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Mean Absolute Error (MAE)

Key: mae · Family: signal fidelity · Better: lower ↓ · Per-lead: yes

MAE asks: on average, how many millivolts apart are a real ECG and its closest synthetic ECG? It is the simplest point-wise error and is reported in the signal's own units. ECGEN-Eval reports RMSE alongside it.

Try it

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What to notice:

  • Noisy: MAE and RMSE rise together. With 20 ms late, RMSE rises faster than MAE, because squaring emphasises the few large errors around the R peak.
  • Inverted T wave: a clinically important change produces only a moderate MAE, because the T wave is small compared with the QRS complex.

How it works

  1. For each real recording, find the nearest synthetic recording (smallest Euclidean distance over all leads).
  2. Per lead, compute MAE and RMSE between the pair.
  3. Average over recordings; the score is the mean MAE over leads. RMSE is in extra.

The math

\[ \mathrm{MAE} = \frac{1}{T}\sum_{t=1}^{T} \left| x_r[t] - x_s[t] \right|, \qquad \mathrm{RMSE} = \sqrt{\frac{1}{T}\sum_{t=1}^{T} \big(x_r[t] - x_s[t]\big)^2} \]

Reading the score

  • In signal units (usually mV), so values depend on scaling and normalisation. Report the units and preprocessing with the number.
  • MAE is robust to a few large errors; RMSE is not. A big gap between them points to localised errors (for example misplaced R peaks).
  • Like all point-wise metrics, MAE punishes timing shifts and baseline offsets that a cardiologist would ignore.

Use it with ECGEN-Eval

ecgen-eval eval --real real.npy --synthetic synth.npy -m mae --output report.html

from ecgen_eval import load_ecg_npy, AVAILABLE_METRICS

real = load_ecg_npy("real.npy", fs=500)
synth = load_ecg_npy("synth.npy", fs=500)

result = AVAILABLE_METRICS["mae"]().compute(real.data, synth.data, lead_names=real.lead_names)
print("MAE:", result.score, "RMSE:", result.extra["rmse"])

Parameters are in the Metric Reference.

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