# Labels, Information, and Computation: Efficient Learning Using Sufficient Labels

Shiyu Duan, Spencer Chang, Jose C. Principe.

Year: 2023, Volume: 24, Issue: 31, Pages: 1−35

#### Abstract

In supervised learning, obtaining a large set of fully-labeled training data is expensive. We show that we do not always need full label information on every single training example to train a competent classifier. Specifically, inspired by the principle of sufficiency in statistics, we present a statistic (a summary) of the fully-labeled training set that captures almost all the relevant information for classification but at the same time is easier to obtain directly. We call this statistic "sufficiently-labeled data" and prove its sufficiency and efficiency for finding the optimal hidden representations, on which competent classifier heads can be trained using as few as a single randomly-chosen fully-labeled example per class. Sufficiently-labeled data can be obtained from annotators directly without collecting the fully-labeled data first. And we prove that it is easier to directly obtain sufficiently-labeled data than obtaining fully-labeled data. Furthermore, sufficiently-labeled data is naturally more secure since it stores relative, instead of absolute, information. Extensive experimental results are provided to support our theory.