Machine-learning techniques for monotonic neural networks

A system comprising:

• a processing device;
• and
• a memory device in which instructions executable by the processing device are stored for causing the processing device to:
• train a neural network model for computing a risk indicator from predictor variables, wherein the neural network model is a memory structure comprising nodes connected via one or more layers, wherein training the neural network model to generate a trained neural network model comprises:
• access training vectors having elements representing training predictor variables and training outputs, wherein a particular training vector comprises (i) particular values for the predictor variables, respectively, and (ii) a particular training output corresponding to the particular values, and
• perform iterative adjustments of parameters of the neural network model to minimize a modified loss function comprising a loss function of the neural network model and a Lagrangian expression approximating a path constraint, the path constraint requiring a monotonic relationship between (i) values of each predictor variable from the training vectors and (ii) the training outputs of the training vectors, wherein one or more of the iterative adjustments comprises adjusting the parameters of the neural network model so that a value of the modified loss function in a current iteration is smaller than the value of the modified loss function in another iteration;
• and
• causing the trained neural network model to be applied to predictor variables associated with a target entity to generate an output risk indicator for the target entity.

A method that includes one or more processing devices performing operations comprising:

• training a neural network model for computing a risk indicator from predictor variables, wherein the neural network model is a memory structure comprising nodes connected via one or more layers, wherein training the neural network model to generate a trained neural network model comprises:
• accessing training vectors having elements representing training predictor variables and training outputs, wherein a particular training vector comprises (i) particular values for the predictor variables, respectively, and (ii) a particular training output corresponding to the particular values, and
• performing iterative adjustments of parameters of the neural network model to minimize a modified loss function comprising a loss function of the neural network model and a Lagrangian expression approximating a path constraint, the path constraint requiring a monotonic relationship between (i) values of each predictor variable from the training vectors and (ii) the training outputs of the training vectors, wherein one or more of the iterative adjustments comprises adjusting the parameters of the neural network model so that a value of the modified loss function in a current iteration is smaller than the value of the modified loss function in another iteration;
• and
• causing the trained neural network model to be applied to predictor variables associated with a target entity to generate an output risk indicator for the target entity.