K01
ICML 2026 · SD4H Workshop · July 2026

Empirical-Distribution Matching for Synthetic ECG Classification.

Benedikt Kolbeinsson · Arinbjörn Kolbeinsson

When a practitioner trains on synthetic data alone, the only thing they control is how the synthetic set is sampled. We test thirteen sampling policies on one ECG generator. None beats matching the real training distribution.

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Abstract

Conditional generative models are increasingly proposed as drop-in substitutes for restricted clinical datasets. Train a generator once, release a synthetic cohort, and let practitioners reuse it without touching the source records. The practitioner's only design surface is then the sampling policy used to draw the synthetic training set. The standard rebalancing recipes from the imbalanced-learning literature in vision and language do not transfer to this regime. The practitioner is better off matching the empirical training distribution as faithfully as possible at sample time. We test the idea by surveying thirteen sampling policies on a single 12-lead ECG latent diffusion model over PTB-XL, using train-on-synthetic, test-on-real macro AUROC. No policy beats the naive bootstrap baseline at matched budget. The failures collapse onto three mechanisms: class-distribution distortion, within-class diversity collapse, and label-by-demographic joint decoupling.

Key findings

  1. Nothing beats the bootstrap. Drawing real training-record conditioning tuples uniformly with replacement gives macro TSTR AUROC 0.8845. Among the alternatives, the best, diversity selection, reaches 0.8814, within noise. Every other policy falls further. The same-size real-data ceiling is 0.9123.
  2. Rebalancing toward rare classes hurts the rare classes. Uniform class sampling and 3× rare oversampling both lose macro AUROC, including on the rare bucket they were meant to help. Each extra rare sample is drawn from the same conditional, so oversampling multiplies generator noise rather than adding real support.
  3. Classifier-driven filtering squeezes the tail. A held-out judge has calibrated probabilities on common classes and noisy ones on rare classes. Iterative relabel lifts common-class AUROC by 0.020 and drops rare-class AUROC by 0.138. Quality filtering by global confidence is among the worst policies for the same reason.
  4. Breaking the label-by-demographic joint costs about as much as breaking the classes. Joint decoupling keeps label prevalence and co-occurrence but draws each demographic axis independently. It loses about as much macro as uniform class sampling. The generator is weaker on conditioning combinations it did not see in training.
  5. The synthetic corpus is additive to real data. A 50/50 blend of 4,000 real and 4,000 synthetic records reaches 0.908, statistically indistinguishable from the same-size real-data ceiling. In the synthetic-only regime that motivates the paper, no policy recovers this.

Why it matters

Synthetic medical data is increasingly released in a setting where the downstream practitioner never sees a real record. A custodian trains the generator, and everyone else works from samples. Anyone who has read the imbalanced-learning literature will want to rebalance toward the minorities. In this regime that instinct is wrong. The rare classes the practitioner most wants to oversample are the ones the generator is weakest on, so oversampling them multiplies noise instead of recovering missing support.

The positive recipe is simple. Track the empirical training distribution at sample time. Do not reweight prevalence, do not filter by classifier signal, and do not synthesise conditioning tuples that never appeared in training. The naive bootstrap does all three by construction, which is why it wins. Where some real data is available, the blend result says the synthetic corpus adds to it rather than diluting it.

Scope and limitations

One dataset, PTB-XL, on its official patient-disjoint folds. One generator, DCDM-ECG, held fixed. One downstream architecture, XResNet1d-50, and a stronger or differently biased classifier might absorb some of the distortion. Three seeds per policy. The failure-mode taxonomy should generalise to other conditional medical time-series generators, but the deltas are dataset-specific and untested elsewhere. Quality filter and diversity selection spend twice the generator budget to reach the same downstream budget.

Cite

@inproceedings{kolbeinsson2026sampling,
  title     = {Empirical-Distribution Matching for Synthetic {ECG} Classification},
  author    = {Kolbeinsson, Benedikt and Kolbeinsson, Arinbj{\"o}rn},
  booktitle = {ICML 2026 Workshop on Structured Data for Health (SD4H)},
  year      = {2026},
  url       = {https://openreview.net/forum?id=EL98YwgkLu}
}