▶ Want to run it yourself? Download the Python notebook — it
recomputes every number on this page, on the same 400 real spectra (Windows-safe, ~2 min):
OSSL_Validation_Methods_WIN.zip
The one idea: a validation method is not a formula for accuracy — it is a
protocol for hiding data. Each of the five hides data differently, so each answers a
different question. Same data, same model, different hiding rule → different number.
Setup — what we're working with
400 soil samples from the Open Soil Spectral Library (OSSL) v1.2. Each sample is a
reflectance spectrum, and we predict soil organic carbon (SOC) from it.
samples 400
bands 1051 (400–2500 nm)
target log10(SOC %)
SOC raw range 0.05–62.37 %
model PLS, 10 components
Drawn from 4 real libraries:
LUCAS.SSL 242, KSSL.SSL 133, ICRAF.ISRIC 23, LUCAS.WOODWELL.SSL 2.
How to read this: left — 12 of the 400 real spectra; each line is one
soil's light fingerprint. Right — SOC on a log scale, because raw SOC is heavily right-skewed
(a few soils are very carbon-rich) and that skew wrecks regression.
All five on one page
How to read this: blue = training data, orange = test,
green = validation. Every method below is just a different way of painting this picture.
How to read this: the first seven bars are all in the same range —
they are all "random" hiding rules. The last red bar is a fundamentally different question.
Keep that gap in mind; section 7 explains it.
1 · Holdout Validation
Rule: split once (here 70/30), train on the big part, test on the small part, report
that one number.
The trap: the answer depends on which samples happened to land in
the test set. Five different random splits, identical model, identical data → R² from
0.694 to 0.796.
How to read this: left — five single splits; the bar heights are
the verdicts from the same model. Right — 20 splits, and the mean sits in the middle with a
real spread around it.
1
You get an unbiased estimate — nothing about
the test rows leaked into training.
2
But with high variance: the number is a
lottery draw. Report one split and you can't tell if the model is good or you got lucky.
Analogy: it's like judging a student on one randomly chosen exam
question. The question is fair, but the verdict swings wildly depending on which question they
got.
2 · Repeated Holdout Validation
Rule: do the same thing many times with different splits, then report the
mean and the spread. Cheapest possible fix for Method 1's variance.
On our data, 20 repeats give R² = 0.723 ± 0.036
(range 0.656–0.786). Note the mean barely moved versus a single split —
what you gained is the error bar.
Analogy: instead of one exam question, you give the student 20
randomly drawn questions and average. The average is a fairer verdict, and the spread tells you
how much the verdict depends on the draw.
3 · Bootstrap Validation
Rule: draw n rows with replacement — some rows appear several
times, and about 37% never appear at all. Train on the drawn rows, then score the ones
you missed. Those leftovers are the out-of-bag (OOB) samples.
How to read this: left — one resample of 400 rows; 143 rows were
never drawn (those are your free test set). Middle — the optimism problem: scoring a
model on its own training rows (apparent error 0.2942) looks better than
reality (OOB 0.3208). Right — the spread across all
200 resamples.
The .632 estimator blends the two:
0.368×apparent + 0.632×OOB = 0.3110. The exact split of the weights
comes from the bootstrap theory of optimism — you don't need to memorise it, just know it exists
to correct the too-rosy apparent error.
The subtlety: because rows are duplicated in the in-bag set, the model
partly memorises them. That is exactly why you must score on the OOB rows and never on the
training rows.
4 · 3-Way Holdout
Rule: three parts, three jobs — train fits the model, validation picks
the hyperparameters, test is touched once at the very end to report.
Here we tune one thing: how many PLS components to use (grid 1–20).
How to read this: left — error curves for all three sets; the
validation curve picks ncomp = 15. Right — if you instead let the test set
pick its own best model (ncomp = 7), the reported error drops to
0.3230 instead of the honest 0.3591.
That 0.0361 RMSE gap is the contamination. It is not a bug — it is what
happens when the test set stops being a neutral examiner and starts being part of the design.
Analogy: practice exams (validation) vs the final exam (test). If the
teacher writes the final after seeing which questions you got right, your final score
flatters you.
5 · Cross-Validation (k-fold, and Leave-One-Out)
Rule: split into k folds; train on k−1, test on the one left
out; rotate so every row is tested exactly once; average the k scores.
How to read this: left — per-fold scores; the box height is the
disagreement between folds. Right — colour shows which fold tested each row, after sorting by
SOC; every row is covered exactly once.
| Scheme | R² (mean) | sd across folds | RMSE (mean) |
|---|
| 5-fold | 0.725 |
0.052 | 0.3229 |
| 10-fold | 0.722 |
0.087 | 0.3196 |
| Leave-one-out (k = n = 400) | 0.737 |
— | 0.3203 |
Counter-intuitive bit: more folds is not automatically better.
LOO trains on n−1 rows every time, so its n folds are nearly identical — the mean is good but
the variance of the estimate can be understated. It also costs 400 model fits instead
of 5. Note 10-fold here has a wider spread (0.087) than 5-fold
(0.052) — smaller test folds means noisier individual scores.
How to read this: left — predicted vs observed; right — residuals.
The far-right panel is the useful one: predictions go wrong at very low and very high SOC,
which is a data-coverage problem, not a validation-method problem.
6 · All five side by side
| Method | R² | RMSE | Note |
|---|
| Holdout (single split) | 0.744 | 0.3315 | one number, high variance |
| Repeated holdout ×20 | 0.723 | — | sd R² 0.036 |
| Bootstrap OOB | 0.737 | 0.3208 | 200 resamples |
| 3-way (test, honest) | 0.704 | 0.3591 | ncomp=15 from validation |
| 5-fold CV | 0.725 | 0.3229 | sd R² 0.052 |
| 10-fold CV | 0.722 | 0.3196 | sd R² 0.087 |
| Leave-one-out | 0.737 | 0.3203 | 400 fits |
| Leave-one-DATASET-out | 0.203 | 0.4551 | the honest one |
7 · The twist that matters for soil data
Every method above hides rows at random. But two soil samples from the same region are
usually similar, so a random split can leave near-copies of your test samples inside the
training set. Your score then partly measures memorisation of neighbours, not the ability
to predict a new place.
The honest version holds out an entire source library: train on the others, predict a
library the model has never seen.
How to read this: left — holding out a whole library gives
0.762 (KSSL), 0.064 (ICRAF), and
-0.215 (LUCAS). The dashed line is what random 5-fold claimed.
Right — the gap: 0.725 vs 0.203.
Read this carefully: R² = 0 means "no better than always predicting the
average". A negative R² means worse than that. LUCAS scored
-0.215 — the model trained on American and African soils actively
mispredicts European soils. Random 5-fold hid that completely behind a score of
0.725.
The lesson: the leakage gap is
0.522 R². The hiding rule must match the question you
actually care about. "A new sample from the same places" and "a new place, new instrument,
new lab" are very different claims — and only one of them survives this test.
📋 Quick answer sheet
| Method | How it hides data | Answers the question | Watch out for |
|---|
| Holdout | one random split | "a new sample, same population" |
high variance — one lucky draw |
| Repeated holdout | many random splits | same, with an error bar |
cost scales with repeats |
| Bootstrap | resample with replacement; score OOB |
same, reusing data efficiently | apparent error is way too optimistic |
| 3-way holdout | separate set for tuning | same, with honest tuning |
tuning on test contaminates the score |
| k-fold CV | rotate k test folds | same, every row tested once |
fold spread; smaller folds are noisier |
| LOO (k = n) | leave exactly one row out | same, maximum training data |
n fits; folds nearly identical → variance understated |
🧠 Checklist before you report a score
1
Is it one split or a distribution? If one,
report the spread too.
2
Was the test set ever used for decisions
(tuning, feature selection, early stopping)? If yes, the score is contaminated.
3
Are you scoring on training rows anywhere?
Remember the apparent-vs-OOB gap of
0.0266 RMSE.
4
Do your folds respect the structure of the
data (region, site, instrument, year)? If not, you are measuring interpolation, not
generalisation.
5
Does your validation rule match the claim you're
making in the paper?