论文标题
通过打破后对称性，有效地进行贝叶斯基质分解的MCMC抽样
Efficient MCMC Sampling for Bayesian Matrix Factorization by Breaking Posterior Symmetries
论文作者
论文摘要
贝叶斯低位基质分解技术已成为关系数据分析和矩阵完成的重要工具。一种标准方法是在列或行矩阵上分配零均值的高斯先验，以创建共轭系统。这种先验的选择会导致简单的实现；但是，这也会导致后验分布的对称性，从而严重降低了马尔可夫链蒙特卡洛（MCMC）采样方法的效率。在本文中，我们提出了对先前选择的简单修改，可证明可以打破这些对称性并保持/提高准确性。具体而言，我们提供的条件表明，高斯先前的平均值和协方差必须满足，因此后验不会表现出会产生抽样困难的不可分率。例如，我们表明，使用非零独立先验的使用表示明显降低MCMC样本的自相关，并且还可能导致较低的重建误差。
Bayesian low-rank matrix factorization techniques have become an essential tool for relational data analysis and matrix completion. A standard approach is to assign zero-mean Gaussian priors on the columns or rows of factor matrices to create a conjugate system. This choice of prior leads to simple implementations; however it also causes symmetries in the posterior distribution that can severely reduce the efficiency of Markov-chain Monte-Carlo (MCMC) sampling approaches. In this paper, we propose a simple modification to the prior choice that provably breaks these symmetries and maintains/improves accuracy. Specifically, we provide conditions that the Gaussian prior mean and covariance must satisfy so the posterior does not exhibit invariances that yield sampling difficulties. For example, we show that using non-zero linearly independent prior means significantly lowers the autocorrelation of MCMC samples, and can also lead to lower reconstruction errors.
