CAJ | 학술논문

为了给对比散度算法的进一步优化提供理论指导，尝试从理论上分析对比散度算法的收敛性.首先从仅含4个结点的玻尔兹曼机入手，利用单纯形表征模型的概率空间，以及流形表征概率空间与模型参数的关系，形象地表示了对比散度算法和极大似然算法的收敛过程，并从理论上推导出对比散度算法的收敛集与极大似然算法的收敛集之差不为空，从而证明了对比散度算法的有偏性.基于该结论，设计了一种先利用对比散度算法进行预训练，再利用极大似然算法调优的训练策略.实验结果表明，在应用该策略获得同等收敛效果的条件下，训练迭代步骤降低了83．3％.
위료급대비산도산법적진일보우화제공이론지도，상시종이론상분석대비산도산법적수렴성.수선종부함4개결점적파이자만궤입수，이용단순형표정모형적개솔공간，이급류형표정개솔공간여모형삼수적관계，형상지표시료대비산도산법화겁대사연산법적수렴과정，병종이론상추도출대비산도산법적수렴집여겁대사연산법적수렴집지차불위공，종이증명료대비산도산법적유편성.기우해결론，설계료일충선이용대비산도산법진행예훈련，재이용겁대사연산법조우적훈련책략.실험결과표명，재응용해책략획득동등수렴효과적조건하，훈련질대보취강저료83．3％.
Some theoretical problems on the convergence property of the contrastive divergence (CD)algo-rithm were investigated,providing theoretical guidance for optimizing the CD algorithm.Simplex was used to represent the probability space of the model,and manifold used to represent the relationship between the probability space and parameters of the model.Both of them help to reveal the convergence process vis-ually.Compared with the results from normal maximum likelihood estimation (MLE)for a Boltzmann ma-chine with only 4 nodes,the CD algorithm actually has biasness.Based on this conclusion,a new training strategy of CD pre-training followed by MLE fine-tuning was designed.The experimental results show that,in the same convergence condition,the procedure of the algorithm with the new strategy is reduced by 83.3% compared with the traditional algorithm.