Is BALD a prediction confidence score?

It is an expected information-gain score for choosing observations, although it is computed from predictive distributions.

Does a high score guarantee the returned label changes the model greatly?

No. It averages over possible labels before the actual result is known.

Can it be used for preferences?

Yes. The original work included preference learning through a probabilistic comparison model.

AI Glossary / Probabilistic machine learning / Advanced

Bayesian active learning by disagreement

Definition

Bayesian active learning by disagreement, usually abbreviated BALD, is an acquisition criterion that selects an example whose unknown label is expected to reveal substantial information about uncertain model parameters. It measures disagreement among predictions supported by the current posterior, rather than simply selecting the most unpredictable label.

What it means

There are different reasons a prediction can be uncertain. Plausible model settings may make conflicting predictions, or all of them may predict the same uncertain outcome. Learning the label is potentially more informative about the model in the first situation.
BALD formalizes this distinction through mutual information. Its score concerns expected learning under the assumed model and current data. It does not directly measure commercial value, the probability of a labeling error, or a guaranteed improvement in future accuracy.

How it works

For candidate input x and existing data D, calculate I(Y;θ|x,D) = H(Y|x,D) − E[H(Y|x,θ)], where the expectation averages over θ drawn from the posterior p(θ|D).
The first term is the entropy of the averaged predictive distribution. The second is the average entropy of predictions conditional on a model setting. Their difference measures information about θ expected from observing Y. Select an informative candidate, obtain its label and update the model. Calculations may use analytical approximations or posterior samples. The criterion originated in work including Gaussian-process classification and preference learning; it is not restricted to neural networks.

Three practical examples

A document classifier could request a label for a form on which plausible model settings disagree about its category. That label could help distinguish competing explanations of the existing examples.
A preference-learning system could choose a comparison whose answer is expected to clarify uncertain preference parameters. The information score would still need to be considered alongside participant effort and the purpose of the study.
A research team could compare BALD with predictive-entropy sampling on a controlled dataset containing ambiguous examples. The comparison would test whether separating types of uncertainty helps the particular task.

Think of it this way

Suppose two forecasters disagree because they use different plausible explanations of the evidence. An observation may help decide between them. Now suppose both agree that an outcome behaves like a fair coin under their explanations. Seeing one result may tell you much less about which explanation is correct. BALD concerns this learning opportunity, not disagreement for its own sake.

Worked example

Construct an original binary classification example with two equally weighted parameter hypotheses, θ1 and θ2. For candidate A, their predicted probabilities of label 1 are 0.80 and 0.20. For B, both probabilities are 0.50. For C, they are 0.90 and 0.70.
Use base-two logarithms and binary entropy h(p)=−p log2(p)−(1−p)log2(1−p). Candidate A's average probability is 0.50, giving predictive entropy one bit. Its average conditional entropy is [h(0.80)+h(0.20)]/2 = 0.721928 bits. BALD(A) is therefore approximately 0.278072 bits.
Candidate B also has one bit of predictive entropy. However, each hypothesis assigns entropy one bit, so BALD(B)=1−1=0. The two hypotheses predict identical distributions for B; its label cannot distinguish them in this stipulated model.
For C, the averaged probability is 0.80 and predictive entropy is 0.721928 bits. Average conditional entropy is [h(0.90)+h(0.70)]/2, approximately 0.675143 bits. BALD(C) is approximately 0.046785 bits.
BALD ranks A above C above B. Predictive entropy instead ties A and B above C. Notice that both hypotheses would assign C the same most likely class, yet their differing probabilities give it a positive information score. These exact toy calculations illustrate probabilistic disagreement; they are not results from an operational labeling project.

Illustrative case study

Fictional forms-processing business Juniper Intake has a small annotation budget for improving document classification. Its researchers compare BALD with random selection and ordinary predictive-entropy selection using the same initial training set. They retain a separate evaluation set reflecting incoming forms.
The team examines selected examples rather than assuming high scores are useful. It records whether requests concern meaningful layout differences, ambiguous category definitions or corrupt scans. After each labeling round, it compares downstream errors and annotation time. This fictional case illustrates an evaluation process; no labeling reduction or accuracy improvement is claimed.

Common misconceptions and mistakes

“BALD selects every example with a probability near 0.50.” Candidate B shows why average uncertainty alone is insufficient.
“Disagreement means different winning class labels.” Candidate C has a positive score despite agreement on the most likely class.
“A zero score means the example has no possible value.” It means no expected information about the modeled parameters under the current predictive assumptions; other tasks or a better model may value it differently.
“An arbitrary ensemble automatically represents the posterior.” How model variants are generated affects the interpretation of the estimated score.
“The top individual scores necessarily form the best batch.” Several candidates can provide overlapping information; batch acquisition requires additional consideration.

Business use

Consider BALD when labels are expensive and probabilistic uncertainty estimates are credible enough to guide requests. Ask which uncertainty is represented, how posterior predictions are approximated and what data define the candidate pool. Compare acquisition strategies under the same annotation budget and evaluate the resulting model on an appropriate independent sample. Include selection computation and review time in the cost assessment instead of treating every requested label as equally expensive.

Check your understanding

Why do A and B have the same predictive entropy but different BALD scores?

Answer: the hypotheses disagree on A's probability and agree on B's distribution.

Which candidate ranks second under BALD?

Answer: C, at approximately 0.046785 bits.

Why is C informative despite a shared winning class?

Answer: its label can still distinguish hypotheses assigning different probabilities to that class.

Related terms

Active learning
Mutual information
Query by committee
BatchBALD
Preference learning
predictive entropy
posterior distribution
epistemic uncertainty

Learn next

Calculate entropy before and after averaging several predictive distributions. Then examine how posterior quality and candidate selection affect an active-learning experiment's downstream results.

Active learning

Sources

Houlsby, N., Huszár, F., Ghahramani, Z., and Lengyel, M. Bayesian Active Learning for Classification and Preference Learning, 2011, especially Section 2 and Equations 1–2: https://mlg.eng.cam.ac.uk/pub/pdf/HouHusGha11a.pdf The three-candidate calculation and fictional business scenarios are original illustrations.

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