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Bayesian Additive Adaptive Basis Tensor Product Models for Modeling High Dimensional Surfaces: An Application to High-throughput Toxicity Testing.
  • Published Date:
    August 06 2018
  • Source:
    Biometrics. 75(1):193-201
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Public Access Version Available on: March 01, 2020, 12:00 AM information icon
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    Many modern datasets are sampled with error from complex high-dimensional surfaces. Methods such as tensor product splines or Gaussian processes are effective and well suited for characterizing a surface in two or three dimensions, but they may suffer from difficulties when representing higher dimensional surfaces. Motivated by high throughput toxicity testing where observed dose-response curves are cross sections of a surface defined by a chemical's structural properties, a model is developed to characterize this surface to predict untested chemicals' dose-responses. This manuscript proposes a novel approach that models the multidimensional surface as a sum of learned basis functions formed as the tensor product of lower dimensional functions, which are themselves representable by a basis expansion learned from the data. The model is described and a Gibbs sampling algorithm is proposed. The approach is investigated in a simulation study and through data taken from the US EPA's ToxCast high throughput toxicity testing platform.

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