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Predicting paleoclimate from compositional data using multivariate Gaussian process inverse prediction

December 1, 2019

Multivariate compositional count data arise in many applications including ecology, microbiology, genetics and paleoclimate. A frequent question in the analysis of multivariate compositional count data is what underlying values of a covariate(s) give rise to the observed composition. Learning the relationship between covariates and the compositional count allows for inverse prediction of unobserved covariates given compositional count observations. Gaussian processes provide a flexible framework for modeling functional responses with respect to a covariate without assuming a functional form. Many scientific disciplines use Gaussian process approximations to improve prediction and make inference on latent processes and parameters. When prediction is desired on unobserved covariates given realizations of the response variable, this is called inverse prediction. Because inverse prediction is often mathematically and computationally challenging, predicting unobserved covariates often requires fitting models that are different from the hypothesized generative model. We present a novel computational framework that allows for efficient inverse prediction using a Gaussian process approximation to generative models. Our framework enables scientific learning about how the latent processes co-vary with respect to covariates while simultaneously providing predictions of missing covariates. The proposed framework is capable of efficiently exploring the high dimensional, multi-modal latent spaces that arise in the inverse problem. To demonstrate flexibility, we apply our method in a generalized linear model framework to predict latent climate states given multivariate count data. Based on cross-validation, our model has predictive skill competitive with current methods while simultaneously providing formal, statistical inference on the underlying community dynamics of the biological system previously not available.

Publication Year 2019
Title Predicting paleoclimate from compositional data using multivariate Gaussian process inverse prediction
DOI 10.1214/19-AOAS1281
Authors John R. Tipton, Mevin Hooten, Connor Nolan, Robert K. Booth, Jason McLachlan
Publication Type Article
Publication Subtype Journal Article
Series Title Annals of Applied Statistics
Index ID 70227737
Record Source USGS Publications Warehouse
USGS Organization Coop Res Unit Seattle