The recent work by Rendle et al. (2020), based on empirical observations, argues that matrix-factorization collaborative filtering (MCF) compares favorably to neural collaborative filtering (NCF), and conjectures the dot product's superiority over the feed-forward neural network as similarity function. In this paper, we address the comparison rigorously by answering the following questions: 1. what is the limiting expressivity of each model; 2. under the practical gradient descent, to which solution does each optimization path converge; 3. how would the models generalize under the inductive and transductive learning setting. Our results highlight the similar expressivity for the overparameterized NCF and MCF as kernelized predictors, and reveal the relation between their optimization paths. We further show their different generalization behaviors, where MCF and NCF experience specific tradeoff and comparison in the transductive and inductive collaborative filtering setting. Lastly, by showing a novel generalization result, we reveal the critical role of correcting exposure bias for model evaluation in the inductive setting. Our results explain some of the previously observed conflicts, and we provide synthetic and real-data experiments to shed further insights to this topic.
翻译:根据经验观察,Rendle等人(2020年)最近根据经验观察开展的工作认为,矩阵因素合作过滤(MCF)与神经合作过滤(NCF)相比有利,并推测点产品相对于进进取神经网络的优势是相似功能。在本文件中,我们严谨地处理这一比较,回答下列问题:1. 每种模型的表达度是有限的;2. 在实际的梯度下,每种优化路径都能找到解决办法;3. 模型如何在进化和转导学习设置下概括化。我们的结果突出了过度量化的NCF和MCF作为内向型预测器的类似表达性,并揭示了它们之间的优化路径关系。我们进一步展示了它们不同的概括行为,即MCFF和NCF在转导和感化协作过滤设置中经历了具体的交换和比较。最后,通过展示新的概括性结果,我们揭示了在进化环境中纠正暴露暴露偏向模式评估的关键作用。我们的成果解释了以往观察到的冲突的一些初步认识,我们提供了合成和真实的实验。