Completing a joint PMF from projections: A low-rank coupled tensor factorization approach
Completing a joint PMF from projections: A low-rank coupled tensor factorization approach
复制标题
从投影完成联合 PMF：低秩耦合张量分解方法
DOI：
10.1109/ita.2017.8023474
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
N. Sidiropoulos
中科院分区：
文献类型：
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作者：
Nikos Kargas;N. Sidiropoulos
最近，只有只有很小的部分（或很少的线性组合），对完成低升级矩阵或张量的兴趣很大。在机器学习下，相关方法在推荐系统领域发现了巨大的成功。从统计估计的角度来看，黄金标准是可以访问所有相关随机变量的关节概率分布，任何所需的最佳估计器都可以轻易得出。实际上，很难估计高维的联合分布，并且只能对低维预测进行估计。我们表明，可以使用耦合的低级张量分解从低阶边缘化PMF中鉴定出高阶关节PMF。当完整的关节PMF的排名低且有效的近似值时，我们的方法具有可确保可识别性。我们提供了一种算法方法来计算寻求的因素，并以评级预测为例说明了我们方法的优点。
There has recently been considerable interest in completing a low-rank matrix or tensor given only a small fraction (or few linear combinations) of its entries. Related approaches have found considerable success in the area of recommender systems, under machine learning. From a statistical estimation point of view, the gold standard is to have access to the joint probability distribution of all pertinent random variables, from which any desired optimal estimator can be readily derived. In practice high-dimensional joint distributions are very hard to estimate, and only estimates of low-dimensional projections may be available. We show that it is possible to identify higher-order joint PMFs from lower-order marginalized PMFs using coupled low-rank tensor factorization. Our approach features guaranteed identifiability when the full joint PMF is of low-enough rank, and effective approximation otherwise. We provide an algorithmic approach to compute the sought factors, and illustrate the merits of our approach using rating prediction as an example.