Deep Variational Autoencoder Based Parameter Learning of Bayesian Network with Multiple Latent Variables

Intelligent systems could be increasingly powerful by applying probabilistic inferences over the dependence relations among observed and latent variables, which could be represented by the Bayesian network with multiple latent variables (BNML). As the critical task in BNML construction, parameter learning is fulfilled by extending the classic EM algorithm in most of the existing methods, but the time complexity is exponential to the number of latent variables. To address this issue, we first propose to reduce the number of latent variables by training a vector quantized variational autoencoder (VQVAE). Specifically, we incorporate the initial probability parameters in conditional probability tables (CPTs) of BNML as the regularization term of VQVAE to guarantee that the probability parameters after reduction are similar (i.e., consistent) to those before reduction. Then, we incorporate efficient gradient calculations to augment the EM algorithm and propose the efficient algorithm for parameter learning of the BN with reduced latent variables (BNRL). Finally, we present the efficient method for probabilistic inferences in BNRL by encoding evidence variable, decoding query variables and updating query variable values via back-propagation. Experimental results on real and synthetic BNs demonstrate that our method outperforms the state-of-the-art methods on efficiency and effectiveness.