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Learning Constant-Depth Circuits

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  • First Online:
Encyclopedia of Algorithms

  • 128 Accesses

Years and Authors of Summarized Original Work

  • 1993; Linial, Mansour, Nisan

Problem Definition

This problem deals with learning “simple” Boolean functions \(f :\{ 0,1\}^{n} \rightarrow \{-1,1\}\) from uniform random labeled examples. In the basic uniform-distribution PAC framework, the learning algorithm is given access to a uniform random example oracle E X(f, U) which, when queried, provides a labeled random example (x, f(x)) where x is drawn from the uniform distribution U over the Boolean cube {0, 1}n. Successive calls to the EX(f, U) oracle yield independent uniform random examples. The goal of the learning algorithm is to output a representation of a hypothesis function \(h :\{ 0,1\}^{n} \rightarrow \{-1,1\}\) which with high probability has high accuracy; formally, for any ε, δ > 0, given ε and δ the learning algorithm should output an h which with probability at least 1 −δ has \(\Pr _{x\in U}[h(x)\neq f(x)] \leq \epsilon.\)

Many variants of the basic framework described above...

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Author information

Authors and Affiliations

  1. Computer Science, Columbia University, 1214 Amsterdam Ave, Mailcode 0401, 10027-7003, New York, NY, USA

    A. A. Servedio

Authors
  1. A. A. Servedio
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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© 2016 Springer Science+Business Media New York

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Servedio, A.A. (2016). Learning Constant-Depth Circuits. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_195

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