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The Stochastic Score Classification Problem

Authors Dimitrios Gkenosis, Nathaniel Grammel, Lisa Hellerstein, Devorah Kletenik

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Author Details

Dimitrios Gkenosis
  • Department of Informatics and Telecommunications, University of Athens, Athens, Greece
Nathaniel Grammel
  • Department of Computer Science, University of Maryland, College Park, Maryland, USA
Lisa Hellerstein
  • Department of Computer Science and Engineering, NYU Tandon School of Engineering, Brooklyn, NY, USA
Devorah Kletenik
  • Department of Computer and Information Science, Brooklyn College, CUNY, Brooklyn, New York, USA

Funding

The authors were partially supported by NSF Award IIS-1217968.
  • Kletenik, Devorah: Partially supported by a PSC-CUNY Award, jointly funded by The Professional Staff Congress and The City University of New York

Cite AsGet BibTex

Dimitrios Gkenosis, Nathaniel Grammel, Lisa Hellerstein, and Devorah Kletenik. The Stochastic Score Classification Problem. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.ESA.2018.36

Abstract

Consider the following Stochastic Score Classification Problem. A doctor is assessing a patient's risk of developing a certain disease, and can perform n tests on the patient. Each test has a binary outcome, positive or negative. A positive result is an indication of risk, and a patient's score is the total number of positive test results. Test results are accurate. The doctor needs to classify the patient into one of B risk classes, depending on the score (e.g., LOW, MEDIUM, and HIGH risk). Each of these classes corresponds to a contiguous range of scores. Test i has probability p_i of being positive, and it costs c_i to perform. To reduce costs, instead of performing all tests, the doctor will perform them sequentially and stop testing when it is possible to determine the patient's risk category. The problem is to determine the order in which the doctor should perform the tests, so as to minimize expected testing cost. We provide approximation algorithms for adaptive and non-adaptive versions of this problem, and pose a number of open questions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
Keywords
  • approximation algorithms
  • symmetric Boolean functions
  • stochastic probing
  • sequential testing
  • adaptivity

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