Generalized Additive Models for Large Data Sets

Abstract

Summary.We consider an application in electricity grid load prediction, where generalized additive models are appropriate, but where the data set's size can make their use practically intractable with existing methods. We therefore develop practical generalized additive model fitting methods for large data sets in the case in which the smooth terms in the model are represented by using penalized regression splines. The methods use iterative update schemes to obtain factors of the model matrix while requiring only subblocks of the model matrix to be computed at any one time.We show that efficient smoothing parameter estimation can be carried out in a well-justified manner. The grid load prediction problem requires updates of the model fit, as new data become available, and some means for dealing with residual auto-correlation in grid load. Methods are provided for these problems and parallel implementation is covered. The methods allow estimation of generalized additive models for large data sets by using modest computer hardware, and the grid load prediction problem illustrates the utility of reduced rank spline smoothing methods for dealing with complex modelling problems.

The cave of shadows: Addressing the human factor with generalized additive mixed models

“…Pinheiro and Bates (2000) and Ga lecki and Burzykowski (2013) provide extensive discussion of how autocorrelation processes can be accounted for within the mixed modeling framework; Wood et al (2015) provides technical details for gamms. With a mild proportionality constant ρ = 0.15, autocorrelations are almost completely removed.…”

“…A generalized additive mixed model (Hastie and Tibshirani, 1990;Lin and Zhang, 1999;Wood, 2006Wood, , 2011Wood et al, 2015) is a glmm in which part of the linear predictor η is itself specified as a sum of smooth functions of one or more predictor variables. Thus, a generalized additive (mixed) model is additive in two ways.…”

Spatio-temporal modelling of lightning climatologies for complex terrain

“…7 309 152 data points, is feasible, e.g. via function bam() (for big additive models) implemented in the mgcv package (Wood et al, 2015;Wood, 2016) of the statistical software R (R Core Team, 2016).…”

Modeling of sea surface temperature using linear models with autocorrelation Indian Ocean

“…From equation (5) we assume Hi ~ N(0, V 2 ), [7]. In GAM model, [7] used loess smoothers or smoothing splines functions, whereas GAM via mgcv package by Simon Wood [9] and the model for large data sets [10]. By using spline regression method, we used knots to minimalize penalize as in the following:…”