing weighted subsets in vector summarization.

Main Results:

  • Introduced average-case coresets with bounded average error over query sets.
  • Demonstrated that coreset size is independent of input size and VC dimension.
  • Achieved a linear-time algorithm for vector summarization, improving upon prior work.
  • Experimental results show significant practical improvements.

Conclusions:

  • Average-case coresets provide a more efficient alternative to worst-case coresets.
  • The proposed methods offer substantial computational advantages for data approximation.
  • The new approach has broad applicability, including principal component analysis (PCA).