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We report a scalable hybrid quantum-classical machine learning framework tobuild Bayesian networks (BN) that captures the conditional dependence andcausal relationships of random variables. The generation of a BN consists offinding a directed acyclic graph (DAG) and the associated joint probabilitydistribution of the nodes consistent with a given dataset. This is acombinatorial problem of structural learning of the underlying graph, startingfrom a single node and building one arc at a time, that fits a given ensembleusing maximum likelihood estimators (MLE). It is cast as an optimizationproblem that consists of a scoring step performed on a classical computer,penalties for acyclicity and number of parents allowed constraints, and asearch step implemented using a quantum annealer. We have assumed uniformpriors in deriving the Bayesian network that can be relaxed by formulating theproblem as an estimation Dirichlet parameters. We demonstrate the utility ofthe framework by applying to the problem of elucidating the gene regulatorynetwork for the MAPK/Raf pathway in human T-cells using proteomics data wherethe concentration of proteins, nodes of the BN, are interpreted asprobabilities.

Bayesian Networks based Hybrid Quantum-Classical Machine Learning Approach to Elucidate Gene Regulatory Pathways