A Note on Bayesian Networks with Latent Root Variables
<|reference_start|>A Note on Bayesian Networks with Latent Root Variables: We characterise the likelihood function computed from a Bayesian network with latent variables as root nodes. We show that the marginal distribution over the remaining, manifest, variables also factorises as a Bayesian network, which we call empirical. A dataset of observations of the manifest variables allows us to quantify the parameters of the empirical Bayesian net. We prove that (i) the likelihood of such a dataset from the original Bayesian network is dominated by the global maximum of the likelihood from the empirical one; and that (ii) such a maximum is attained if and only if the parameters of the Bayesian network are consistent with those of the empirical model.<|reference_end|>
@article{zaffalon2024a,
    title={A Note on Bayesian Networks with Latent Root Variables},
    author={Marco Zaffalon and Alessandro Antonucci},
    journal={arXiv preprint arXiv:2402.17087},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.17087},
    primaryClass={stat.ML cs.AI cs.LG}
}