Rare Disease Detection: SMOTE Class-Imbalance Correction (2D)

SMOTE Oversampling

Synthetic minority samples 60

Neighbors k (interpolation) 3

Classifier

Decision threshold 0.50

Live Metrics (real patients)

Recall (sensitivity)

Precision

F1 score

0.00

Synthetic pts

Healthy (majority class)

Rare disease (real minority)

SMOTE synthetic minority

How it works

Each dot is a patient plotted at two standardized clinical biomarker values (x, y). Rare-disease patients are a small minority — 14 real cases against 160 healthy — so a classifier trained naively on the raw data learns to just predict "healthy" and still scores high accuracy while missing almost every real case.

SMOTE interpolation (Chawla et al., 2002):
for a minority point x_i and one of its k nearest
minority neighbors x_zi, pick λ ~ U(0,1):
  x_new = x_i + λ · (x_zi − x_i)

Logistic regression:  p(x) = σ(w·x + b) = 1 / (1 + e^-(w·x+b))
Trained by gradient descent on cross-entropy loss,
minority class labeled 1, healthy labeled 0.

Decision boundary: the line w·x + b = logit(threshold)
(the 2D analogue of the decision-boundary plane in the
original 3D version — same classifier, one fewer axis).

Recall    = TP / (TP + FN)
Precision = TP / (TP + FP)
F1        = 2 · Precision · Recall / (Precision + Recall)

Synthetic samples slider — how many SMOTE points to interpolate along minority-to-minority segments before training.
k slider — how many nearest same-class neighbors each synthetic point is allowed to interpolate toward.
SMOTE ON/OFF — toggles whether the classifier trains on the augmented set or only the original imbalanced one, holding everything else fixed.
Decision threshold — the probability cutoff above which a patient is flagged positive; moving it trades recall against precision along the same trained boundary.
Scatter panel — drag to pan, scroll/pinch to zoom; the bottom panel tracks recall, precision and F1 as live bars.

Metrics are always evaluated against the real patients only — synthetic points influence training but are never counted as ground truth, which is standard SMOTE practice.

drag to pan · scroll to zoom