### 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.

Original language | English (US) |
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Title of host publication | 26th European Symposium on Algorithms, ESA 2018 |

Editors | Hannah Bast, Grzegorz Herman, Yossi Azar |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

Volume | 112 |

ISBN (Print) | 9783959770811 |

DOIs | |

State | Published - Aug 1 2018 |

Event | 26th European Symposium on Algorithms, ESA 2018 - Helsinki, Finland Duration: Aug 20 2018 → Aug 22 2018 |

### Other

Other | 26th European Symposium on Algorithms, ESA 2018 |
---|---|

Country | Finland |

City | Helsinki |

Period | 8/20/18 → 8/22/18 |

### Fingerprint

### Keywords

- Adaptivity
- Approximation algorithms
- Sequential testing
- Stochastic probing
- Symmetric boolean functions

### ASJC Scopus subject areas

- Software

### Cite this

*26th European Symposium on Algorithms, ESA 2018*(Vol. 112). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ESA.2018.36

**The stochastic score classification problem.** / Gkenosis, Dimitrios; Grammel, Nathaniel; Hellerstein, Lisa; Kletenik, Devorah.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*26th European Symposium on Algorithms, ESA 2018.*vol. 112, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 26th European Symposium on Algorithms, ESA 2018, Helsinki, Finland, 8/20/18. https://doi.org/10.4230/LIPIcs.ESA.2018.36

}

TY - GEN

T1 - The stochastic score classification problem

AU - Gkenosis, Dimitrios

AU - Grammel, Nathaniel

AU - Hellerstein, Lisa

AU - Kletenik, Devorah

PY - 2018/8/1

Y1 - 2018/8/1

N2 - 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 pi of being positive, and it costs ci 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.

AB - 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 pi of being positive, and it costs ci 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.

KW - Adaptivity

KW - Approximation algorithms

KW - Sequential testing

KW - Stochastic probing

KW - Symmetric boolean functions

UR - http://www.scopus.com/inward/record.url?scp=85052512208&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85052512208&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ESA.2018.36

DO - 10.4230/LIPIcs.ESA.2018.36

M3 - Conference contribution

SN - 9783959770811

VL - 112

BT - 26th European Symposium on Algorithms, ESA 2018

A2 - Bast, Hannah

A2 - Herman, Grzegorz

A2 - Azar, Yossi

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

ER -