关键词: 半参数图模型, 动态图模型, 联合学习, 交替方向乘子法, 脑网络

Abstract: This paper proposes a joint semi-parameter probability graphical model to learn the conditional dependence relationship of non-normal distribution heterogeneous data. Considering the smoothly varying heterogeneous data, this paper further proposes a joint dynamic semi-parameter probability graphical model. Moreover, combining non-parametric rank-based correlation matrix estimator with fused graphical Lasso, this paper proposes a semi-parametric fused graphical Lasso to estimate the joint models. In particular, it proposes a novel kernel smoothing Kendall's tau correlation coefficient matrix to estimate the dynamic graphical models. Due to relaxing the normal distribution assumption, the proposed models are more flexible than the existing joint Gaussian graphical models. At the same time, due to using non-parametric rank-based correlation matrix estimator, the proposed models are also more robust. Moreover, this paper uses an efficient alternating direction method of multipliers (ADMM) to optimize the proposed models. Finally, some numerical results on simulations and real datasets such as brain imaging data and stock trading data demonstrate the effectiveness of the proposed models.

Key words: semi-parameter graphical models, dynamic graphical models, joint learning, alternating direction method of multipliers, brain network