An analysis on document length retrieval trends in language modelling smoothing

Document length is widely recognized as an important factor for adjusting retrieval systems. Many models tend to favor the retrieval of either short or long documents and, thus, a length-based correction needs to be applied for avoiding any length bias. In Language Modeling for Information Retrieval, smoothing methods are applied to move probability mass from document terms to unseen words, which is often dependant upon document length. In this paper, we perform an in-depth study of this behavior, characterized by the document length retrieval trends, of three popular smoothing methods across a number of factors, and its impact on the length of documents retrieved and retrieval performance. First, we theoretically analyze the Jelinek-Mercer, Dirichlet prior and two-stage smoothing strategies and, then, conduct an empirical analysis. In our analysis we show how Dirichlet prior smoothing caters for document length more appropriately than Jelinek-Mercer smoothing which leads to its superior retrieval performance. In a follow up analysis, we posit that length-based priors can be used to offset any bias in the length retrieval trends stemming from the retrieval formula derived by the smoothing technique. We show that the performance of Jelinek-Mercer smoothing can be significantly improved by using such a prior, which provides a natural and simple alternative to decouple the query and document modeling roles of smoothing. With the analysis of retrieval behavior conducted in this paper, it is possible to understand why the Dirichlet Prior smoothing performs better than the Jelinek-Mercer, and why the performance of the Jelinek-Mercer method is improved by including a length-based prior.

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