An efficient algorithm for Elastic I-optimal design of generalized linear models

The generalized linear models (GLMs) are widely used in statistical analysis and the related design issues are undoubtedly challenging. The state-of-the-art works mostly apply to design criteria on the estimates of regression coefficients. The prediction accuracy is usually critical in modern decision-making and artificial intelligence applications. It is of importance to study optimal designs from the prediction aspects for GLMs. In this work, we consider Elastic I-optimality as a prediction-oriented design criterion for GLMs, and develop an efficient algorithm for such EI-optimal designs. By investigating theoretical properties for the optimal weights of any set of design points and extending the general equivalence theorem to the EI-optimality for GLMs, the proposed efficient algorithm adequately combines the Fedorov-Wynn algorithm and the multiplicative algorithm. It achieves great computational efficiency with guaranteed convergence. Numerical examples are conducted to evaluate the feasibility and computational efficiency of the proposed algorithm.