An unexpected connection between Bayes A-optimal designs and the group lasso

Guillaume Sagnol () and Edouard Pauwels ()
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Guillaume Sagnol: Technische Universität Berlin
Edouard Pauwels: Toulouse 3 Université Paul Sabatier

Statistical Papers, 2019, vol. 60, issue 2, No 14, 565-584

Abstract: Abstract We show that the A-optimal design optimization problem over m design points in $${\mathbb {R}}^n$$ R n is equivalent to minimizing a quadratic function plus a group lasso sparsity inducing term over $$n\times m$$ n × m real matrices. This observation allows to describe several new algorithms for A-optimal design based on splitting and block coordinate decomposition. These techniques are well known and proved powerful to treat large scale problems in machine learning and signal processing communities. The proposed algorithms come with rigorous convergence guarantees and convergence rate estimate stemming from the optimization literature. Performances are illustrated on synthetic benchmarks and compared to existing methods for solving the optimal design problem.

Keywords: A-optimal design; Group Lasso; Optimization; First Order Methods; 62K05; 90C25 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s00362-018-01062-y

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