arXiv subjects

Matthew W. Wheeler

Publications and source records attributed to Matthew W. Wheeler.

5 recordsLinked to original sources

arXiv2020

Bayesian joint modeling of chemical structure and dose response curves

Today there are approximately 85,000 chemicals regulated under the Toxic Substances Control Act, with around 2,000 new chemicals introduced each year. It is impossible to screen all of these chemicals for potential toxic effects either via full organism in vivo studies or in vitro high-throughput screening (HTS) programs. Toxicologists face the challenge of choosing which chemicals to screen, and predicting the toxicity of as-yet-unscreened chemicals. Our goal is to describe how variation in chemical structure relates to variation in toxicological response to enable in silico toxicity characterization designed to meet both of these challenges. With our Bayesian partially Supervised Sparse and Smooth Factor Analysis ($\text{BS}^3\text{FA}$) model, we learn a distance between chemicals targeted to toxicity, rather than one based on molecular structure alone. Our model also enables the prediction of chemical dose-response profiles based on chemical structure (that is, without in vivo or in vitro testing) by taking advantage of a large database of chemicals that have already been tested for toxicity in HTS programs. We show superior simulation performance in distance learning and modest to large gains in predictive ability compared to existing methods. Results from the high-throughput screening data application elucidate the relationship between chemical structure and a toxicity-relevant high-throughput assay. An R package for $\text{BS}^3\text{FA}$ is available online at https://github.com/kelrenmor/bs3fa.

stat.AP↗

arXiv2020

Fast increased fidelity approximate Gibbs samplers for Bayesian Gaussian process regression

The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs in Bayesian models is limited to problems containing at most several thousand observations. Sampling requires matrix operations that scale at $\mathcal{O}(n^3),$ where $n$ is the number of unique inputs. Storage of individual matrices scales at $\mathcal{O}(n^2),$ and can quickly overwhelm the resources of most modern computers. To overcome these bottlenecks, we develop a sampling algorithm using $\mathcal{H}$ matrix approximation of the matrices comprising the GP posterior covariance. These matrices can approximate the true conditional covariance matrix within machine precision and allow for sampling algorithms that scale at $\mathcal{O}(n \ \mbox{log}^2 n)$ time and storage demands scaling at $\mathcal{O}(n \ \mbox{log} \ n).$ We also describe how these algorithms can be used as building blocks to model higher dimensional surfaces at $\mathcal{O}(d \ n \ \mbox{log}^2 n)$, where $d$ is the dimension of the surface under consideration, using tensor products of one-dimensional GPs. Though various scalable processes have been proposed for approximating Bayesian GP inference when $n$ is large, to our knowledge, none of these methods show that the approximation's Kullback-Leibler divergence to the true posterior can be made arbitrarily small and may be no worse than the approximation provided by finite computer arithmetic. We describe $\mathcal{H}-$matrices, give an efficient Gibbs sampler using these matrices for one-dimensional GPs, offer a proposed extension to higher dimensional surfaces, and investigate the performance of this fast increased fidelity approximate GP, FIFA-GP, using both simulated and real data sets.

math.ST↗

arXiv2019

Bayesian Stacked Parametric Survival with Frailty Components and Interval Censored Failure Times

To better understand effects of exposure to food allergens, food challenge studies are designed to slowly increase the dose of an allergen delivered to allergic individuals until an objective reaction occurs. These dose-to-failure studies are used to determine acceptable intake levels and are analyzed using parametric failure time models. Though these models can provide estimates of the survival curve, their parametric form may misrepresent the survival function for doses of interest, and different models that describe the data similarly may produce different dose-to-failure estimates. Motivated by predictive inference, we developed a Bayesian approach to combine survival estimates based upon posterior predictive stacking, where the weights are formed to maximize posterior predictive accuracy. The approach allows for the inclusion of flexible models, and, in our case, allows us to include random effects to account for frailty components entering the model through study-to-study heterogeneity. The methodology is investigated in simulation, and is used to estimate allergic population eliciting doses for multiple food allergens.

stat.AP↗

arXiv2017

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

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.

stat.ML↗

arXiv2016

Bayesian Local Extrema Splines

We consider the problem of shape restricted nonparametric regression on a closed set X ?\in R; where it is reasonable to assume the function has no more than H local extrema interior to X: Following a Bayesian approach we develop a nonparametric prior over a novel class of local extrema splines. This approach is shown to be consistent when modeling any continuously differentiable function within the class of functions considered, and is used to develop methods for hypothesis testing on the shape of the curve. Sampling algorithms are developed, and the method is applied in simulation studies and data examples where the shape of the curve is of interest.

stat.ME↗