### Abstract

The empirical curve bounding problem is defined as follows. Suppose data vectors X, Y are presented such that E(Y[i]) = f(X[i]) where f(x) is an unknown function. The problem is to analyze X, Y and obtain complexity bounds O(gu(x)) and Ω(gl(x)) on the function f(x). As no algorithm for empirical curve bounding can be guaranteed correct, we consider heuristics. Five heuristic algorithms are presented here, together with analytical results guaranteeing correctness for certain families of functions. Experimental evaluations of the correctness and tightness of bounds obtained by the rules for several constructed functions f(x) and real datasets are described. A hybrid method is shown to have very good performance on some kinds of functions, suggesting a general, iterative refinement procedure in which diagnostic features of the results of applying particular methods can be used to select additional methods.

Original language | English (US) |
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Title of host publication | Advances in Intelligent Data Analysis |

Subtitle of host publication | Reasoning about Data - 2nd International Symposium, IDA-1997, Proceedings |

Editors | Xiaohui Liu, Paul Cohen, Michael Berthold |

Publisher | Springer-Verlag |

Pages | 41-52 |

Number of pages | 12 |

ISBN (Print) | 9783540633464 |

DOIs | |

State | Published - 1997 |

Event | 2nd International Symposium on Intelligent Data Analysis, IDA 1997 - London, United Kingdom Duration: Aug 4 1997 → Aug 6 1997 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1280 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 2nd International Symposium on Intelligent Data Analysis, IDA 1997 |
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Country | United Kingdom |

City | London |

Period | 8/4/97 → 8/6/97 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Advances in Intelligent Data Analysis: Reasoning about Data - 2nd International Symposium, IDA-1997, Proceedings*(pp. 41-52). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1280). Springer-Verlag. https://doi.org/10.1007/bfb0052828