Finding the parameters of a latent variable causal model is central to causal inference and causal identification. In this article, we show that existing graphical structures that are used in causal inference are not stable under marginalization of Gaussian Bayesian networks, and present a graphical structure that faithfully represents margins of Gaussian Bayesian networks. We present the first duality between parameter optimization of a latent variable model and training a feed-forward neural network in the parameter space of the assumed family of distributions. Based on this observation, we develop an algorithm for parameter optimization of these graphical structures using the observational distribution. Then, we provide conditions for causal effect identifiability in the Gaussian setting. We propose a meta-algorithm that checks whether a causal effect is identifiable or not. Moreover, we lay a grounding for generalizing the duality between a neural network and a causal model from the Gaussian to other distributions.

MOTIVATION: Laboratory gene regulatory data for a species are sporadic. Despite the abundance of gene regulatory network algorithms that employ single data sets, few algorithms can combine the vast but disperse sources of data and extract the potential information. With a motivation to compensate for this shortage, we developed an algorithm called GENEREF that can accumulate information from multiple types of data sets in an iterative manner, with each iteration boosting the performance of the prediction results. RESULTS: The algorithm is examined extensively on data extracted from the quintuple DREAM4 networks and DREAM5's Escherichia coli and Saccharomyces cerevisiae networks and sub-networks. Many single-dataset and multi-dataset algorithms were compared to test the performance of the algorithm. Results show that GENEREF surpasses non-ensemble state-of-the-art multi-perturbation algorithms on the selected networks and is competitive to present multiple-dataset algorithms. Specifically, it outperforms dynGENIE3 and is on par with iRafNet. Also, we argued that a scoring method solely based on the AUPR criterion would be more trustworthy than the traditional score. AVAILABILITY: The Python implementation along with the data sets and results can be downloaded from github.com/msaremi/GENEREF.