An efficient algorithm for learning to rank from preference graphs

Abstract

In this paper, we introduce a framework for regularized least-squares (RLS) type of ranking cost functions and we propose three such cost functions. Further, we propose a kernel-based preference learning algorithm, which we call RankRLS, for minimizing these functions. It is shown that RankRLS has many computational advantages compared to the ranking algorithms that are based on minimizing other types of costs, such as the hinge cost. In particular, we present efficient algorithms for training, parameter selection, multiple output learning, cross-validation, and large-scale learning. Circumstances under which these computational benefits make RankRLS preferable to RankSVM are considered. We evaluate RankRLS on four different types of ranking tasks using RankSVM and the standard RLS regression as the baselines. RankRLS outperforms the standard RLS regression and its performance is very similar to that of RankSVM, while RankRLS has several computational benefits over RankSVM.

Conditional Ranking on Relational Data

“…One of the earliest and most successful of these methods is the ranking support vector machine RankSVM [8], which optimizes the pairwise hinge loss. Even much more closely related is the ranking regularized least-squares method RankRLS [9,10], previously proposed by some of the present authors. The method is based on minimizing the pairwise regularized squared loss and becomes equivalent to the algorithms proposed in this article, if it is trained directly on the relation graph edges.…”

“…In recent years, several algorithms for learning to rank have been proposed, which can be used for conditional ranking, by interpreting the conditioning node as a query (see e.g. [15,8,5,10,16]). The main application has been in information retrieval, where the examples are joint feature representations of queries and documents, and preferences are induced only between documents connected to the same query.…”

“…Now, we show how the loss function (7) can be represented in a matrix form. This representation is similar to the RankRLS loss introduced by [9,10]. Let…”

“…Thus, in light of Figure 1 that will be explained below, the algorithm is not only able to predict conditional rankings for objects A to E, but also for objects F and G that do not contribute to the training dataset. One might argue that existing ranking methods like RankSVM [8] or RankRLS [9,10] can learn conditional rankings, by interpreting the conditioning object as a query. We will show in Section 4 that these methods become computationally intractable in many applications, unlike our approach, which is much more efficient due to exploiting the knowledge that the objects to be ranked and the queries (here objects too) are sampled from the same domain.…”

Learning Valued Relations from Data

“…To this end, we train the regularized least-squares (RLS) algorithm to regress the relation values [40]. Extensive empirical results have been reported for reciprocal relations in [41], as a consequence we focus in this article on symmetric relations.…”