Probabilistic Matrix Decomposition for Complex Noise Modeling

2020-11-26 14:00-15:00 Room 1304, Sciences Building No. 1

Abstract: Probabilistic matrix decomposition and its variants have been extensively studied for decades and comprehensively applied onto diverse fields. Most of them assume the underlying noise follows a certain independent identical Gaussian distribution. However, the noises in reality are usually heterogeneous, complicated and structured. To this end, we develop novel probabilistic matrix decomposition models for complex noise modeling. We first propose a Bayesian matrix decomposition framework to model the heterogeneous noises of multi-view data and distributed data respectively. We further propose a powerful and intuitive PCA method (MN-PCA) through modeling the graphical noise by the matrix normal distribution, which enables us to explore the structure of noise in both the feature space and the sample space. MN-PCA obtains a low-rank representation of data and the structure of noise simultaneously. And it can be explained as approximating data over the generalized Mahalanobis distance. We develop two algorithms to solve this model: one maximizes the regularized likelihood, the other exploits the Wasserstein distance, which is more robust. Extensive experiments on various data demonstrate their effectiveness.


报告人简介:张世华,中国科学院数学与系统科学研究院研究员、中国科学院随机复杂结构与数据科学重点实验室副主任、中国科学院大学岗位教授。主要从事生物信息计算、机器智能与优化,主要成果发表在Cell、Advanced Science、National Science Review、Nature Communications、Nucleic Acids Research、Bioinformatics、IEEE TPAMI、IEEE TKDE、IEEE TFS、Annals of Applied Statistics等杂志。目前担任BMC Genomics等杂志编委。曾荣获中国青年科技奖、国家自然科学基金优秀青年基金、中组部万人计划青年拔尖人才、中国科学院卢嘉锡青年人才奖、全国百篇优秀博士论文奖等。