  We present a new method to approximate posterior probabilities of Bayesian
Network using Deep Neural Network. Experiment results on several public
Bayesian Network datasets shows that Deep Neural Network is capable of learning
joint probability distri- bution of Bayesian Network by learning from a few
observation and posterior probability distribution pairs with high accuracy.
Compared with traditional approximate method likelihood weighting sampling
algorithm, our method is much faster and gains higher accuracy in medium sized
Bayesian Network. Another advantage of our method is that our method can be
parallelled much easier in GPU without extra effort. We also ex- plored the
connection between the accuracy of our model and the number of training
examples. The result shows that our model saturate as the number of training
examples grow and we don't need many training examples to get reasonably good
result. Another contribution of our work is that we have shown discriminative
model like Deep Neural Network can approximate generative model like Bayesian
Network.
