Weak supervision, also called semi-supervised learning, is a branch of machine learning that combines a small amount of labeled data with a large amount of unlabeled data during training. Semi-supervised learning falls between unsupervised learning (with no labeled training data) and supervised learning (with only labeled training data). Semi-supervised learning aims to alleviate the issue of having limited amounts of labeled data available for training.

Semi-supervised learning is motivated by problem settings where unlabeled data is abundant and obtaining labeled data is expensive. Other branches of machine learning that share the same motivation but follow different assumptions and methodologies are active learning and weak supervision. Unlabeled data, when used in conjunction with a small amount of labeled data, can produce considerable improvement in learning accuracy. The acquisition of labeled data for a learning problem often requires a skilled human agent (e.g. to transcribe an audio segment) or a physical experiment (e.g. determining the 3D structure of a protein or determining whether there is oil at a particular location). The cost associated with the labeling process thus may render large, fully labeled training sets infeasible, whereas acquisition of unlabeled data is relatively inexpensive. In such situations, semi-supervised learning can be of great practical value. Semi-supervised learning is also of theoretical interest in machine learning and as a model for human learning.

More formally, semi-supervised learning assumes a set of ${\displaystyle l}$ independently identically distributed examples ${\displaystyle x_{1},\dots ,x_{l}\in X}$ with corresponding labels ${\displaystyle y_{1},\dots ,y_{l}\in Y}$ and ${\displaystyle u}$ unlabeled examples ${\displaystyle x_{l+1},\dots ,x_{l+u}\in X}$ are processed. Semi-supervised learning combines this information to surpass the classification performance that can be obtained either by discarding the unlabeled data and doing supervised learning or by discarding the labels and doing unsupervised learning.

Semi-supervised learning may refer to either transductive learning or inductive learning. The goal of transductive learning is to infer the correct labels for the given unlabeled data ${\displaystyle x_{l+1},\dots ,x_{l+u}}$ only. The goal of inductive learning is to infer the correct mapping from ${\displaystyle X}$ to ${\displaystyle Y}$.

Intuitively, the learning problem can be seen as an exam and labeled data as sample problems that the teacher solves for the class as an aid in solving another set of problems. In the transductive setting, these unsolved problems act as exam questions. In the inductive setting, they become practice problems of the sort that will make up the exam.

It is unnecessary (and, according to Vapnik's principle, imprudent) to perform transductive learning by way of inferring a classification rule over the entire input space; however, in practice, algorithms formally designed for transduction or induction are often used interchangeably.