Classifier Threshold & ROC Curve Explorer

Data

Samples per class 60

Class separation 0.60

Score noise (σ) 0.16

Classifier

Decision threshold 0.50

Confusion Matrix

True Positive (TP) — 0 False Negative (FN) — 0 False Positive (FP) — 0 True Negative (TN) — 0

Live Metrics

TPR (Recall)

0.000

FPR

0.000

Precision

0.000

F1-score

0.000

Accuracy

0.000

ROC-AUC

0.000

How it works

Each of the two classes produces a classifier score in [0,1] — a noisy, overlapping Gaussian per class, exactly what a real logistic regression or SVM outputs before thresholding. Moving the threshold t reclassifies every point as "predicted positive" when score ≥ t:

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

Sweeping t from 1 down to 0 traces the ROC curve (FPR on x, TPR on y, right-hand panel) — every possible operating point of this classifier at once. The bright marker shows exactly where the current threshold sits on that curve. The diagonal is a coin-flip classifier; the further the curve bows toward the top-left corner, the better the separation.

AUC = ∫₀¹ TPR(FPR) dFPR   (trapezoidal, 240 threshold steps)

Samples per class / separation / noise — regenerate the underlying score distributions; more separation and less noise push AUC toward 1.0, full overlap pushes it toward 0.5.
Decision threshold — the vertical plane in the left panel; points are colored by confusion-matrix outcome live as you drag it.

This is the same tradeoff every binary classifier in the article faces — a spam filter, a fraud detector, a cancer screen — moving the threshold always trades false positives against false negatives along this exact curve.

Left: score distribution · threshold plane Right: ROC curve (FPR → TPR)

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