Search-engines like Google provide a list of websites that are suitable for the user's query in the sense that the first websites that are displayed are expected to be the most relevant ones. Mathematically spoken, the search-engine has to solve a ranking problem which is done by the PageRank algorithm (Page et al. ) for Google. In their seminal paper (Clémençon et al. ), Clémençon and coauthors proposed a statistical framework for ranking problems and proved that the common approach of empirical risk minimization is indeed suitable for ranking problems. Although there already existed ranking techniques, most of them indeed follow the ERM principle and can directly be embedded into the framework of Clémençon et al. .
Anya Shrubsole has broken into the top 10 of the International Cricket Council's one-day bowler rankings for the first time, after taking six wickets in England's World Cup final win over India at Lord's on Sunday. Team-mate Katherine Brunt is fifth with South Africa's Marizanne Kapp first. Australians Meg Lanning and Ellyse Perry top the batter and all-rounder rankings respectively. Shrubsole, who leads the Twenty20 bowling rankings, took 6-46 as England won a thrilling final against the team they lost to in the World Cup opening match. England spinner Laura Marsh has moved up one position to 19th in the ODI bowling rankings, while seamer Jenny Gunn has moved up two places to 20th.
Most studies were devoted to the design of efficient algorithms and the evaluation and application on diverse ranking problems, whereas few work has been paid to the theoretical studies on ranking learnability. In this paper, we study the relation between uniform convergence, stability and learnability of ranking. In contrast to supervised learning where the learnability is equivalent to uniform convergence, we show that the ranking uniform convergence is sufficient but not necessary for ranking learnability with AERM, and we further present a sufficient condition for ranking uniform convergence with respect to bipartite ranking loss. Considering the ranking uniform convergence being unnecessary for ranking learnability, we prove that the ranking average stability is a necessary and sufficient condition for ranking learnability.
Ranking plays a central role in many Web search and information retrieval applications. Ensemble ranking, sometimes called meta-search, aims to improve the retrieval performance by combining the outputs from multiple ranking algorithms. Many ensemble ranking approaches employ supervised learning techniques to learn appropriate weights for combining multiple rankers. The main shortcoming with these approaches is that the learned weights for ranking algorithms are query independent. This is suboptimal since a ranking algorithm could perform well for certain queries but poorly for others. In this paper, we propose a novel semi-supervised ensemble ranking (SSER) algorithm that learns query-dependent weights when combining multiple rankers in document retrieval. The proposed SSER algorithm is formulated as an SVM-like quadratic program (QP), and therefore can be solved efficiently by taking advantage of optimization techniques that were widely used in existing SVM solvers. We evaluated the proposed technique on a standard document retrieval testbed and observed encouraging results by comparing to a number of state-of-the-art techniques.