Nonlinear model structure detection using optimum experimental design and orthogonal least squares.

Area of Science:

• Statistics
• Machine Learning
• Computational Science

Background:

• Model selection is crucial for building accurate and parsimonious predictive models.
• Existing methods may not effectively balance approximation accuracy with parameter estimate reliability.

Discussion:

• Introduces a novel composite cost function for efficient model subset selection.
• Integrates an A-optimality design criterion to minimize parameter estimate variance, enhancing model adequacy.
• Employs forward orthogonal least squares for parameter estimation.

Key Insights:

• The composite cost function effectively optimizes both model approximation ability and adequacy.
• The A-optimality criterion ensures parsimony and reduces the variance of parameter estimates.
• The algorithm demonstrates superior performance in selecting optimal model subsets.

Outlook:

• Potential applications in various fields requiring parsimonious and adequate models, such as econometrics and engineering.
• Further research could explore extensions to non-linear models or different optimality criteria.
• The developed algorithm offers a robust framework for efficient model selection in complex datasets.