Title: Extrema-weighted feature extraction for functional data,
Abstract: Motivation: Although there is a rich literature on methods for assessing the
impact of functional predictors, the focus has been on approaches for dimension
reduction that can fail dramatically in certain applications. Examples of
standard approaches include functional linear models, functional principal
components regression, and cluster-based approaches, such as latent trajectory
analysis. This article is motivated by applications in which the dynamics in a
predictor, across times when the value is relatively extreme, are particularly
informative about the response. For example, physicians are interested in
relating the dynamics of blood pressure changes during surgery to post-surgery
adverse outcomes, and it is thought that the dynamics are more important when
blood pressure is significantly elevated or lowered.
Methods: We propose a novel class of extrema-weighted feature (XWF)
extraction models. Key components in defining XWFs include the marginal density
of the predictor, a function up-weighting values at high quantiles of this
marginal, and functionals characterizing local dynamics. Algorithms are
proposed for fitting of XWF-based regression and classification models, and are
compared with current methods for functional predictors in simulations and a
blood pressure during surgery application.
Results: XWFs find features of intraoperative blood pressure trajectories
that are predictive of postoperative mortality. By their nature, most of these
features cannot be found by previous methods.