Distributed Flexible Nonlinear Tensor Factorization
  Tensor factorization is a powerful tool to analyse multi-way data. Compared with traditional multi-linear methods, nonlinear tensor factorization models are capable of capturing more complex relationships in the data. However, they are computationally expensive and may suffer severe learning bias in case of extreme data sparsity. To overcome these limitations, in this paper we propose a distributed, flexible nonlinear tensor factorization model. Our model can effectively avoid the expensive computations and structural restrictions of the Kronecker-product in existing TGP formulations, allowing an arbitrary subset of tensorial entries to be selected to contribute to the training. At the same time, we derive a tractable and tight variational evidence lower bound (ELBO) that enables highly decoupled, parallel computations and high-quality inference. Based on the new bound, we develop a distributed inference algorithm in the MapReduce framework, which is key-value-free and can fully exploit the memory cache mechanism in fast MapReduce systems such as SPARK. Experimental results fully demonstrate the advantages of our method over several state-of-the-art approaches, in terms of both predictive performance and computational efficiency. Moreover, our approach shows a promising potential in the application of Click-Through-Rate (CTR) prediction for online advertising. 
Shandian Zhe, Kai Zhang, Pengyuan Wang, Kuang-chih Lee, Zenglin Xu,   Yuan Qi, Zoubin Ghahramani
cs.LG cs.AI cs.DC stat.ML