### Abstract

In the distribution-independent model of concept learning of Valiant, Angluin and Laird have introduced a formal model of noise process, called classification noise process, to study how to compensate for randomly introduced errors, or noise, in classifying the example data. In this article, we investigate the problem of designing efficient learning algorithms in the presence of classification noise. First, we develop a technique of building efficient robust learning algorithms, called noise-tolerant Occam algorithms, and show that using them, one can construct a polynomial-time algorithm for learning a class of Boolean functions in the presence of classification noise. Next, as an instance of such problems of learning in the presence of classification noise, we focus on the learning problem of Boolean functions represented by decision trees. We present a noise-tolerant Occam algorithm for k-DL (the class of decision lists with conjunctive clauses of size at most k at each decision introduced by Rivest) and hence conclude that k-DL is polynomially learnable in the presence of classification noise. Further, we extend the noise-tolerant Occam algorithm for k-DL to one for r-DT (the class of decision trees of rank at most r introduced by Ehrenfeucht and Haussler) and conclude that r-DT is polynomially learnable in the presence of classification noise.

Original language | English |
---|---|

Pages (from-to) | 37-62 |

Number of pages | 26 |

Journal | Machine Learning |

Volume | 11 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1993 Apr |

Externally published | Yes |

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### ASJC Scopus subject areas

- Artificial Intelligence
- Control and Systems Engineering

### Cite this

**Noise-tolerant Occam algorithms and their applications to learning decision trees.** / Sakakibara, Yasubumi.

Research output: Contribution to journal › Article

*Machine Learning*, vol. 11, no. 1, pp. 37-62. https://doi.org/10.1023/A:1022679002094

}

TY - JOUR

T1 - Noise-tolerant Occam algorithms and their applications to learning decision trees

AU - Sakakibara, Yasubumi

PY - 1993/4

Y1 - 1993/4

N2 - In the distribution-independent model of concept learning of Valiant, Angluin and Laird have introduced a formal model of noise process, called classification noise process, to study how to compensate for randomly introduced errors, or noise, in classifying the example data. In this article, we investigate the problem of designing efficient learning algorithms in the presence of classification noise. First, we develop a technique of building efficient robust learning algorithms, called noise-tolerant Occam algorithms, and show that using them, one can construct a polynomial-time algorithm for learning a class of Boolean functions in the presence of classification noise. Next, as an instance of such problems of learning in the presence of classification noise, we focus on the learning problem of Boolean functions represented by decision trees. We present a noise-tolerant Occam algorithm for k-DL (the class of decision lists with conjunctive clauses of size at most k at each decision introduced by Rivest) and hence conclude that k-DL is polynomially learnable in the presence of classification noise. Further, we extend the noise-tolerant Occam algorithm for k-DL to one for r-DT (the class of decision trees of rank at most r introduced by Ehrenfeucht and Haussler) and conclude that r-DT is polynomially learnable in the presence of classification noise.

AB - In the distribution-independent model of concept learning of Valiant, Angluin and Laird have introduced a formal model of noise process, called classification noise process, to study how to compensate for randomly introduced errors, or noise, in classifying the example data. In this article, we investigate the problem of designing efficient learning algorithms in the presence of classification noise. First, we develop a technique of building efficient robust learning algorithms, called noise-tolerant Occam algorithms, and show that using them, one can construct a polynomial-time algorithm for learning a class of Boolean functions in the presence of classification noise. Next, as an instance of such problems of learning in the presence of classification noise, we focus on the learning problem of Boolean functions represented by decision trees. We present a noise-tolerant Occam algorithm for k-DL (the class of decision lists with conjunctive clauses of size at most k at each decision introduced by Rivest) and hence conclude that k-DL is polynomially learnable in the presence of classification noise. Further, we extend the noise-tolerant Occam algorithm for k-DL to one for r-DT (the class of decision trees of rank at most r introduced by Ehrenfeucht and Haussler) and conclude that r-DT is polynomially learnable in the presence of classification noise.

UR - http://www.scopus.com/inward/record.url?scp=0027585704&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027585704&partnerID=8YFLogxK

U2 - 10.1023/A:1022679002094

DO - 10.1023/A:1022679002094

M3 - Article

AN - SCOPUS:0027585704

VL - 11

SP - 37

EP - 62

JO - Machine Learning

JF - Machine Learning

SN - 0885-6125

IS - 1

ER -