Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1602.05208

Smoothing spline ANOVA for super-large samples: Scalable computation via rounding parameters

Nathaniel E. Helwig·Ping Ma
View original source ↗Read source document ↗Export metadata ↓

Abstract

In the current era of big data, researchers routinely collect and analyze data of super-large sample sizes. Data-oriented statistical methods have been developed to extract information from super-large data. Smoothing spline ANOVA (SSANOVA) is a promising approach for extracting information from noisy data; however, the heavy computational cost of SSANOVA hinders its wide application. In this paper, we propose a new algorithm for fitting SSANOVA models to super-large sample data. In this algorithm, we introduce rounding parameters to make the computation scalable. To demonstrate the benefits of the rounding parameters, we present a simulation study and a real data example using electroencephalography data. Our results reveal that (using the rounding parameters) a researcher can fit nonparametric regression models to very large samples within a few seconds using a standard laptop or tablet computer.

Explore related subjects

stat.CO

Keep this discovery

BibTeXRIS

Nathaniel E. Helwig, Ping Ma. 2016-02-16. Smoothing spline ANOVA for super-large samples: Scalable computation via rounding parameters. https://arxiv.org/abs/1602.05208

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Estimating Hierarchically Rank Structured Covariance Matrices

We consider the problem of estimating a high-dimensional covariance matrix from a very limited number of samples. This problem is ubiquitous in computational fluid dynamics, where a small number of fluid snapshots must be used to construct a Gramian matrix determining a reduced-order model, as well as in computational geoscience, where a small ensemble of Earth system forecasts must be used to estimate the covariance matrix associated with the forecast uncertainty. It is common practice to regularize the small-sample covariance by imposing a "localization" structure that enforces a physically realistic correlation length scale, imposing a sparsity constraint, "shrinking" towards a prescribed target, or attenuating small correlations. We propose an alternate technique that regularizes the small-sample covariance by imposing hierarchical rank structure. Compared to regularization methods that assume sparsity such as spatial localization, hierarchical rank structure accommodates a wider range of covariance matrices, roughly corresponding to situations where long-range correlations vary more smoothly than short-range ones. It also results in a data-sparse matrix format that permits highly efficient matrix-vector products. We present theory and algorithms which show how to efficiently estimate a high-dimensional, hierarchically rank structured covariance matrix from limited samples. Through an error analysis and numerical experiments with a variety of model problems, we demonstrate that these techniques are effective at reducing sampling errors, and that in many cases they achieve smaller estimation error than conventional techniques.

stat.CO↗
arXiv2026

Optimal Slice-Adaptive Tuning of Hybrid Slice Sampling

Slice sampling is a Markov chain Monte Carlo algorithm that draws its next state uniformly from a "slice"---a super-level set of the target density function---at each iteration, thereby providing automatic local adaptivity to the scale of the target. In practice the exact slice is not known, so general-purpose implementations use an approximate slice that is grown from a starting interval of length $w>0$, with a computational cost that depends on $w$. This work presents an analysis of the average per-iteration number of target density evaluations, as a function of $w$, of hybrid slice sampling with various slice-finding schemes for targets with contiguous slices. The paper uses the results of the analysis to develop automated, slice-adaptive tuning schemes along with suboptimality bounds and asymptotic convergence guarantees. Simulations demonstrate that the tuning schemes reliably yield near-optimal slice-adaptive tuning with essentially no dependence on the initial setting of $w$.

stat.CO↗