This paper presents an initial study on hyperspherical query likelihood models (QLMs) for information retrieval (IR). Our motivation is to naturally utilize pre-trained word embeddings for probabilistic IR. To this end, key idea is to directly leverage the word embeddings as random variables for directional probabilistic models based on von Mises-Fisher distributions that are familiar to cosine distances. The proposed method enables us to theoretically take semantic similarities between document and target queries into consideration without introducing heuristic expansion techniques. In addition, this paper reveals relationships between hyperspherical QLMs and conventional QLMs. Experiments show document retrieval evaluation results in which a hyperspherical QLM is compared to conventional QLMs and document distance metrics using word or document embeddings.
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