Query-by-Committee: Vote-Entropy Active Learning

Committee

Committee size K 5

Labeling noise 5%

Query strategy

Show true boundary

Live readouts

Iteration

Labeled points

Committee accuracy

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Max pool uncertainty

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How it works

Query-by-Committee (QBC) trains K classifiers on bootstrap resamples of the current labeled set. Each unlabeled point in the pool gets a vote from every committee member; the point the committee disagrees about most is the one worth labeling next.

vote entropy:  H(x) = -Σ_y  (V(y)/K) · log2(V(y)/K)
V(y) = number of committee members voting class y
next query x* = argmax_x  H(x)   (over the unlabeled pool)

Each committee member is a logistic-regression classifier over features [x, y, x·y, 1], trained by gradient descent on a bootstrap sample (drawn with replacement) of the labeled points — the resampling plus random weight initialization is what makes the K decision boundaries disagree, especially while few labels exist.

Bars over the pool show vote entropy — taller means the committee is more split, so it's a better query candidate.
Colored lines on the ground are the K committee decision boundaries; where they fan apart is exactly where disagreement (and the tall bars) concentrate.
Committee accuracy is the majority vote of all K members measured against a fixed, noise-free test grid — this is what active learning is trying to improve using as few labels as possible.
Random baseline queries a uniformly random pool point instead of the highest-entropy one, so you can compare how much faster QBC reaches the same accuracy.

Real-world relevance: QBC and its relatives (uncertainty sampling, core-set/diversity sampling) are exactly what labeling pipelines at ML teams use to decide which of millions of unlabeled examples are worth sending to a human annotator next.

Unlabeled pool Labeled class 0 Labeled class 1

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