Recently, linear regression models, such as EASE and SLIM, have shown to often produce rather competitive results against more sophisticated deep learning models. On the other side, the (weighted) matrix factorization approaches have been popular choices for recommendation in the past and widely adopted in the industry. In this work, we aim to theoretically understand the relationship between these two approaches, which are the cornerstones of model-based recommendations. Through the derivation and analysis of the closed-form solutions for two basic regression and matrix factorization approaches, we found these two approaches are indeed inherently related but also diverge in how they "scale-down" the singular values of the original user-item interaction matrix. This analysis also helps resolve the questions related to the regularization parameter range and model complexities. We further introduce a new learning algorithm in searching (hyper)parameters for the closed-form solution and utilize it to discover the nearby models of the existing solutions. The experimental results demonstrate that the basic models and their closed-form solutions are indeed quite competitive against the state-of-the-art models, thus, confirming the validity of studying the basic models. The effectiveness of exploring the nearby models are also experimentally validated.
翻译:最近,EASE和SLIM等线性回归模型显示,与更先进的深层次学习模型相比,通常会产生相当竞争性的结果。另一方面,(加权)矩阵乘数化法在过去是普遍选择的建议,在行业中被广泛采用。在这项工作中,我们的目标是从理论上理解这两种方法之间的关系,它们是基于模型的建议的基石。通过对两种基本回归和矩阵乘数化方法的封闭式解决方案的衍生和分析,我们发现这两种方法确实具有内在的内在关联性,但在它们如何“缩小”原始用户-项目互动矩阵的单值方面也有差异。这一分析也有助于解决与正规化参数范围和模型复杂性有关的问题。我们进一步引入了一种新的学习算法,以寻找封闭式解决方案的(节能)参数,并利用它来发现现有解决方案的临近模型模型。实验结果表明,基本模型及其封闭式解决方案确实与最新模型具有相当的竞争力,从而证实了研究基本模型的有效性。探索附近模型的有效性也是实验性的。