Graphical model for tensor factorization by sparse sampling
Angelo Giorgio Cavaliere, Riki Nagasawa, Shuta Yokoi, Tomoyuki Obuchi, Hajime Yoshino
我们根据张量组件的稀疏测量来考虑张量因子化。 测量设计的方式是,相互作用的底层图是一个随机图。 在缺少大量数据的情况下,这种设置将非常有用,如在社交网络服务中大量使用的推荐系统。 为了获得关于设置的理论见解,我们考虑高维极限中张量因子化的统计推断,我们称之为致密极限,其中图形大而致密但不完全连接。 我们构建消息传递算法,并在贝叶斯最佳师生设置中进行测试。 我们还开发了一个复制理论,在密集极限中变得精确,以检查统计推断的性能。
We consider tensor factorizations based on sparse measurements of the tensor components. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful in cases where a substantial amount of data is missing, as in recommendation systems heavily used in social network services. In order to obtain theoretical insights on the setup, we consider statistical inference of the tensor factorization in a high dimensional limit, which we call a...
