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MSPE of ridge regression

Source: vignettes/articles/criterion-mspe.Rmd
criterion-mspe.Rmd

The expected mean squared prediction error of ridge regression for the target individuals (Chen et al., 2024). Without a test set, all candidates are the target.

Type Model-based
Direction Smaller is better
Uses a test set yes; without a test set, all candidates
Score a given set mspe_score()
Search with it optTrain(method = "MSPE")

Definition

With A=X′(XX′+I)−1A = X'(XX' + I)^{-1} and target rows XcX_c (ncn_c rows): MSPE=1+tr(XcAA′Xc′)/nc+‖Xc−XcAX‖F2\mathrm{MSPE} = 1 + \mathrm{tr}(X_c A A' X_c')/n_c + \lVert X_c - X_c A X\rVert_F^2 (Eq. 4 of Chen et al., 2024).

Use in TSDFGS 

library(TSDFGS)
data(geno)
mspe_score(geno[1:50, ], geno[51:100, ])
## [1] 636411
fit <- optTrain(geno, cand = 1:404, n.train = 50, method = "MSPE",
                 min.iter = 300, console = FALSE, seed = 1)
fit$OPTtrain
##  [1]   3 324 119 299 379 129 149  85 277 254 330 263  32 162 158 133  97 217 392
## [20] 312 391 287 142  89  65 110 329 372  42 308  20 190 199 311  28 376 172  15
## [39] 138 221  39 298  82 160  38 390 185 256 304 127
# targeted: the test set is known
fit2 <- optTrain(geno, cand = 1:300, n.train = 50, test = 301:404,
                  method = "MSPE", min.iter = 300, console = FALSE, seed = 1)
fit2$OPTtrain
##  [1]  52 129  76 196  85 260  99 148 298  43  74 217 165  89 157  66 127  44 216
## [20]  31  40 172 108 162 193 116 160  71  72  97 245 283  65 183 164 254 300  16
## [39]  58  17 189  34 202 204 173 212 268 199  78 136

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

Chen, S.-P., Sung, W.-H., & Liao, C.-T. (2024). Constructing training sets for genomic selection to identify superior genotypes in candidate populations. Theoretical and Applied Genetics, 137, 270. https://doi.org/10.1007/s00122-024-04766-y

Repository or website of the original authors: R package TSODBG of Chen et al. (2024): github.com/spcspin/TSODBG (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: TSODBG, GPL (>= 3); we compared with its mspe_score and did not copy.
  • Article license: CC BY-NC-ND 4.0; cited, not reproduced.
  • Verdict: included.

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