Approximation and Relaxation Approaches for Parallel and Distributed Machine Learning

Large scale machine learning requires tradeoffs. Commonly this tradeoff has led practitioners to choose simpler, less powerful models, e.g. linear models, in order to process more training examples in a limited time. In this work, we introduce parallelism to the training of non-linear models by leveraging a different tradeoff--approximation. We demonstrate various techniques by which non-linear models can be made amenable to larger data sets and significantly more training parallelism by strategically introducing approximation in certain optimization steps. For gradient boosted regression tree ensembles, we replace precise selection of tree splits with a coarse-grained, approximate split selection, yielding both faster sequential training and a significant increase in parallelism, in the distributed setting in particular. For metric learning with nearest neighbor classification, rather than explicitly train a neighborhood structure we leverage the implicit neighborhood structure induced by task-specific random forest classifiers, yielding a highly parallel method for metric learning. For support vector machines, we follow existing work to learn a reduced basis set with extremely high parallelism, particularly on GPUs, via existing linear algebra libraries. We believe these optimization tradeoffs are widely applicable wherever machine learning is put in practice in large scale settings. By carefully introducing approximation, we also introduce significantly higher parallelism and consequently can process more training examples for more iterations than competing exact methods. While seemingly learning the model with less precision, this tradeoff often yields noticeably higher accuracy under a restricted training time budget

Speeding up neighborhood search in local Gaussian process prediction

Recent implementations of local approximate Gaussian process models have pushed computational boundaries for non-linear, non-parametric prediction problems, particularly when deployed as emulators for computer experiments. Their flavor of spatially independent computation accommodates massive parallelization, meaning that they can handle designs two or more orders of magnitude larger than previously. However, accomplishing that feat can still require massive supercomputing resources. Here we aim to ease that burden. We study how predictive variance is reduced as local designs are built up for prediction. We then observe how the exhaustive and discrete nature of an important search subroutine involved in building such local designs may be overly conservative. Rather, we suggest that searching the space radially, i.e., continuously along rays emanating from the predictive location of interest, is a far thriftier alternative. Our empirical work demonstrates that ray-based search yields predictors with accuracy comparable to exhaustive search, but in a fraction of the time - bringing a supercomputer implementation back onto the desktop.Comment: 24 pages, 5 figures, 4 table