Bayesian Additive Adaptive Basis Tensor Product Models for Modeling High Dimensional Surfaces: An application to high-throughput toxicity testing
This work addresses the challenge of high-dimensional surface modeling in high-throughput toxicity testing for environmental and chemical safety applications, representing an incremental improvement over existing methods like tensor product splines or Gaussian processes.
The authors tackled the problem of modeling high-dimensional surfaces with error, specifically for predicting dose-response curves of untested chemicals based on structural properties, by developing a Bayesian additive adaptive basis tensor product model that demonstrated effectiveness in simulations and on ToxCast data.
Many modern data sets are sampled with error from complex high-dimensional surfaces. Methods such as tensor product splines or Gaussian processes are effective/well suited for characterizing a surface in two or three dimensions but 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, a Gibbs sampling algorithm proposed, and is investigated in a simulation study as well as data taken from the US EPA's ToxCast high throughput toxicity testing platform.