The decision
An extraction system reads a field and reports a confidence p: the probability that the value is correct. For each field there are two options. Accept it automatically, or send it to a person for review.
Two costs
Reviewing a field costs cr, the time of a person. Accepting a field that is wrong costs cf, the rework or the failed downstream step. Accepting a correct field costs nothing. The expected costs of the two options are:
The rule
Accept when accepting is cheaper in expectation than reviewing:
Rearranging gives a threshold on the confidence:
If a review costs a tenth of a mistake (cr/cf = 0.1), the threshold is 0.90. If a mistake costs only twice a review, the threshold falls to 0.50. These ratios are illustrative; real ones must be measured.
What the derivation assumes
The rule is valid only if p is calibrated: among fields reported at 90%, about 90% must be correct. An overconfident model makes the threshold accept too much, and the real error rate among accepted fields rises above the one the rule promises.
Limits
- Costs differ by field, and critical fields may need mandatory review regardless of confidence.
- The derivation treats fields independently.
- It says nothing about errors the model is confidently wrong about in a systematic way.
Background reading
Works by other authors that treat the underlying methods. They are not Menlo Tech publications.
- Guo, C., Pleiss, G., Sun, Y. & Weinberger, K. "On Calibration of Modern Neural Networks." ICML, 2017.
- Berger, J. Statistical Decision Theory and Bayesian Analysis, 2nd ed. Springer, 1985.
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