# US 2020/0401894 A1 · Machine-learning techniques for monotonic neural networks > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2020/0401894 A1 - Document ID: US20200401894A1 - Status: Published application - Kind: A1 - Application number: 17/015,056 - Filed: 2020-09-08 - Published: 2020-12-24 - Earliest claimed: 2018-10-24 - Assignees: Equifax Inc. - Applicants: Equifax Inc. - Inventors: Matthew TURNER; Lewis JORDAN; Allan JOSHUA - Web page: https://patentgrep.com/patent/US20200401894A1 ## CPC - G06N 3/08: Learning methods - G06N 3/047: Probabilistic or stochastic networks - G06N 3/048: Activation functions - G06N 3/0499: Feedforward networks - G06N 3/082: modifying the architecture, e.g. adding, deleting or silencing nodes or connections - G06N 3/09: Supervised learning - G06N 3/0985: Hyperparameter optimisation; Meta-learning; Learning-to-learn - G06N 5/01: Dynamic search techniques; Heuristics; Dynamic trees; Branch-and-bound - G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS ## 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 ### Claim 1 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 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. ### Claim 2 (depends on 1) The non-transitory computer-readable storage medium 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 applied to the nodes in the input layer, the one or more hidden layers, and the output layer. ### Claim 3 (depends on 2) The non-transitory computer-readable storage medium 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. ### Claim 4 (depends on 1) The non-transitory computer-readable storage medium of claim 1, wherein the Lagrangian expression approximating the path constraint comprises a smooth differentiable expression, and wherein the smooth differentiable expression is introduced into the modified loss function through a hyperparameter. ### Claim 5 (depends on 4) The non-transitory computer-readable storage medium of claim 4, 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. ### Claim 6 (depends on 5) The non-transitory computer-readable storage medium 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. ### Claim 7 (depends on 5) The non-transitory computer-readable storage medium 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. ### Claim 8 (depends on 4) The non-transitory computer-readable storage medium of claim 4, 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. ### Claim 9 (depends on 8) The non-transitory computer-readable storage medium of claim 8, wherein the one or more regularization terms comprise one or more of: a function of an L-2 norm of a weight vector comprising weights of the neural network model, or a function of an L-1 norm of the weight vector. ### Claim 10 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. ### Claim 11 (depends on 10) The system of claim 10, 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 applied to the nodes of the input layer, the one or more hidden layers, and the output layer. ### Claim 12 (depends on 11) The system of claim 11, 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. ### Claim 13 (depends on 11) The system of claim 11, wherein the instructions further cause the processing device to transmit, to a 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. ### Claim 14 (depends on 10) The system of claim 10, wherein the Lagrangian expression approximating the path constraint comprises a smooth differentiable expression, and wherein the smooth differentiable expression is introduced into the modified loss function through a hyperparameter. ### Claim 15 (depends on 14) The system of claim 14, 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. ### Claim 16 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. ### Claim 17 (depends on 16) The method of claim 16, wherein the path constraint is approximated by a smooth differentiable expression in the modified loss function. ### Claim 18 (depends on 17) The method 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. ### Claim 19 (depends on 18) The method 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. ### Claim 20 (depends on 16) The method 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 applied to the nodes of 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.