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Interactive Clustering of Linear Classes and Cryptographic Lower Bounds

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Algorithmic Learning Theory (ALT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9355))

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Abstract

We study an interactive model of supervised clustering introduced by Balcan and Blum [7], where the clustering algorithm has query access to a teacher. We give an efficient algorithm clustering linear functionals over finite fields, which implies the learnability of parity functions in this model. We also present an efficient clustering algorithm for hyperplanes which are a natural generalization of the problem of clustering linear functionals over \(\mathbb R^d\). We also give cryptographic hardness results for interactive clustering. In particular, we show that, under plausible cryptographic assumptions, the interactive clustering problem is intractable for the concept classes of polynomial-size constant-depth threshold circuits, Boolean formulas, and finite automata.

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Authors and Affiliations

  1. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL, 60607, USA

    Ádám D. Lelkes & Lev Reyzin

Authors
  1. Ádám D. Lelkes
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  2. Lev Reyzin
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Correspondence to Ádám D. Lelkes .

Editor information

Editors and Affiliations

  1. University of California, La Jolla, California, USA

    Kamalika Chaudhuri

  2. UNIV DEL INSUBRIA, 21100 VARESE, Italy

    CLAUDIO GENTILE

  3. REGINA, Saskatchewan, Canada

    Sandra Zilles

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Lelkes, Á.D., Reyzin, L. (2015). Interactive Clustering of Linear Classes and Cryptographic Lower Bounds. In: Chaudhuri, K., GENTILE, C., Zilles, S. (eds) Algorithmic Learning Theory. ALT 2015. Lecture Notes in Computer Science(), vol 9355. Springer, Cham. https://doi.org/10.1007/978-3-319-24486-0_11

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  • DOI: https://doi.org/10.1007/978-3-319-24486-0_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24485-3

  • Online ISBN: 978-3-319-24486-0

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