PEVmean (ridge, PCs) • TSDFGS

The prediction error variance (PEV) measures how uncertain the model predictions are for the test set. TSDFGS sums it over the test individuals.

Type	Model-based
Direction	Smaller is better
Uses a test set	yes
Score a given set	`pev_score()`
Search with it	`optTrain(method = "PEV")`

Definition

With an intercept column added, $B = (X'X + \lambda I)^{-1}$ and $\lambda = 1/p$ :

$\mathrm{PEV} = \mathrm{tr}(X_0 B X_0').$

Dividing by $n_0$ gives PEVmean. This is the PC-ridge form of Akdemir et al. (2015). The relationship-matrix PEV of Rincent et al. (2012) uses contrasts instead; see CDmean.

Use in TSDFGS

library(TSDFGS)
data(geno)
pev_score(geno[1:50, ], geno[51:100, ])

## [1] 257145357

fit <- optTrain(geno, cand = 1:404, n.train = 50, method = "PEV",
                 min.iter = 300, console = FALSE, seed = 1)
fit$OPTtrain

##  [1]   3 324 119 299 379 129 149  85 277 254 330 263  32 162 158 133  97 217 392
## [20] 312 391 287 142  89  65 110 329 372  42 308  20 190 199 311  28 376 172  15
## [39] 138 221  39 298  82 160  38 390 185 256 304 127

# targeted: the test set is known
fit2 <- optTrain(geno, cand = 1:300, n.train = 50, test = 301:404,
                  method = "PEV", min.iter = 300, console = FALSE, seed = 1)
fit2$OPTtrain

##  [1] 183 218  17 129 171 112  41  93  75  71 261  16 143 162 146  76 298 122 289
## [20] 163 272  59  13 180 164 190 245 199 157 216 160  69   2  97 130 152 113  47
## [39]  44  35  31 151 165 300  65 264  43  89 221 240

The search is a random-start exchange (hill-climbing) search; see How the scores are computed. Use min.iter larger than 300 on real data and check fit$converged.

Original work

Akdemir, D., Sanchez, J. I., & Jannink, J.-L. (2015). Optimization of genomic selection training populations with a genetic algorithm. Genetics Selection Evolution, 47, 38. https://doi.org/10.1186/s12711-015-0116-6

Rincent, R., Laloë, D., Nicolas, S., Altmann, T., Brunel, D., Revilla, P., et al. (2012). Maximizing the reliability of genomic selection by optimizing the calibration set of reference individuals: comparison of methods in two diverse groups of maize inbreds (Zea mays L.). Genetics, 192, 715-728. https://doi.org/10.1534/genetics.112.141473

Repository or website of the original authors: R package STPGA by Akdemir and colleagues: CRAN.R-project.org/package=STPGA (GPL-3). Rincent et al. (2012) give no software link.

License review

Formulas and algorithms are ideas and methods, which copyright does not protect. Where an original package is under a GPL license, we read it to check our results and credit it; TSDFGS is GPL-3, which is compatible with GPL-3 and GPL (>= 3) code. This is our reading of the public record, not legal advice; see the license review.

Original software: STPGA, GPL-3; we compared outputs and did not copy code.
Article license: Akdemir et al. (2015) CC BY 4.0; Rincent et al. (2012) CHORUS public access.
Patents: none in the articles. TrainSel (2021) says its concepts may be patented; PEV predates it and TSDFGS does not use TrainSel.
Verdict: included.

Reviewed 2026-11-04. All criteria and the ones left out.