Conditional Ranking on Relational Data

Abstract

Abstract. In domains like bioinformatics, information retrieval and social network analysis, one can find learning tasks where the goal consists of inferring a ranking of objects, conditioned on a particular target object. We present a general kernel framework for learning conditional rankings from various types of relational data, where rankings can be conditioned on unseen data objects. Conditional ranking from symmetric or reciprocal relations can in this framework be treated as two important special cases. Furthermore, we propose an efficient algorithm for conditional ranking by optimizing a squared ranking loss function. Experiments on synthetic and real-world data illustrate that such an approach delivers state-of-the-art performance in terms of predictive power and computational complexity. Moreover, we also show empirically that incorporating domain knowledge in the model about the underlying relations can improve the generalization performance.

Fast Kronecker Product Kernel Methods via Generalized Vec Trick

“…Several efficient machine learning algorithms have been proposed for the special case, where the training sets consists of a complete bipartite graph, meaning that each possible start-end vertex pair appears exactly once, and a ridge regression loss is minimized. Specifically [13], [14], [16], [17], [6] derive closed form solutions based on Kronecker algebraic optimization (see also [33] for the basic mathematical results underlying these studies). Further, iterative methods based on Kronecker product kernel matrix -vector multiplications, have been proposed (see e.g.…”

“…Further, iterative methods based on Kronecker product kernel matrix -vector multiplications, have been proposed (see e.g. [10], [14], [16]). …”

“…Much of the work done in multi-task learning can be considered to fall under the bipartite graph prediction, and even zero-shot learning framework [25], [34], [14], [31], [17], [6], [35]. For example, in multi-label data one might have as training data images and labels describing the properties of the images (e.g.…”

“…Further, following works such as [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [6], we assume that the feature representation of an edge is defined as the product of the start and end vertex kernels, resulting in the so-called Kronecker product kernel. Kronecker product kernel methods can be trained by plugging this edge kernel to any existing kernel machine solver.…”

Learning Valued Relations from Data

“…When computing the test performance, we consider all the edges in the test set, except those starting and ending at the same node. We train the RLS algorithm using conjugate gradient optimization with early stopping [42], optimization is terminated once the MSE on the validation set has failed to decrease for 10 consecutive iterations. The mean predictor achieves around 145 MSE test performance on this data.…”