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If domain knowledge can be integrated as an appropriate constraint, it is highly possible that the generalization performance of a neural network model can be improved. We propose Sensitivity Direction Learning (SDL) for learning about the neural network model with user-specified relationships (e.g., monotonicity, convexity) between each input feature and the output of the model by imposing soft shape constraints which represent domain knowledge. To impose soft shape constraints, SDL uses a novel penalty function, Sensitivity Direction Error (SDE) function, which returns the squared error between coefficients of the approximation curve for each Individual Conditional Expectation plot and coefficient constraints which represent domain knowledge. The effectiveness of our concept was verified by simple experiments. Similar to those such as L2 regularization and dropout, SDL and SDE can be used without changing neural network architecture. We believe our algorithm can be a strong candidate for neural network users who want to incorporate domain knowledge.

Sensitivity Direction Learning with Neural Networks Using Domain Knowledge as Soft Shape Constraints