Numerical experiments on SMOTE

Numerical illustrations accompanying the presentation of:

Sakho, Malherbe & Scornet (2024). Do we need rebalancing strategies? A theoretical and empirical study around SMOTE and its variants. arXiv:2402.03819v5

Prepared for the Guidelines in ML course (M2 Mathématiques & IA, Université Paris-Saclay).

Experiments

Experiment 1 — Diversity measure (experiments/diversity_measure.py)

Illustrates Theorem 3.4 and Corollary 3.5: when K is fixed (default K=5), SMOTE asymptotically copies the original minority samples. We reproduce the diversity metric from Appendix B on three different distributions (uniform square, uniform disk, Gaussian mixture) to show the phenomenon is distribution-agnostic.

Experiment 2 — Boundary artifact (experiments/boundary_artifact.py)

Illustrates Theorem 3.6: SMOTE density vanishes near the boundary of the minority class support. We provide scatter plots (absent from the paper) on a disk and an annulus, plus radial density profiles. The annulus case additionally demonstrates Lemma 3.1 (SMOTE fills non-convex holes).

Usage

pip install -r requirements.txt
mkdir -p figures
python experiments/diversity_measure.py
python experiments/boundary_artifact.py

Figures are saved in figures/.

Note on methodology

We used an LLM (Claude, Anthropic) as an aid for code structuring and discussion of theoretical results. The experimental design, distribution choices, and analysis are our own.

Reference

Original paper code: github.com/artefactory/smote_strategies_study