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Inductive inference is the process of extracting general rules from specificobservations. This problem also arises in the analysis of biological networks,such as genetic regulatory networks, where the interactions are complex and theobservations are incomplete. A typical task in these problems is to extractgeneral interaction rules as combinations of Boolean covariates, that explain ameasured response variable. The inductive inference process can be consideredas an incompletely specified Boolean function synthesis problem. Thisincompleteness of the problem will also generate spurious inferences, which area serious threat to valid inductive inference rules. Using random Boolean dataas a null model, here we attempt to measure the competition between valid andspurious inductive inference rules from a given data set. We formulate twogreedy search algorithms, which synthesize a given Boolean response variable ina sparse disjunct normal form, and respectively a sparse generalized algebraicnormal form of the variables from the observation data, and we evaluatenumerically their performance.

On the inherent competition between valid and spurious inductive inferences in Boolean data