Semi-subsumed Events: A Probabilistic Semantics of the BM25 Term Frequency Quantification

Authors:
Hengzhi Wu;Thomas Roelleke
Affiliations:
Queen Mary, University of London,;Queen Mary, University of London,
Venue:
ICTIR '09 Proceedings of the 2nd International Conference on Theory of Information Retrieval: Advances in Information Retrieval Theory
Year:
2009

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Abstract

Through BM25, the asymptotic term frequency quantification TF = tf/(tf+K ), where ${\textmd{tf}}$ is the within-document term frequency and K is a normalisation factor, became popular. This paper reports a finding regarding the meaning of the TF quantification: in the triangle of independence and subsumption, the TF quantification forms the altitude, that is, the middle between independent and subsumed events. We refer to this new assumption as semi-subsumed. While this finding of a well-defined probabilistic assumption solves the probabilistic interpretation of the BM25 TF quantification, it is also of wider impact regarding probability theory.