论文标题
部分可观测时空混沌系统的无模型预测
Unitary Approximate Message Passing for Matrix Factorization
论文作者
论文摘要
我们考虑具有某些约束的矩阵分解（MF），在各个领域找到广泛的应用。利用变异推理（VI）和单一近似消息传递（UAMP），我们通过有效的消息传递实现（称为UAMPMF）开发了MF的贝叶斯方法。通过对因子矩阵施加的适当先验，UAMPMF可用于解决许多可以表达为MF的问题，例如非负基质分解，词典学习，具有矩阵不确定性的压缩感，可靠的主成分分析和稀疏矩阵分解。提供了广泛的数值示例，以表明UAMPMF在恢复精度，鲁棒性和计算复杂性方面显着优于最先进的算法。
We consider matrix factorization (MF) with certain constraints, which finds wide applications in various areas. Leveraging variational inference (VI) and unitary approximate message passing (UAMP), we develop a Bayesian approach to MF with an efficient message passing implementation, called UAMPMF. With proper priors imposed on the factor matrices, UAMPMF can be used to solve many problems that can be formulated as MF, such as non negative matrix factorization, dictionary learning, compressive sensing with matrix uncertainty, robust principal component analysis, and sparse matrix factorization. Extensive numerical examples are provided to show that UAMPMF significantly outperforms state-of-the-art algorithms in terms of recovery accuracy, robustness and computational complexity.
