MACHINE-LEARNING TECHNIQUES FOR MONOTONIC NEURAL NETWORKS

• US 20200134439A1
• Filed: 10/24/2018
• Published: 04/30/2020
• Est. Priority Date: 10/24/2018
• Status: Active Grant

• Current Assignee: Equifax, Inc.
• Original Assignee: Equifax, Inc.
• Inventors: Turner, Matthew, Jordan, Lewis, Joshua, Allan
• Granted Patent: US 11,468,315 B2
• Time in Patent Office: Days
• CPC Class Codes: G06N 3/047 Probabilistic or stochastic networks
• CPC Class Codes: G06N 3/048 Activation functions
• CPC Class Codes: G06N 3/08 Learning methods
• CPC Class Codes: G06N 5/01 Dynamic search techniques; Heuristics; Dynamic trees; Branch-and-bound

Abstract

In some aspects, a computing system can generate and optimize a neural network for risk assessment. The neural network can be trained to enforce a monotonic relationship between each of the input predictor variables and an output risk indicator. The training of the neural network can involve solving an optimization problem under a monotonic constraint. This constrained optimization problem can be converted to an unconstrained problem by introducing a Lagrangian expression and by introducing a term approximating the monotonic constraint. Additional regularization terms can also be introduced into the optimization problem. The optimized neural network can be used both for accurately determining risk indicators for target entities using predictor variables and determining explanation codes for the predictor variables. Further, the risk indicators can be utilized to control the access by a target entity to an interactive computing environment for accessing services provided by one or more institutions.

Claims

1. 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 loss function of the neural network model subject to 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 a modified loss function in a current iteration is smaller than the value of the modified loss function in another iteration, and wherein the modified loss function comprises the loss function of the neural network model and the path constraint;

receiving, from a remote computing device, a risk assessment query for a target entity; and

computing, responsive to the risk assessment query, an output risk indicator for the target entity by applying the trained neural network model to predictor variables associated with the target entity.

2. The method of claim 1, wherein the neural network model comprises at least an input layer, one or more hidden layers, and an output layer, and wherein the parameters for the neural network model comprise weights of connections among the input layer, the one or more hidden layers, and the output layer.

3. The method of claim 2, wherein the path constraint comprises, for each path comprising a respective set of nodes across the layers of the neural network model from the input layer to the output layer, a positive product of the respective weights applied to the respective set of nodes in the path.

4. The method of claim 1, wherein the path constraint is approximated by a smooth differentiable expression in the modified loss function.

5. The method of claim 4, wherein the smooth differentiable expression is introduced into the modified loss function through a hyperparameter, and wherein training the neural network model further comprises:

setting the hyperparameter to a random initial value prior to performing the iterative adjustments; and

in one or more of the iterative adjustments, determining a particular set of parameter values for the parameters of the neural network model based on the random initial value of the hyperparameter.

6. The method of claim 5, wherein training the neural network model further comprises:

determining a value of the loss function of the neural network model based on the particular set of parameter values associated with the random initial value of the hyperparameter;

determining that the value of the loss function is greater than a threshold loss function value;

updating the hyperparameter by decrementing the value of the hyperparameter; and

determining an additional set of parameter values for the neural network model based on the updated hyperparameter.

7. The method of claim 5, wherein training the neural network model further comprises:

determining that the path constraint is violated by the particular set of parameter values for the neural network model;

updating the hyperparameter by incrementing the value of the hyperparameter; and

determining an additional set of parameter values for the neural network model based on the updated hyperparameter.

8. The method of claim 5, wherein the hyperparameter is a Lagrangian multiplier.

9. 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 loss function of the neural network model subject to 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 a modified loss function in a current iteration is smaller than the value of the modified loss function in another iteration, and wherein the modified loss function comprises the loss function of the neural network model and the path constraint; and

compute, responsive to a risk assessment query for a target entity received from a remote computing device, an output risk indicator for the target entity by applying the trained neural network model to predictor variables associated with the target entity.

10. The system of claim 9, wherein the neural network model comprises at least an input layer, one or more hidden layers, and an output layer, and wherein the parameters for the neural network model comprise weights of connections among the input layer, the one or more hidden layers, and the output layer.

11. The system of claim 10, wherein the path constraint comprises, for each path comprising a respective set of nodes across the layers of the neural network model from the input layer to the output layer, a positive product of the respective weights applied to the respective set of nodes in the path.

12. The system of claim 9, wherein the instructions further cause the processing device to transmit, to the remote computing device, a responsive message including the output risk indicator, wherein the output risk indicator is usable for controlling access to one or more interactive computing environments by the target entity.

13. The system of claim 9, wherein the path constraint is approximated by a smooth differentiable expression in the modified loss function, and wherein the smooth differentiable expression is introduced into the modified loss function through a hyperparameter.

14. The system of claim 13, wherein training the neural network model further comprises, adding one or more regularization terms into the modified loss function through the hyperparameter, wherein the one or more regularization terms represent quantitative measurements of the parameters of the neural network model, wherein the 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 with the regularization terms in a current iteration is smaller than the value of the modified loss function with the regularization terms in another iteration.

15. The system of claim 14, wherein the one or more regularization terms comprise one or more of:

a function of an L−

2 norm of a weight vector comprising the weights of the neural network model, and

a function of an L−

1 norm of the weight vector.

16. A non-transitory computer-readable storage medium having program code that is executable by a processor device to cause a computing device to perform operations, the 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 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 loss function of the neural network model subject to 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 a modified loss function in a current iteration is smaller than the value of the modified loss function in another iteration, and wherein the modified loss function comprises the loss function of the neural network model and the path constraint;

computing, responsive to a risk assessment query for a target entity received from a remote computing device, an output risk indicator for the target entity by applying the trained neural network model to predictor variables associated with the target entity; and

transmitting, to the remote computing device, a responsive message including the output risk indicator.

17. The non-transitory computer-readable storage medium of claim 16, wherein the path constraint is approximated by a smooth differentiable expression in the modified loss function.

18. The non-transitory computer-readable storage medium of claim 17, wherein the smooth differentiable expression is introduced into the modified loss function through a hyperparameter, and wherein training the neural network model further comprises:

setting the hyperparameter to a random initial value prior to performing the iterative adjustments; and

in one or more of the iterative adjustments, determining a particular set of parameter values for the parameters of the neural network model based on the random initial value of the hyperparameter.

19. The non-transitory computer-readable storage medium of claim 18, wherein training the neural network model further comprises, adding one or more regularization terms into the modified loss function through the hyperparameter, wherein the one or more regularization terms represent quantitative measurements of the parameters of the neural network model, wherein the 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 with the regularization terms in a current iteration is smaller than the value of the modified loss function with the regularization terms in another iteration.

20. The non-transitory computer-readable storage medium of claim 16,

wherein the neural network model comprises at least an input layer, one or more hidden layers, and an output layer,

wherein the parameters for the neural network model comprise weights of connections among the input layer, the one or more hidden layers, and the output layer, and

wherein the path constraint comprises, for each path comprising a respective set of nodes across the layers of the neural network model from the input layer to the output layer, a positive product of the respective weights applied to the respective set of nodes in the path.