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Local Term Weight Models from Power Transformations
Development of BM25IR: A Best Match Model based on Inverse Regression

In this article we show how power transformations can be used as a common framework for the derivation of local term weights. We found that under some parametric conditions, BM25 and inverse regression produce equivalent results. As a special case of inverse regression, we show that the largest increment in term weight occurs when a term is mentioned for the second time. A model based on inverse regression (BM25IR) is presented. Simulations suggest that BM25IR works fairly well for different BM25 parametric conditions and document lengths.

Source: http://www.minerazzi.com/tutorials/bm25ir.pdf