Binary independence model

Creator
Creator
Seonglae Cho
Created
Created
2025 Jan 29 12:56
Editor
Edited
Edited
2025 Jan 29 12:58
Refs
Refs
BM25

BIM

IR as Classification (relevant or not) with
Bayes Decision Rule
Assumes the relevance between documents and queries as binary variables (0 or 1)
P(DR)=i:di=1pii:di=0(1pi) P(D | R) = \prod_{i: d_i = 1} p_i \prod_{i: d_i = 0} (1 - p_i) 
 
P(DNR)=i:di=1sii:di=0(1si) P(D | NR) = \prod_{i: d_i = 1} s_i \prod_{i: d_i = 0} (1 - s_i) 

Scoring function

S(D)=logP(DR)P(DNR) S(D) = \log \frac{P(D | R)}{P(D | NR)} S(D)=i:di=1logpisi+i:di=0log1pi1si S(D) = \sum_{i: d_i = 1} \log \frac{p_i}{s_i} + \sum_{i: d_i = 0} \log \frac{1 - p_i}{1 - s_i} 
 
 
 
 
 

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