Extensions of Generalized Binary Search to group identification and exponential costs

Gowtham Bellala, Suresh K. Bhavnani, Clayton Scott

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

Generalized Binary Search (GBS) is a well known greedy algorithm for identifying an unknown object while minimizing the number of "yes" or "no" questions posed about that object, and arises in problems such as active learning and active diagnosis. Here, we provide a coding-theoretic interpretation for GBS and show that GBS can be viewed as a top-down algorithm that greedily minimizes the expected number of queries required to identify an object. This interpretation is then used to extend GBS in two ways. First, we consider the case where the objects are partitioned into groups, and the objective is to identify only the group to which the object belongs. Then, we consider the case where the cost of identifying an object grows exponentially in the number of queries. In each case, we present an exact formula for the objective function involving Shannon or Rényi entropy, and develop a greedy algorithm for minimizing it.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 23
Subtitle of host publication24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010
StatePublished - Dec 1 2010
Event24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010 - Vancouver, BC, Canada
Duration: Dec 6 2010Dec 9 2010

Publication series

NameAdvances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010

Other

Other24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010
CountryCanada
CityVancouver, BC
Period12/6/1012/9/10

ASJC Scopus subject areas

  • Information Systems

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  • Cite this

    Bellala, G., Bhavnani, S. K., & Scott, C. (2010). Extensions of Generalized Binary Search to group identification and exponential costs. In Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010 (Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010).