▶Bernoulli entropy
The uncertainty of a binary probability peaks at one half.
Entropy-Constrained Learning
Guarding against certainty unsupported by data
With very little data, maximum likelihood can become certain after a lucky or unlucky sample. An entropy constraint keeps the model honest about what the evidence supports.
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The essential idea: uncertainty can be imposed as useful structure when data alone are insufficient.
One Concept · One Example
What to notice
- Entropy is largest for balanced probabilities.
- Extreme probabilities have low entropy.
- A constraint can exclude unjustified certainty.
Constrain confidence, not evidence
Limited-data constraint
A minimum entropy rules out probabilities too close to zero or one.
What can two coin flips really tell us?
Choose the number of observed heads and a minimum entropy. Compare unconstrained and constrained estimates.
Entropy constraints prevent scarce data from producing overconfident, unstable predictions.