Regression Model Selection Using Closed-Form Predictive Power
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Solution Overview
Problem
Existing methods for measuring the predictive power of regression models are computationally expensive and inefficient, especially for large datasets, due to the need for repetitive model fitting and data splitting in cross-validation processes.
Innovation Solution
A method that uses a predictive analytics engine to acquire an input dataset, receive multiple regression models through a forward selection procedure, and measure the predictive power of each model using a closed-form estimator based on the square cross-validated correlation, allowing for the selection of an optimal model that meets a predictive power threshold.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional cross-validation methods are used to measure predictive power, then measurement accuracy is improved, but computational cost and time consumption increase significantly
Solution Approach 1:
The patent extracts the core predictive power measurement from the complex cross-validation process by using a closed-form estimator based on the coefficient of multiple determination. This estimator directly computes predictive power without requiring repetitive model fitting and data splitting, thus maintaining measurement accuracy while dramatically reducing computational cost.
Solution Approach 2:
The patent replaces the mechanical iterative process of cross-validation (repetitive model fitting, data splitting, and aggregation) with a direct mathematical computation using a closed-form estimator. This substitution eliminates the need for multiple model training cycles while preserving the essential measurement function.
2Reliability
If repetitive model fitting is performed for each data split in cross-validation, then predictive power measurement reliability is improved, but processing time increases
Solution Approach 1:
The patent performs a single model fitting operation on the complete dataset beforehand, then uses this pre-fitted model to compute predictive power for different data splits using the closed-form estimator. This preliminary action eliminates the need for repetitive model fitting while maintaining the reliability of predictive power measurement across different data configurations.
3Measurement precision
If data splitting is performed for cross-validation, then model generalization assessment is improved, but computational complexity increases
Solution Approach 1:
The patent extracts the generalization assessment function from the complex data splitting and model refitting process by using a closed-form estimator that computes predictive power directly from a single model fit. This approach maintains the ability to assess model generalization while eliminating the computational complexity of multiple data splits and model training cycles.
Data Source
AI summary
Selecting an optimal model by acquiring, via a predictive analytics engine of a learning machine, an input dataset, and receiving a number of possible regression models for selection, the input dataset includes a plurality of labeled cases. Each candidate regression which is generated through a forward selection procedure is fitted to the input dataset to describe a relationship between one or more explanatory variable values and response variable values of the input dataset. A predictive power of the possible regression model is measured by computing a usual square coefficient of multiple determination, and either a point estimate of the square cross-validated correlation or a two-sided confidence interval of the square cross-validated correlation associated with the given regression sample. Based on the predictive power, the possible regression model that meets a predictive power threshold is selected as an optimal regression model.