We propose a decision-theoretic sparsification method for Gaussian process preference learning. This method overcomes the loss-insensitive nature of popular sparsification approaches such as the Informative Vector Machine (IVM). Instead of selecting a subset of users and items as inducing points based on uncertainty-reduction principles, our sparsification approach is underpinned by decision theory and directly incorporates the loss function inherent to the underlying preference learning problem. We show that by selecting different specifications of the loss function, the IVM's differential entropy criterion, a value of information criterion, and an upper confidence bound (UCB) criterion used in the bandit setting can all be recovered from our decision-theoretic framework. We refer to our method as the Valuable Vector Machine (VVM) as it selects the most useful items during sparsification to minimize the corresponding loss. We evaluate our approach on one synthetic and two real-world preference datasets, including one generated via Amazon Mechanical Turk and another collected from Facebook. Experiments show that variants of the VVM significantly outperform the IVM on all datasets under similar computational constraints.
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