BN parameter learning based on improved QMAP algorithm under small data set conditions

Abstract

Under the condition of Bayesian network (BN) small data set, the qualitative maximum a posteriori (QMAP) estimation tends to violate expert constraints, which causes the QMAP estimation to deviate the true value. In order to overcome the shortcomings of this algorithm, an improved QMAP algorithm was proposed. Firstly, the QMAP estimation was learned. Next, the parameters that violated the inequality constraints were regulated by the isotonic regression method. Then, the regulated parameters were further adjusted by using a fine-tuning strategy, in order to make the obtained parameters satisfy the expert constraints. Finally, a comparison was made with the maximum likelihood estimation (MLE) algorithm and QMAP algorithm. The simulation results show that under the condition of small data set, the proposed algorithm meets all the constraints:(1) the KL (Kullback-Leibler) divergence is always lower than the other two algorithms; (2) the running time is approximately 0.1 s more than the other two algorithms, which has little influence; and (3) the inference results are close to the real value, with the deviation maintaining between ±0.05. The comprehensive performance of the improved QMAP algorithm is better than that of MLE and QMAP algorithm, and it has good practicability.

Keywords

• bayesian networks
• parameter learning
• small data set
• qualitative maximum a posteriori
• isotonic regression
• kullback-leibler divergence