Query-level learning to rank using isotonic regression

Ranking functions determine the relevance of search results of search engines, and learning ranking functions has become an active research area at the interface between Web search, information retrieval and machine learning. Generally, the training data for learning to rank come in two different forms: (1) absolute relevance judgments assessing the degree of relevance of a document with respect to a query. This type of judgments is also called labeled data and are usually obtained through human editorial efforts; and (2) relative relevance judgments indicating that a document is more relevant than another with respect to a query. This type of judgments is also called preference data and can usually be extracted from the abundantly available user click-through data recording users´ interactions with the search results. Most existing learning to rank methods ignore the query boundaries, treating the labeled data or preference data equally across queries. In this paper, we propose a minimum effort optimization method that takes into account the entire training data within a query at each iteration. We tackle this optimization problem using functional iterative methods where the update at each iteration is computed by solving an isotonic regression problem. This more global approach results in faster convergency and signficantly improved performance of the learned ranking functions over existing state-of-the-art methods. We demonstrate the effectiveness of the proposed method using data sets obtained from a commercial search engine as well as publicly available data.