We propose a novel Bayesian learning algorithm, Bayesian clique learning (BCL), for searching the optimal electromagnetic ( EM) design parameter by using the structural property of EM simulation data set. Our method constructs a new topological structure called statistical clique that encodes EM information, which reduces our search space by cutting down unnecessary data. Our BCL then search optimum design parameters by exploiting embedded cliques in the data. Our BCL allows us to reuse learning parameters from the trained EM data set to the new EM data set with little modifications. We classify our data in three ranges and run our learning to find range specific parameters. Our learning algorithm is scalable, and works on any general EM structure for automated design. We have given a bound for the computational complexity of our method and discuss the tradeoff of the complexity with the uncertainty. We compare the computational complexity of two different EM structures that has weakly linear negative correlated data sets.