Learning Probabilistic Box Embeddings for Effective and Efficient Ranking

Ranking has been one of the most important tasks in information retrieval. With the development of deep representation learning, many researchers propose to encode both the query and items into embedding vectors and rank the items according to the inner product or distance measures in the embedding space. However, the ranking models based on vector embeddings may have shortages in effectiveness and efficiency. For effectiveness, they lack the intrinsic ability to model the diversity and uncertainty of queries and items in ranking. For efficiency, nearest neighbor search in a large collection of item vectors can be costly. In this work, we propose to use the recently proposed probabilistic box embeddings for effective and efficient ranking, in which queries and items are parameterized as high-dimensional axis-aligned hyper-rectangles. For effectiveness, we utilize probabilistic box embeddings to model the diversity and uncertainty with the overlapping relations of the hyper-rectangles, and prove that such overlapping measure is a kernel function which can be adopted in other kernel-based methods. For efficiency, we propose a box embedding-based indexing method, which can safely filter irrelevant items and reduce the retrieval latency. We further design a training strategy to increase the proportion of irrelevant items that can be filtered by the index. Experiments on public datasets show that the box embeddings and the box embedding-based indexing approaches are effective and efficient in two ranking tasks: ad hoc retrieval and product recommendation.