# Bayesian Additive Adaptive Basis Tensor Product Models for Modeling High Dimensional Surfaces: An application to high-throughput toxicity testing

arXiv: https://arxiv.org/abs/1702.04775 · HTML: https://mlsanity.com/paper/1702.04775/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2017.

## Built on by (most cited first, 2 of 2)

- [Multi-Output Robust and Conjugate Gaussian Processes](https://mlsanity.com/paper/2510.26401/) (2025)
- [Structured Nonparametric Variational Inference for Dependent Latent Modeling](https://mlsanity.com/paper/2606.15458/) (2026)

## Abstract (arXiv)

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.