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Handling hard affine SDP shape constraints in RKHSs

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Listed:
  • Aubin-Frankowski, Pierre-Cyril
  • Szabo, Zoltan

Abstract

Shape constraints, such as non-negativity, monotonicity, convexity or supermodularity, play a key role in various applications of machine learning and statistics. However, incorporating this side information into predictive models in a hard way (for example at all points of an interval) for rich function classes is a notoriously challenging problem. We propose a unified and modular convex optimization framework, relying on second-order cone (SOC) tightening, to encode hard affine SDP constraints on function derivatives, for models belonging to vector-valued reproducing kernel Hilbert spaces (vRKHSs). The modular nature of the proposed approach allows to simultaneously handle multiple shape constraints, and to tighten an infinite number of constraints into finitely many. We prove the convergence of the proposed scheme and that of its adaptive variant, leveraging geometric properties of vRKHSs. Due to the covering-based construction of the tightening, the method is particularly well-suited to tasks with small to moderate input dimensions. The efficiency of the approach is illustrated in the context of shape optimization, robotics and econometrics.

Suggested Citation

  • Aubin-Frankowski, Pierre-Cyril & Szabo, Zoltan, 2022. "Handling hard affine SDP shape constraints in RKHSs," LSE Research Online Documents on Economics 115724, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:115724
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    File URL: http://eprints.lse.ac.uk/115724/
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    References listed on IDEAS

    as
    1. Wu, Ximing & Sickles, Robin, 2018. "Semiparametric estimation under shape constraints," Econometrics and Statistics, Elsevier, vol. 6(C), pages 74-89.
    2. Rahul Mazumder & Arkopal Choudhury & Garud Iyengar & Bodhisattva Sen, 2019. "A Computational Framework for Multivariate Convex Regression and Its Variants," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 318-331, January.
    3. Yining Chen & Richard J. Samworth, 2016. "Generalized additive and index models with shape constraints," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 729-754, September.
    4. Gad Allon & Michael Beenstock & Steven Hackman & Ury Passy & Alexander Shapiro, 2007. "Nonparametric estimation of concave production technologies by entropic methods," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(4), pages 795-816.
    5. Varian, Hal R, 1984. "The Nonparametric Approach to Production Analysis," Econometrica, Econometric Society, vol. 52(3), pages 579-597, May.
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    More about this item

    Keywords

    vector-valued reproducing kernel Hilbert space; shape-constrained optimization; matrix-valued kernel; kernel derivatives;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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