## Abstract

Contextual probability (G) provides an alternative, efficient way of estimating (primary) probability (P) in a principled way. G is defined in terms of P in a combinatorial way, and they have a simple linear relationship. Consequently, if one is known, the other can be calculated. It turns out G can be estimated based on a set of data samples through a simple process called neighbourhood counting. Many results about contextual probability are obtained based on the assumption that the event space is the power set of the sample space. However, the real world is usually not the case. For example, in a multidimensional sample space, the event space is typically the set of hyper tuples which is much smaller than the power set. In this paper, we generalise contextual probability to multidimensional sample space where the attributes may be categorical or numerical. We present results about the normalisation constant, the relationship between G and P and the neighbourhood counting process.

Original language | English |
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Title of host publication | Rough Sets - International Joint Conference, IJCRS 2018, Proceedings |

Editors | Quang-Thuy Ha, Małgorzata Przybyła-Kasperek, Tianrui Li, Hung Son Nguyen |

Publisher | Springer Verlag |

Pages | 337-349 |

Number of pages | 13 |

ISBN (Electronic) | 9783319993683 |

ISBN (Print) | 9783319993676 |

DOIs | |

Publication status | Published - 15 Aug 2018 |

Externally published | Yes |

Event | International Joint Conference on Rough Sets, IJCRS 2018 - Quy Nhon, Viet Nam Duration: 20 Aug 2018 → 24 Aug 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11103 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | International Joint Conference on Rough Sets, IJCRS 2018 |
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Country/Territory | Viet Nam |

City | Quy Nhon |

Period | 20/08/2018 → 24/08/2018 |

### Bibliographical note

Funding Information:Hui Wang gratefully acknowledges support by EU Horizon 2020 Programme (700381, ASGARD).

Publisher Copyright:

© Springer Nature Switzerland AG 20118.

## Keywords

- Contextual probability
- Neighbourhood counting
- Probability estimation

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science