Exogenous variables are specially used in Structural Causal Models (SCM), which, however, have some characteristics that are still useful under the property of the Bayesian network. In this paper, we propose a novel causal discovery learning algorithm called Endogenous and Exogenous Markov Blankets Intersection (EEMBI), which combines the properties of Bayesian networks and SCM. Through intersecting the Markov blankets of exogenous variables and endogenous variables (the original variables), EEMBI can remove the irrelevant connections and find the true causal structure theoretically. Furthermore, we propose an extended version of EEMBI, named EEMBI-PC, which integrates the last step of the PC algorithm into EEMBI. This extension enhances the algorithm's performance by leveraging the strengths of both approaches. Plenty of experiments are provided to prove that EEMBI have state-of-the-art performance on continuous datasets, and EEMBI-PC outperforms other algorithms on discrete datasets.

In this paper, we develop the notion of the difference of evidence lower bounds (DELBO), based on which an efficient score algorithm is presented to implement feature selection on latent variables of VAE and its variants. Furthermore, we propose marginalization approximation algorithms to optimize VAE-related models by weighting the "more important" latent variables selected and accordingly increasing evidence lower bound. We discuss two kinds of different Gaussian posteriors, mean-field and full-covariance, for latent variables, and make the corresponding theoretical analyses to support the effectiveness of algorithms. Plenty of comparative experiments are carried out between our algorithms and the other 9 feature selection methods on 7 public datasets to address generative tasks. The results demonstrate the superior performance of our algorithms. Finally, we extend DELBO to its generalized version and apply the latter to tackling classification tasks of 5 new public datasets with satisfactory experimental results.