## Abstract

In recent years, there are many attempts to understand popular heuristics. An example of such heuristic algorithm is the ID3 algorithm for learning decision trees. This algorithm is commonly used in practice, but there are very few theoretical works studying its behavior. In this paper, we analyze the ID3 algorithm, when the target function is a k-Junta, a function that depends on k out of n variables of the input. We prove that when k = log n, the ID3 algorithm learns in polynomial time k-Juntas, in the smoothed analysis model of Kalai and Teng (2008). That is, we show a learnability result when the observed distribution is a “noisy” variant of the original distribution.

Original language | English |
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Pages (from-to) | 902-915 |

Number of pages | 14 |

Journal | Proceedings of Machine Learning Research |

Volume | 125 |

State | Published - 2020 |

Event | 33rd Conference on Learning Theory, COLT 2020 - Virtual, Online, Austria Duration: 9 Jul 2020 → 12 Jul 2020 |

### Bibliographical note

Funding Information:This research was supported by the Yandex Initiative in Machine Learning.

Publisher Copyright:

© 2020 A. Brtuzkus, A. Daniely & E. Malach.

## Keywords

- Decision Trees
- ID3
- Junta
- Parity