Systems and method for perturbing a system include obtaining directed acyclic/cyclic graph candidates {G I,..., G N} for the system. Each G i in {G j,.... G N} includes a causal relationship between a parent and child node. {G I., G N} demonstrate Markov equivalence. Observed data D is obtained for the nodes. For each respective G i, the marginal probability of a parent node x i in G i is clamped by D while computing a distribution of marginal probabilities for a child node y i,· by Bayesian network or Dynamic Bayesian network belief propagation using an interaction function. The observed distribution for the child node y i , in D and the computed distribution of marginal probabilities for the child node y i are scored using a nonparametric function, and such scores inform the selection of a directed /cyclic graph from (G I,..., GN}. The system is perturbed using a perturbation that relies upon a causal relationship in the selected directed acyclic/cyclic graph.
SYSTEMS AND METHODS FOR CAUSAL INFERENCE IN NETWORK STRUCTURES USING BELIEF PROPAGATION