Weakly Supervised Learning
You know who bought. What you cannot tell is who decided against buying and who simply has not bought yet. Data from practice is full of situations like this, where only some of the labels ever arrive. This topic covers classification and treatment effect estimation under incomplete labels, centered on PU learning, which learns from positive and unlabeled data. The main result here is Learning from Positive and Unlabeled Data with a Selection Bias (Kato, Teshima, and Honda, 2019), published at ICLR 2019.
Problems addressed
The standard theory of PU learning assumes that the labeled positives were drawn at random from all positives. Real data rarely works that way. The customers who stand out get found first, and the patients with the worst symptoms get diagnosed first. Our work gives a learning method that still works when this selection bias is present.
The line has since spread into applications. Double PU learning narrows down prospects using two positive-unlabeled datasets at once, one of existing customers and one of the general population, and PUATE estimates the average treatment effect from treated units and unlabeled units alone. A third strand trains classifiers on advertising data where the true label arrives late. There is also work on language data, including an attempt to analyze tanka from a newspaper poetry column with PU learning.
Core research
The PU Learning with a Selection Bias page sets out how the selection bias is formalized, what the proposed method does, and the conditions under which it holds.
Research thread
- 2025
- PUATE: Efficient ATE Estimation from Treated (Positive) and Unlabeled Units (NeurIPS 2025). Average treatment effect estimation from treated and unlabeled units.
- 2025
- Learning from Double Positive and Unlabeled Data for Potential-Customer Identification. Treats potential-customer identification as a double PU structure.
- 2022
- Learning Classifiers under Delayed Feedback with a Time Window Assumption (KDD 2022). Learning from data whose true labels arrive late.
Relation to earlier work
PU learning begins with the formulation of Elkan and Noto (2008, Learning classifiers from only positive and unlabeled data), and du Plessis and coauthors built the statistical learning theory around risk estimation (2015, Convex Formulation for Learning from Positive and Unlabeled Data). For the overfitting that deep models show, the known remedy is the non-negative risk estimator of Kiryo and coauthors (2017, Positive-Unlabeled Learning with Non-Negative Risk Estimator). All of these rest on the assumption that labeled positives are selected at random, and our work takes on the case where that assumption is dropped. For the field as a whole, the survey by Bekker and Davis (2020, Learning from positive and unlabeled data: a survey) is a useful guide.
Where it applies
These methods are for data where only one side of the label is observed. You can narrow down prospects from purchase records, predict advertising effects while allowing for conversions that arrive late, or screen for fraud with only the already-detected cases to work from. For inquiries, including which method suits the data you have, write to mkato-csecon@g.ecc.u-tokyo.ac.jp.