By ranking we mean here imposing a partial ordering over some objects. Various forms of ranking appear, for example, in information retrieval:

• Given a query string, find the 20 most relevant web pages from the Internet.
• Given a news article and a fixed list of categories (politics, sports, football, Europe, ...), produce a ranked list of categories that match the article. (If we are happy with an unordered list of categories, this is called multilabel classification.)

If the user can provide feedback on the quality of the ranking, we can use that to improve our ranking method (or match it to the preferences of that individual user). The simplest form of feedback might consist of just clicking or not clicking on any of the links in the top-20 list. One interesting approach is learning to combine rankings (say, building a web search engine on top of existing search engines).

Material:

• Learning to Rank. Workshop at NIPS 2005.
• Shai Shalev-Shwartz and Yoram Singer (2006). Efficient Learning of Label Ranking by Soft Projections onto Polyhedra. Journal of Machine Learning 7:1567–1599.