Document Type

Technical Report

Department

Computer Science and Engineering

Publication Date

1998-01-01

Filename

WUCS-98-28.PDF

Technical Report Number

WUCS-98-28

Abstract

We introduce the UAV learning model in which some of the attributes in the examples are unspecified. In our model, an example x is classified positive (resp., negative) if all possible assignments for the unspecified attributes result in a positive (resp., negative) classification. Otherwise the classificatoin given to x is "?" (for unknown). Given an example x in which some attributes are unspecified, the oracle UAV-MQ responds with the classification of x. Given a hypothesis h, the oracle UAV-EQ returns an example x (that could have unspecified attributes) for which h(x) is incorrect. We show that any class learnable in the exact model using the MQ and EQ oracles is also learnable in the UAV model using the MQ and UAV-EQ oracles as long as the counterexamples provided by the UAV-EQ oracle have a logarithmic number of unspecified attributes. We also show that any class learnable in the exact model using the MQ and EQ oracles is also learnable in the UAV model using the UAV-MQ and UAV-EQ oracles as well as an oracle to evaluate a given boolean formula on an example with unspecified attributes. (For some hypothesis classes such as decision trees and unate formulas the evaluation can be done in polynomial time without an oracle.) We also study the learnability of a universal class of decision trees under the UAV model and of DNF formulas under a representation-dependent variation of the UAV model.

Comments

Permanent URL: http://dx.doi.org/10.7936/K7Z31WWR

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