PUATE: Semiparametric Efficient Average Treatment Effect Estimation from Treated (Positive) and Unlabeled Units

Masahiro Kato, Fumiaki Kozai, and Ryo Inokuchi

Advances in Neural Information Processing Systems (NeurIPS), 2025.

In one sentence. Efficiency bounds and efficient ATE estimators for the case where the data contain a treated group and an unlabeled group whose treatment status is unknown.

A common data problem

Textbook treatment effect estimation assumes each unit is known to be treated or untreated. In practice one often has a record of who was treated and a much larger pool of units whose treatment status was simply never recorded. The unlabeled pool is a mixture of treated and untreated units, in unknown proportion.

This is a variant of learning from positive and unlabeled data, and equivalently a special case of treatment effect estimation with missing data — but the missingness is in the treatment indicator rather than in the outcome, which changes the identification and efficiency analysis.

Results

The results connect two literatures that rarely talk to each other: causal inference with missing data, and weakly supervised learning.

Related

See the full publication list.