Journal of Data Science

With the growing scale of big datasets, fitting novel statistical models on larger-than-memory datasets becomes correspondingly challenging. This document outlines the development and use of an API for large scale modelling, with a demonstration given by the proof of concept platform largescaler, developed specifically for the development of statistical models for big datasets.

For spatial kriging (prediction), the Gaussian process (GP) has been the go-to tool of spatial statisticians for decades. However, the GP is plagued by computational intractability, rendering it infeasible for use on large spatial data sets. Neural networks (NNs), on the other hand, have arisen as a flexible and computationally feasible approach for capturing nonlinear relationships. To date, however, NNs have only been scarcely used for problems in spatial statistics but their use is beginning to take root. In this work, we argue for equivalence between a NN and a GP and demonstrate how to implement NNs for kriging from large spatial data. We compare the computational efficacy and predictive power of NNs with that of GP approximations across a variety of big spatial Gaussian, non-Gaussian and binary data applications of up to size $n={10^{6}}$. Our results suggest that fully-connected NNs perform similarly to state-of-the-art, GP-approximated models for short-range predictions but can suffer for longer range predictions.

Subsampling is an effective way to deal with big data problems and many subsampling approaches have been proposed for different models, such as leverage sampling for linear regression models and local case control sampling for logistic regression models. In this article, we focus on optimal subsampling methods, which draw samples according to optimal subsampling probabilities formulated by minimizing some function of the asymptotic distribution. The optimal subsampling methods have been investigated to include logistic regression models, softmax regression models, generalized linear models, quantile regression models, and quasi-likelihood estimation. Real data examples are provided to show how optimal subsampling methods are applied.