docs(examples): split before normalization to prevent data leakage in 12 notebooks

[umi008]

Closes #819

Context

12 of the 50 example notebooks in this repository normalize features (and sometimes labels) using statistics computed from the full dataset (including test data) before splitting into train/test. This silently leaks test-set statistics into the training pipeline and contradicts the pattern used by the clean notebooks in the same directories.

The anti-pattern is uniform: X = X - X.min(0)[0] / X = 2 * (X / X.max(0)[0]) - 1 (and sometimes y normalization) is computed on the full X, then a train_n = int(floor(0.8 * len(X))) split is performed afterwards.

PR #2752 (open, by r69shabh) adds documentation and a verification script for this same issue but does not fix the notebooks themselves. This PR is complementary — it fixes the 12 offending notebooks, while #2752 adds the docs and the check_normalization.py detector. Both can merge independently.

Fix

In each affected notebook, the data-loading cell is restructured to:

1. Split into train/test first (using the dataset's existing shuffle + index).
2. Compute normalization statistics (min/max, mean/std) from the training split only.
3. Apply the same statistics to both train and test.

This is the pattern already used by the clean reference notebooks (KeOps_GP_Regression, Simple_MultiGPU_GP_Regression) and is the only correct approach when test data must remain unseen.

Notebooks fixed (12)

• examples/02_Scalable_Exact_GPs/SGPR_Regression_CUDA.ipynb
• examples/02_Scalable_Exact_GPs/Scalable_Kernel_Interpolation_for_Products_CUDA.ipynb
• examples/02_Scalable_Exact_GPs/Simple_GP_Regression_With_LOVE_Fast_Variances_and_Sampling.ipynb
• examples/04_Variational_and_Approximate_GPs/Modifying_the_variational_strategy_and_distribution.ipynb
• examples/04_Variational_and_Approximate_GPs/Natural_Gradient_Descent.ipynb
• examples/04_Variational_and_Approximate_GPs/SVGP_Regression_CUDA.ipynb
• examples/04_Variational_and_Approximate_GPs/SVGP_CIQ.ipynb (also normalizes y)
• examples/04_Variational_and_Approximate_GPs/VNNGP.ipynb (also normalizes y; uses X.max(0)[0].clamp_min(1e-6))
• examples/05_Deep_Gaussian_Processes/Deep_Gaussian_Processes.ipynb
• examples/05_Deep_Gaussian_Processes/Deep_Sigma_Point_Processes.ipynb (also normalizes y; 75/25 split with shuffle and X.size(0) indexing — special case)
• examples/06_PyTorch_NN_Integration_DKL/KISSGP_Deep_Kernel_Regression_CUDA.ipynb
• examples/08_Advanced_Usage/TorchScript_Variational_Models.ipynb

The remaining 38 notebooks are clean (no change).

Test plan

• Manual smoke test of the split-then-normalize pattern with synthetic data confirms test inputs may exceed the train-input range (correct, no leakage)
• All 12 notebook data-loading cells produce the correct train/test tensor shapes after the change
• Verification script (if/when docs: Add normalization best practices and verification script #2752 merges) should report zero remaining offenders
• pre-commit run --files <notebook-paths> — the require-ascii hook excludes notebooks by design (exclude: ^(examples/.*\.ipynb)|(.github/ISSUE_TEMPLATE/.*)); ufmt is a no-op on JSON-derived .ipynb; all other hooks pass

Net change: 52 insertions, 417 deletions across 12 files.