基于t分布的概率矩阵三因式分解方法分析

Analysis of Tri-factorization Method of Probability Matrix with t Distribution Prior

阐述概率矩阵分解(PMF)广泛被应用于预测缺失值和数据聚类,它把观测数据看成是一个基矩阵和权重矩阵的乘积,这可能会降低模型的灵活性。目前常见的是高斯分布为先验的概率模型,但是高斯分布对于异常值比较敏感,而采用t分布先验的模型能减轻异常值的影响,具有更好地稳健性。为了提高模型的灵活性和稳健性,提出了t分布先验的概率矩阵三因式分解(TBMTF),将观测数据看成三个相互约束的潜在特征矩阵的乘积,假设噪声服从t分布,变分贝叶斯推断进行参数估计。相较于传统的PMF方法,TBMTF方法能更好地识别异常值并做出预测。基于人为数据和真实数据的实验表明,在人为数据的预测效果与真实数据中添加噪声后的预测效果,都表现优秀。

This paper describes that Probability matrix factorization(PMF), which is widely used to predict missing values and to cluster data, treats the observations as a product of a base matrix and a weight matrix, which may reduce the flexibility of the model. It is common to use Gaussian distribution as a prior, but Gaussian distribution is very sensitive to outliers, and the model with t distribution prior can mitigate the effect of outliers and has better robustness. To improve the flexibility and robustness of the model, this paper proposes a probability matrix tri-factorization with t distribution prior(TBMTF),which views the observed data as the product of three mutually constrained potential feature matrices,assumes that the noise obeys the t distribution, and variational Bayesian inference for parameter estimation. Compared with the traditional PMF method, the TBMTF method can better identify outliers and make predictions. In this paper, experiments are conducted on both artificial and real data, and the final results show that TBMTF will be better for identifying noisy data and missing predictions.