Performative Prediction with
Selective Labels

Giovani Valdrighi¹   Isabel Valera²   Marcos Medeiros Raimundo¹

¹Universidade Estadual de Campinas   ²Saarland University

NeurIPS 2026

The influence of predictions on the population

The problem

Client profile
features x

Model
parameters \theta

Prediction
will they repay?

Decision
loan accepted

Decisions change people

Training data ≠ Post-deployment data

Performative prediction

The problem

Each deployed model \theta induces its own distribution D(\theta)

Repeated retraining Retraining model \theta_t with newly collected data from D(\theta_{t-1})

Stable point

Repeated training converges to a model that is optimal for the distribution it induces

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But we only see outcomes for those we accept

The problem

Accepted

Outcome observed: repaid or default

Rejected

Outcome never observed

It happens in

Lendingrepayment of rejected applicants

Hiringperformance of candidates not hired

Medical testingdiagnosis of untested patients

Selective labels: observation of labels (outcomes) is defined by model acceptance.

Can we still reach the stable point when labels are selective?

Retraining only on accepted applicants can fail

Accept-only retraining can end arbitrarily far from the stable point

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Assumption: a plausible range of the probability of the positive outcome

l(x) \;\le\; \alpha(x) \;\le\; u(x)

For each profile x, the decision-maker knows a range that contains the probability of repaying.

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Robust RRM

Our method

Accepted
loss with the observed outcome

Rejected
worst-case loss over the plausible range

The distance to the stable solution is small when:

  1. Acceptance rate is high
  2. Loss is not too sensitive to the outcome
  3. Plausible ranges are narrow

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Takeaway

When models shape the population and we only see outcomes of those we accept, naive retraining can go wrong. A robust worst-case objective gets us close to the right answer.

Performative Prediction with Selective Labels
Giovani Valdrighi, Isabel Valera, Marcos Medeiros Raimundo