论文标题
时间非阴性基质分解的伽马马座链的比较研究
A Comparative Study of Gamma Markov Chains for Temporal Non-Negative Matrix Factorization
论文作者
论文摘要
非负矩阵分解（NMF）已成为一类良好的非负数据分析方法。特别是，在描述数据的概率模型中，大量努力已致力于概率的NMF，即估计或推理任务，例如基于泊松或指数的可能性。在处理时间序列数据时，已经提出了一些工作，以将激活系数的演变建模为非负Markov链，大部分时间与伽马分布有关，从而引起所谓的时间NMF模型。在本文中，我们回顾了NMF文献的四个Gamma Markov链，并表明它们都有相同的缺点：缺乏定义明确的固定分布。然后，我们引入了第五个过程，这是一个名为Bgar（1）的时间序列文献的被忽视模型，该过程克服了这一限制。然后，在泊松可能性的背景下，在预测任务的地图框架中比较了这些时间NMF模型。
Non-negative matrix factorization (NMF) has become a well-established class of methods for the analysis of non-negative data. In particular, a lot of effort has been devoted to probabilistic NMF, namely estimation or inference tasks in probabilistic models describing the data, based for example on Poisson or exponential likelihoods. When dealing with time series data, several works have proposed to model the evolution of the activation coefficients as a non-negative Markov chain, most of the time in relation with the Gamma distribution, giving rise to so-called temporal NMF models. In this paper, we review four Gamma Markov chains of the NMF literature, and show that they all share the same drawback: the absence of a well-defined stationary distribution. We then introduce a fifth process, an overlooked model of the time series literature named BGAR(1), which overcomes this limitation. These temporal NMF models are then compared in a MAP framework on a prediction task, in the context of the Poisson likelihood.
