solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看5055次
Dimension Reduction via Gaussian Ridge Functions. (arXiv:1802.00515v1 [stat.ME])
来源于:arXiv
Ridge functions have recently emerged as a powerful set of ideas for
subspace-based dimension reduction. In this paper we begin by drawing parallels
between ridge subspaces, sufficient dimension reduction and active subspaces;
contrasting between techniques rooted in statistical regression to those rooted
in approximation theory. This sets the stage for our new algorithm that
approximates what we call a Gaussian ridge function---the posterior mean of a
Gaussian process on a dimension reducing subspace---suitable for both
regression and approximation problems. To compute this subspace we develop an
iterative algorithm that optimizes over the Grassmann manifold to compute the
subspace, followed by an optimization of the hyperparameters of the Gaussian
process. We demonstrate the utility of the algorithm on an analytical function,
where we obtain near exact ridge recovery, and a turbomachinery case study,
where we compare the efficacy of our approach with four well known sufficient
dimens 查看全文>>