标题： 核化贝叶斯矩阵分解 显示英文标题

标题： Kernelized Bayesian Matrix Factorization

摘要： 我们扩展了核化矩阵分解，采用了完全贝叶斯处理，并且能够处理以不同核函数表示的多个辅助信息源。 核函数已经被引入到矩阵分解中，用于整合关于行和列的辅助信息（例如推荐系统中的对象和用户），这对于进行矩阵外（即冷启动）预测是必要的。 我们特别讨论了二分图推断，在这种情况下输出矩阵是二值的，但将其扩展到更一般的矩阵是直接可行的。 我们在两个关键方面改进了现有技术：(i) 核化矩阵分解问题的完全共轭概率公式使有效的变分近似成为可能，而早期方法中的完全贝叶斯处理在计算上不可行。(ii) 包括多个辅助信息源，将其作为多核学习中的不同核函数，这还进一步揭示了哪些辅助信息源是有用的。 我们的方法在两个数据集上预测药物-蛋白质相互作用时优于替代方法。然后我们展示了我们的框架还可以通过将样本和标签视为矩阵分解操作的两个领域来解决多标签学习问题。相比五种最先进的多标签学习算法，我们的算法在14个多标签分类数据集中有10个获得了最低的汉明损失值。 显示英文摘要

摘要： We extend kernelized matrix factorization with a fully Bayesian treatment and with an ability to work with multiple side information sources expressed as different kernels. Kernel functions have been introduced to matrix factorization to integrate side information about the rows and columns (e.g., objects and users in recommender systems), which is necessary for making out-of-matrix (i.e., cold start) predictions. We discuss specifically bipartite graph inference, where the output matrix is binary, but extensions to more general matrices are straightforward. We extend the state of the art in two key aspects: (i) A fully conjugate probabilistic formulation of the kernelized matrix factorization problem enables an efficient variational approximation, whereas fully Bayesian treatments are not computationally feasible in the earlier approaches. (ii) Multiple side information sources are included, treated as different kernels in multiple kernel learning that additionally reveals which side information sources are informative. Our method outperforms alternatives in predicting drug-protein interactions on two data sets. We then show that our framework can also be used for solving multilabel learning problems by considering samples and labels as the two domains where matrix factorization operates on. Our algorithm obtains the lowest Hamming loss values on 10 out of 14 multilabel classification data sets compared to five state-of-the-art multilabel learning algorithms.