Margin Relaxed Schrodinger Bridge Synthetic Data Generation
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Solution Overview
Problem
There is a need for methods and systems to generate synthetic datasets that have distributions similar to those used as training sets for generative models, while ensuring a predefined feature of the dataset is close to a predefined value.
Innovation Solution
The method involves receiving a first dataset, determining an expression of the Schrödinger Bridge problem, modifying it by introducing a transformation function term, optimizing this transformation function with respect to a predetermined feature, and using the optimized function to generate a synthetic dataset.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional generative models are used to generate synthetic datasets, then the generation process is simple, but the predefined feature of the dataset cannot be controlled to be close to a predefined value
Solution Approach 1:
The patent introduces a marginal relaxation term as an intermediary component in the Schrödinger bridge objective function. This term acts as a mediator that connects the distribution matching objective with the feature control objective, allowing the model to simultaneously achieve both goals without direct complex coupling between them.
Solution Approach 2:
The patent modifies the traditional Schrödinger bridge objective function by adding a marginal relaxation parameter (epsilon) that controls the trade-off between distribution fidelity and feature constraint satisfaction. By adjusting this parameter, the system can dynamically balance between the two competing objectives.
2Adaptability or versatility
If the Schrödinger Bridge problem is solved exactly without marginal relaxation, then the distribution matching is optimal, but the feature control capability is lost
Solution Approach 1:
The patent applies partial action by introducing marginal relaxation that partially relaxes the distribution matching constraint to enable feature control. Instead of fully enforcing the original Schrödinger bridge constraints, the method selectively relaxes them to the extent necessary to achieve feature control while maintaining sufficient distribution fidelity.
Solution Approach 2:
The patent changes the parameter space of the objective function by adding the marginal relaxation term with a controllable weight parameter. This allows dynamic adjustment of the balance between distribution matching accuracy and feature control capability through parameter optimization.
3Reliability
If multiple constraints are enforced strictly in the generative model, then the feature control is precise, but the optimization becomes intractable
Solution Approach 1:
The patent uses the marginal relaxation term as an intermediary that transforms hard constraints into soft constraints. This intermediary mechanism allows the optimization process to handle multiple constraints in a unified, tractable manner by converting them into a regularized objective function that can be optimized using standard techniques.
Solution Approach 2:
The patent transforms the constraint satisfaction problem into a parameter optimization problem by introducing relaxation parameters. This changes the nature of the optimization from a constrained optimization (which is intractable) to an unconstrained or softly-constrained optimization (which is tractable), while still achieving reliable constraint satisfaction through proper parameter tuning.
Data Source
AI summary
Systems and methods for generating synthetic datasets having distributions that are close to those used as training sets for a generative model and for which a predefined feature of the dataset is close to a predefined value are provided. The method includes: receiving a first dataset that includes original data; determining an expression of a Schrodinger Bridge problem that corresponds to the first dataset; modifying the expression by introducing a term that relates to a transformation function; optimizing the transformation function with respect to a predetermined feature of the first dataset; and using the optimized transformation function to generate a second dataset that includes synthetic data.