StableBoost: Stable XGBoost Predictions Under Data Shuffling

1 | Why It Matters

Even with a fixed random seed, shuffling the order of training rows changes XGBoost’s histogram bins (tree_method='hist'). Those altered cut-points yield a different forest and, consequently, different predictions on exactly the same data. Symptoms in production:

• Apparent “drift” after a routine retrain
• Flaky regression tests on model outputs
• Spurious monitoring alerts

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2 | Root Causes of Instability

1. Multi-thread histogram binning is row-order sensitive
   When tree_method='hist' and n_jobs > 1, each thread builds a local quantile sketch on its chunk of rows; merging those sketches makes the final bin boundaries depend on how the chunks were formed—hence on row order. Single-thread hist and tree_method='exact' avoid this effect.

2. Row subsampling amplifies sensitivity
   With subsample < 1, every boosting round trains on only a sample of rows.
   Shuffling the dataset changes which rows fall into that sample—even under a fixed random_state—so the gradient seen by each new tree differs.

3. Column subsampling is a smaller, second-order factor
   With colsample_bytree < 1, each tree sees a random subset of features. Different feature subsets nudge split choices; the resulting drift is typically an order of magnitude smaller than the first two causes, but still measurable.

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3 | Remedies

Concept	Example Implementation	Impact	Drawbacks
Fix the seed	Set random_state=...	Reduces randomness in sampling	No effect unless subsampling present
Eliminate subsampling	Set subsample=1, colsample*=1	Removes stochasticity in data use	Slower training; higher overfit risk
Use deterministic tree construction	Use tree_method='exact'	Fully reproducible split decisions (if subsampling off)	Much slower; infeasible on large datasets
Ensembling over multiple fits	Average predictions across K shuffles	Smooths variance; improves stability	Higher training + inference cost
Use inherently stable learners	CatBoost (ordered boosting); LightGBM deterministic mode	Near-zero drift out of the box	May require reengineering and tuning

ℹ️ The exact method performs greedy split finding by checking all possible thresholds for each feature value—no binning or approximation. It eliminates histogram-induced variance, but subsampling can still introduce model differences unless disabled.

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4 | Our Baseline & Metric

Experimental design

1. Fixed train/test split (75% / 25%)
2. No resampling – same rows every time, only shuffled order
3. Fit K independent XGB models (different permutations)
4. Evaluate on the held-out test set

Stability metric

For test observation j and K models:

$$\displaystyle \text{RMSE}j = \sqrt{2,\text{Var}{i}!\bigl(\hat p_{ij}\bigr)}
\quad\Longrightarrow\quad \text{MeanRMSE} = \frac{1}{N_{\text{test}}}\sum_j \text{RMSE}_j$$

Interprets as the expected RMSE between predictions from two fresh retrains.

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5 | Illustrative Results (synthetic data, K = 15)

Variant	Accuracy	ROC_AUC	Stability_RMSE
Single XGB (K=15)	0.9285	0.9643	0.0313
Ensemble (K=15) × 5	0.9310	0.9647	0.0072
XGB Random-Forest	0.8957	0.9514	0.0086
XGB Exact (subsample = 1, colsample = 1)	0.9250	0.9632	0.0000

Row-order alone ≈ 3 pp RMSE; bagging drives it to (near) zero.

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6 | Clean Reproducible Notebook

• Notebook

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7 | Using This in Practice

1. Drop-in your real feature matrix in place of make_classification.

2. Tune K for runtime vs. stability; RMSE shrinks ∼1/√K.

3. Integrate the metric into CI—fail builds when Stability_RMSE exceeds your tolerance (e.g., 0.01).

4. Optionally extend with bootstrap or CV resamples to capture full pipeline variance.

5. For stricter determinism:

   • Set subsample=1, colsample_bytree=1, and related knobs.
   • Use random_state for all randomness.
   • Consider tree_method='exact' if dataset is small.

8 | Authors

Victor Shia and Gaurav Sood