@article{Kouritzin2026, 
author = {Michael A. Kouritzin},
title = {Deep Bayesian networks},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {1},
pages = {272-290},
keywords = {recurrent neural network, hidden Markov model, model selection, big data, Girsanov's theorem, machine learning},
url = {https://www.sciopen.com/article/10.3934/math.2026011},
doi = {10.3934/math.2026011},
abstract = {Deep Bayesian networks (DBNs) having deep recurrent neural network (DRNN) topography, effective forward-backward learning and innate model selection capabilities are introduced. DBNs provided randomness, Bayes' factor methods and efficient gradient-free expectation-maximization-based (EM) learning to the DRNN layout. DBN's learning, simulation and Bayes' factor capabilities provided an effective generative adversarial network (GAN) in the sequential (RNN) setting. Consequently, deep fakes with real probabilistic models could be created, based upon training data. Alternatively, DBNs could be thought of as some super generalization of hidden Markov models (HMMs), which have inputs and multiple hidden layers. The proofs establishing the above claims were based upon the novel idea to transform the whole network to a completely independent network where the analysis is trivial using a Girsanov like theorem.}
}