Efficient distribution-free population learning of simple concepts

Atsuyoshi Nakamura, Junnichi Takeuchi, Naoki Abe

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider a variant of the 'population learning model' proposed by Kearns and Seung [8], in which the learner is required to be 'distribution-free' as well as computationally efficient. A population learner receives as input hypotheses from a large population of agents and produces as output its final hypothesis. Each agent is assumed to independently obtain labeled sample for the target concept and output a hypothesis. A polynomial time population learner is said to PAC-learn a concept class, if its hypothesis is probably approximately correct whenever the population size exceeds a certain bound which is polynomial, even if the sample size for each agent is fixed at some constant. We exhibit some general population learning strategies, and some simple concept classes that can be learned by them. These strategies include the 'supremum hypothesis finder', the 'minimum superset finder' (a special case of the 'supremum hypothesis finder'), and various voting schemes. When coupled with appropriate agent algorithms, these strategies can learn a variety of simple concept classes, such as the 'high-low game', conjunctions, axis-parallel rectangles and others. We give upper bounds on the required population size for each of these cases, and show that these systems can be used to obtain a speed up from the ordinary PAC-learning model [11], with appropriate choices of sample and population sizes. With the population learner restricted to be a voting scheme, what we have is effectively a model of 'population prediction', in which the learner is to predict the value of the target concept at an arbitrarily drawn point, as a threshold function of the predictions made by its agents on the same point. We show that the population learning model is strictly more powerful than the population prediction model. Finally, we consider a variant of this model with classification noise, and exhibit a population learner for the class of conjunctions in this model.

Original languageEnglish
Pages (from-to)53-82
Number of pages30
JournalAnnals of Mathematics and Artificial Intelligence
Volume23
Issue number1-2
Publication statusPublished - 1998
Externally publishedYes

Fingerprint

Distribution-free
Population Size
Voting
Supremum
Polynomials
Sample Size
PAC Learning
Model
Concepts
Learning
Threshold Function
Target
Learning Strategies
Prediction
Output
Population Model
Rectangle
Prediction Model
Polynomial time
Exceed

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Applied Mathematics

Cite this

Efficient distribution-free population learning of simple concepts. / Nakamura, Atsuyoshi; Takeuchi, Junnichi; Abe, Naoki.

In: Annals of Mathematics and Artificial Intelligence, Vol. 23, No. 1-2, 1998, p. 53-82.

Research output: Contribution to journalArticle

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