Maximum expected entropy transformed Latin hypercube designs.

Area of Science:

• Statistics
• Experimental Design
• Machine Learning

Background:

• Traditional projection designs aim for uniform space-filling properties.
• Model-based criteria like entropy are more suitable for Gaussian processes (GPs).
• Existing methods may not be optimal for GP-based modeling.

Purpose of the Study:

• To develop projection designs optimized for Gaussian process models using the expected entropy criterion (EEC).
• To investigate the impact of input transformations on EEC designs.
• To enhance the performance of Latin hypercube designs (LHDs) for GP modeling.

Main Methods:

• Utilizing the expected entropy criterion (EEC) for generating projection designs.
• Applying monotonic transformations to columns of Latin hypercube designs (LHDs).
• Considering quantile functions of Beta and non-parametric symmetric densities for transformations.

Main Results:

• Maximum EEC designs are invariant to monotonic response transformations, ensuring broad applicability.
• Transformed LHDs significantly improve EEC compared to standard LHDs.
• Proposed designs yield higher projection entropies and lower maximum prediction variances (MPVs).

Conclusions:

• Input transformations effectively enhance LHDs for robust maximum EEC designs.
• The developed designs offer improved prediction accuracy and efficiency for GP models.
• These methods provide a valuable alternative to traditional space-filling designs in GP applications.