Learning to rank from examples is an important task in modern Information Retrieval systems like Web search engines, where the large number of available features makes hard to manually devise high-performing ranking functions. This paper presents a novel approach to learning-to-rank, which can natively integrate any target metric with no modifications. The target metric is optimized via maximum-likelihood estimation of a probability distribution over the ranks, which are assumed to follow a Boltzmann distribution. Unlike other approaches in the literature like BoltzRank, this approach does not rely on maximizing the expected value of the target score as a proxy of the optimization of target metric. This has both theoretical and performance advantages as the expected value can not be computed both accurately and efficiently. Furthermore, our model employs the pseudo-likelihood as an accurate surrogate of the likelihood to avoid to explicitly compute the normalization factor of the Boltzmann distribution, which is intractable in this context. The experimental results show that the approach provides state-of-the-art results on various benchmarks and on a dataset built from the logs of a commercial search engine.
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