两两关系马尔科夫网的自适应组稀疏化学习

稀疏化学习能显著降低无向图模型的参数学习与结构学习的复杂性, 有效地处理无向图模型的学习问题. 两两关系马尔科夫网在多值变量情况下, 每条边具有多个参数, 本文对此给出边参数向量的组稀疏化学习, 提出自适应组稀疏化, 根据参数向量的模大小自适应调整惩罚程度. 本文不仅对比了不同边势情况下的稀疏化学习性能, 为了加速模型在复杂网络中的训练过程, 还对目标函数进行伪似然近似、平均场自由能近似和Bethe自由能近似. 本文还给出自适应组稀疏化目标函数分别使用谱投影梯度算法和投 影拟牛顿算法时的最优解, 并对比了两种优化算法进行稀疏化学习的性能. 实验表明自适 应组稀疏化具有良好的性能.

Adaptive Group Sparse Learning of Pairwise Markov Network

Sparse learning can significantly reduce the complexity of parameter learning and structure learning and effectively deal with learning problems of undirected graphical models. In the case of pairwise Markov network, in which each variable has more than two values, the number of parameters associated with an edge is more than one. This paper proposes a group sparse learning approach for the parameters associated with edges, and puts forward an adaptive group sparse learning algorithm, which can adaptively adjust the degree of penalty according to the norm of the parameters vector. This paper compares the performance of sparse learning using different edge potentials. In order to speed up the training process, three approximate object functions are given, including pseudo likelihood approximation, mean field approximation and Bethe free energy approximation. Two optimization algorithms, i.e., projected quasi-Newton algorithm and spectral projected gradient algorithm, are also compared. Experimental results show that the proposed adaptive group sparse learning algorithm outperforms the normal sparse learning ones.