An Explicit Concept-Based Approach for Incorporating Expert Rules into Machine Learning Models

An approach for solving a problem of incorporating the expert rules into machine learning models, in particular, into neural networks, in the framework of the concept-based learning is proposed in the paper. The first idea behind the approach is to consider the expert rules as logical functions on concepts, which restrict a joint probability distribution over all combinations of concept values, i.e. it is supposed that each combination of concepts must satisfy the expert rules, otherwise the probability of the combination is assigned to zero. The second idea is to add a neural network producing probabilities of the concept combinations by a layer which maps the probabilities of the concepts to the marginal probabilities of concepts and guarantees that the probabilities will satisfy expert rules for any input. The proposed approach can be viewed as a way for combining the inductive and deductive learning. A numerical example illustrates the approach.