Logical Statistical Model Composition for Data Fidelity
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Solution Overview
Problem
Existing methods for composing mathematical models of existing systems face challenges in interpretability, convergence guarantees, and compatibility with background theory, particularly when dealing with incomplete or noisy data, and require large amounts of data.
Innovation Solution
A programmable computer system that uses novel logical & statistical (L&S) model composition techniques to generate a composed model by analyzing candidate functions and known background theory in a polynomial mathematical expression domain, ensuring target data fidelity and compatibility, and allowing for efficient semidefinite programming solutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If data-driven analysis techniques are used to generate mathematical models, then model fitting to data is improved, but interpretability deteriorates and theoretical guarantees are lost
Solution Approach 1:
The patent merges data-driven statistical inference with logic-based symbolic inference into a unified framework. The system combines neural network-based statistical models with formal logical representations, allowing the model to simultaneously achieve high data fitting accuracy through statistical learning and maintain interpretability through symbolic logic. This integration enables the model to provide both numerical predictions and explanatory reasoning about system behavior.
2Reliability
If logic-based analysis techniques are used to reason over mathematical formulas, then theoretical compatibility is improved, but performance with noisy or incomplete data deteriorates
Solution Approach 1:
The patent introduces an intermediary layer that translates between logical representations and statistical models. This intermediary enables the system to handle noisy or incomplete data by using statistical inference to fill gaps where logical completeness is lacking, while maintaining theoretical compatibility through the logical framework. The intermediary allows flexible reasoning that accommodates real-world data imperfections without sacrificing theoretical grounding.
3Adaptability or versatility
If both data-driven and logic-based techniques are used, then model comprehensiveness is improved, but computational complexity increases
Solution Approach 1:
The patent segments the model composition task into distinct modules: a statistical inference component for handling data, a logical inference component for handling theory, and a composition component for integrating them. This segmentation allows each component to be optimized independently and enables the system to selectively activate appropriate components based on the specific problem requirements, reducing overall computational complexity while maintaining comprehensive modeling capability.
4Productivity
If existing model composition techniques are used, then model generation is achieved, but convergence guarantees are lost
Solution Approach 1:
The patent implements feedback mechanisms that continuously monitor and adjust the model generation process. The system uses feedback from both data-driven training and logical consistency checking to guide the composition process, ensuring convergence to valid solutions. This feedback loop allows the system to detect when a model fails to converge or produces inconsistent results and automatically adjust the generation process to achieve reliable convergence guarantees.
Data Source
AI summary
Embodiments of the invention are directed to a programmable computer system having a processor system operable to perform processor system operations that include representing a set of candidate functions in a mathematical expression domain. The set of candidate functions defines relationships between data of an existing system. A set of known background theory is represented in the mathematical expression domain. The set of known background theory defines known relationships associated with the existing system. A model composition operation is performed that includes analyzing, in the mathematical expression domain, the set of candidate functions and the set of known background theory to generate a composed model that satisfies a target data fidelity in a manner that also satisfies a predetermined level of compatibility between the composed model and the set of known background theory.