Probabilistic logic methods and some applications to biology and medicine

For the computational analysis of biological problems-analyzing data, inferring networks and complex models, and estimating model parameters-it is common to use a range of methods based on probabilistic logic constructions, sometimes collectively called machine learning methods. Probabilistic modeling methods such as Bayesian Networks (BN) fall into this class, as do Hierarchical Bayesian Networks (HBN), Probabilistic Boolean Networks (PBN), Hidden Markov Models (HMM), and Markov Logic Networks (MLN). In this review, we describe the most general of these (MLN), and show how the above-mentioned methods are related to MLN and one another by the imposition of constraints and restrictions. This approach allows us to illustrate a broad landscape of constructions and methods, and describe some of the attendant strengths, weaknesses, and constraints of many of these methods. We then provide some examples of their applications to problems in biology and medicine, with an emphasis on genetics. The key concepts needed to picture this landscape of methods are the ideas of probabilistic graphical models, the structures of the graphs, and the scope of the logical language repertoire used (from First-Order Logic [FOL] to Boolean logic.) These concepts are interlinked and together define the nature of each of the probabilistic logic methods. Finally, we discuss the initial applications of MLN to genetics, show the relationship to less general methods like BN, and then mention several examples where such methods could be effective in new applications to specific biological and medical problems.