We give an nO(loglogn)-time membership query algorithm for properly and agnostically learning decision trees under the uniform distribution over {±1}n. Even in the realizable setting, the previous fastest runtime was nO(logn), a consequence of a classic algorithm of Ehrenfeucht and Haussler. Our algorithm shares similarities with practical heuristics for learning decision trees, which we augment with additional ideas to circumvent known lower bounds against these heuristics. To analyze our algorithm, we prove a new structural result for decision trees that strengthens a theorem of O'Donnell, Saks, Schramm, and Servedio. While the OSSS theorem says that every decision tree has an influential variable, we show how every decision tree can be “pruned” so that every variable in the resulting tree is influential.
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Properly Learning Decision Trees in almost Polynomial Time
We give an nO(log log n)-time membership query algorithm for properly and agnostically learning decision trees under the uniform distribution over { ± 1}n. Even in the realizable setting, the previous fastest runtime was nO(log n), a consequence of a classic algorithm of Ehrenfeucht and Haussler.
Our algorithm shares similarities with practical heuristics for learning decision trees, which we augment with additional ideas to circumvent known lower bounds against these heuristics. To analyze our algorithm, we prove a new structural result for decision trees that strengthens a theorem of O’Donnell, Saks, Schramm, and Servedio. While the OSSS theorem says that every decision tree has an influential variable, we show how every decision tree can be “pruned” so that every variable in the resulting tree is influential.
more »
« less
- Award ID(s):
- 2006664
- NSF-PAR ID:
- 10434313
- Date Published:
- Journal Name:
- Journal of the Association for Computing Machinery
- Volume:
- 69
- Issue:
- 6
- ISSN:
- 0004-5411
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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