E-optimality • TSDFGS

E-optimality limits the worst-estimated direction: the inverse of the smallest eigenvalue of the information matrix.

Type	Optimal design
Direction	Smaller is better
Uses a test set	no (a test set given to `optTrain()` is ignored)
Score a given set	`eopt_score()`
Search with it	`optTrain(method = "EOpt")`

Definition

$\mathrm{E} = 1/(\lambda_{\min}(X'X) + \lambda)$ . When $p > n$ the smallest eigenvalue is zero and the score is the constant $1/\lambda$ , so the criterion does not discriminate between training sets.

Use in TSDFGS

library(TSDFGS)
data(geno)
eopt_score(geno[1:50, ])

## [1] 404

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

##  [1] 324 167 129 299 270 187 307  85 277 362 330 263 329  79 213  37 105 217 366
## [20] 165 290 395 382  89 289 340 326 394  42 111  20  44 343  70 121  40 172  25
## [39] 248 198  39 298 280 160  14 130  45  22 206 230

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., & Isidro-Sánchez, J. (2019). Design of training populations for selective phenotyping in genomic prediction. Scientific Reports, 9, 1446. https://doi.org/10.1038/s41598-018-38081-6

Repository or website of the original authors: R package STPGA by Akdemir and colleagues: CRAN.R-project.org/package=STPGA (GPL-3).

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 (EOPT); compared, not copied.
Verdict: included.

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