Towards a statistical theory of data selection under weak supervision

Understand

Given a sample of size $N$, it is often useful to select a subsample of smaller size $n<N$ to be used for statistical estimation or learning.

• Such a data selection step is useful to reduce the requirements of data labeling and the computational complexity of learning.
• We assume to be given $N$ unlabeled samples $\{{\boldsymbol x}_i\}_{i\le N}$, and to be given access to a `surrogate model' that can predict labels $y_i$ better than random guessing.
• Our goal is to select a subset of the samples, to be denoted by $\{{\boldsymbol x}_i\}_{i\in G}$, of size $|G|=n<N$.