2018/01/27 by Lenka Filová, Filová, Lenka, Radoslav Harman +1 · 3 citations
Computer Science · Decision Sciences · #62K05 #Advanced Multi-Objective Optimization Algorithms #Advanced Statistical Process Monitoring #Computation (stat.CO) #FOS: Computer and information sciences #Optimal Experimental Design Methods
paper · pdf · doi:10.48550/arxiv.1801.09124
openalex publication_date 2018/01/27 · openalex created_date 2022/10/07 · openalex updated_date 2026/08/04
In the area of statistical planning, there is a large body of theoretical\nknowledge and computational experience concerning so-called optimal approximate\ndesigns of experiments. However, for an approximate design to be executed in\npractice, it must be converted into an exact, i.e., integer, design, which is\nusually done via rounding procedures. Although rapid, rounding procedures have\nmany drawbacks; in particular, they often yield worse exact designs than\nheuristics that do not require approximate designs at all.\n In this paper, we build on an alternative principle of utilizing optimal\napproximate designs for the computation of optimal, or nearly-optimal, exact\ndesigns. The principle, which we call ascent with quadratic assistance (AQuA),\nis an integer programming method based on the quadratic approximation of the\ndesign criterion in the neighborhood of the optimal approximate information\nmatrix.\n To this end, we present quadratic approximations of all Kiefer's criteria\nwith an integer parameter, including D- and A-optimality and, by a model\ntransformation, I-optimality. Importantly, we prove a low-rank property of the\nassociated quadratic forms, which enables us to apply AQuA to large design\nspaces, for example via mixed integer conic quadratic solvers. We numerically\ndemonstrate the robustness and superior performance of the proposed method for\nmodels under various types of constraints. More precisely, we compute optimal\nsize-constrained exact designs for the model of spring-balance weighing, and\noptimal symmetric marginally restricted exact designs for the Scheffe mixture\nmodel. We also show how can iterative application of AQuA be used for a\nstratified information-based subsampling of large datasets under a lower bound\non the quality and an upper bound on the cost of the subsample.\n