Monotonic Neural Network Training with Lagrangian Constraints
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Solution Overview
Problem
Machine learning using neural networks for risk assessment and prediction is resource-intensive, particularly when dealing with large datasets, and struggles to provide efficient computational performance and explainable outcomes due to the complexity of neural network structures and interconnections.
Innovation Solution
A monotonic neural network is trained with a path constraint to maintain a monotonic relationship between input variables and outputs, using iterative adjustments and regularization techniques to minimize loss functions, allowing for efficient computation and explainable predictions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional neural networks are used for risk assessment with large datasets, then prediction accuracy can be improved, but computational resource consumption increases and training time extends
Solution Approach 1:
The patent transforms the neural network training problem by changing the parameter space through monotonic constraints. By enforcing monotonicity on the neural network parameters (weights and biases), the search space is significantly reduced, allowing faster convergence with fewer computational resources while maintaining prediction accuracy on large datasets.
Solution Approach 2:
The patent segments the training process into two distinct phases: (1) training with monotonic constraints to establish interpretable parameter relationships, and (2) optional fine-tuning without constraints. This segmentation allows the model to achieve both interpretability and accuracy efficiently, reducing overall computational burden.
2Adaptability or versatility
If complex neural network structures are used to handle large datasets, then model capacity increases, but training time and computational complexity increase
Solution Approach 1:
By imposing monotonic constraints on network parameters, the patent effectively changes the parameter landscape to enable faster optimization. The constrained parameter space allows standard gradient descent methods to converge more quickly, reducing training time while maintaining the model's capacity to handle large datasets through appropriate architecture design.
3Productivity
If standard neural networks are trained without constraints, then training speed can be improved, but interpretability and explainability of outcomes deteriorate
Solution Approach 1:
The patent applies monotonic constraints to specific parameters (weights and biases) to ensure that the neural network maintains interpretable relationships between inputs and outputs. This parameter-level constraint approach enables the model to preserve domain knowledge (e.g., higher risk factors should not decrease risk scores) while still achieving efficient training through optimized convergence in the constrained parameter space.
4Loss of information
If monotonic constraints are applied during training, then model interpretability improves, but optimization complexity increases
Solution Approach 1:
The patent transforms the optimization problem by changing to a parameterized monotonic neural network formulation. Instead of adding complex constraint-solving machinery, the patent uses parameter transformations and reparameterization techniques that naturally enforce monotonicity, thereby improving interpretability without significantly increasing optimization complexity.
Solution Approach 2:
The patent segments the optimization process by separating monotonic constraint enforcement from standard gradient descent. The monotonic constraints are integrated into the loss function or parameterization, allowing the use of standard optimization algorithms while maintaining interpretability, thus avoiding the need for complex constrained optimization solvers.
Data Source
AI summary
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.