### Abstract

In this paper, we introduce a probabilistic distribution, called a smooth distribution, which is a generalization of variants of the uniform distribution such as q-bounded distribution and product distribution. Then, we give an algorithm that, under the smooth distribution, properly learns the class of functions of k terms given as ℱ_{k} ○ script T sign^{k}_{n} = {g(f_{1}(v), ..., f_{k}(v))\g∈ ℱ_{k}, f_{1}, ..., f_{k} ∈ script T sign_{n}} in polynomial time for constant k, where ℱ_{k} is the class of all Boolean functions of k variables and sript T sign_{n} is the class of terms over n variables. Although class ℱ_{k} ○ script T sign^{k}_{n} was shown by Blum and Singh to be learned using DNF as the hypothesis class, it has remained open whether it is properly learnable under a distribution-free setting.

Original language | English |
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Pages (from-to) | 188-204 |

Number of pages | 17 |

Journal | Information and Computation |

Volume | 152 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1999 Aug 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Computer Science Applications
- Computational Theory and Mathematics

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## Cite this

*Information and Computation*,

*152*(2), 188-204. https://doi.org/10.1006/inco.1998.2785