判别贝叶斯网络的CEM学习算法

CEM Learning Method of Discriminative Bayesian Networks

当数据存在缺值时,通常应用EM算法学习贝叶斯网络.然而,EM算法以联合似然作为目标函数,与判别预测问题的目标相偏离.与EM算法不同,CEM(Conditional Expectation Maximum)算法直接以条件似然作为目标函数.研究了判别贝叶斯网络学习的CEM算法,提出一种使得CEM算法具有单调性和收敛性的Q函数.为了简化计算,在CEM算法的E步,应用Q函数的一种简化形式;在CEM算法的M步,应用梯度下降法的一次搜索结果作为最优值的近似.最后,在UCI数据集上的实验结果表明了CEM算法在判别贝叶斯网络学习中的有效性.

EM is usually used to learn Bayesian networks when training data has missing values. However, EM can not used to learn discriminative Bayesian networks because it takes joint likelihood as objective. In contrast, CEM （ Conditional Expectation Maxi- mum） takes conditional likelihood as objective directly. CEM learning method of discriminative Bayesian networks is researched and a Q function is proposed accordingly. Then, monotonic and convergence of CEM learning method is proved. In E step of CEM a simple Q function is proposed and in M step of CEM optimal procedure is replaced by a search procedure of gradient descent. Lastly, experiment results on UCI datasets show that CEM learning method is effective.