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Publication Detail
Nonlinear generalization of the monotone single index model
  • Publication Type:
    Journal article
  • Publication Sub Type:
    Article
  • Authors:
    Kereta Ž, Klock T, Naumova V
  • Publisher:
    Oxford University Press (OUP)
  • Publication date:
    2021
  • Journal:
    Information and Inference: A Journal of the IMA
  • Status:
    Published
  • Print ISSN:
    2049-8764
  • Language:
    en
Abstract
Abstract Single index model is a powerful yet simple model, widely used in statistics, machine learning and other scientific fields. It models the regression function as $g(\left <{a},{x}\right>)$, where $a$ is an unknown index vector and $x$ are the features. This paper deals with a nonlinear generalization of this framework to allow for a regressor that uses multiple index vectors, adapting to local changes in the responses. To do so, we exploit the conditional distribution over function-driven partitions and use linear regression to locally estimate index vectors. We then regress by applying a k-nearest neighbor-type estimator that uses a localized proxy of the geodesic metric. We present theoretical guarantees for estimation of local index vectors and out-of-sample prediction and demonstrate the performance of our method with experiments on synthetic and real-world data sets, comparing it with state-of-the-art methods.
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