Probability based statistical learning methods such as mutual information and Bayesian networks have emerged as a major category of tools for reverse engineering mechanistic relationships from quantitative biological data. In this work we introduce a new statistical learning strategy, MI3 that addresses three common issues in previous methods simultaneously: (1) handling of continuous variables, (2) detection of more complex three-way relationships and (3) better differentiation of causal versus confounding relationships. With these improvements, we provide a more realistic representation of the underlying biological system.