Inductive vs Transductive Learning

Most machine learning is inductive: you fit a model on training data, and the goal is a general rule $f$ that will make good predictions on any new point drawn from the same distribution — points you haven't seen and may never see specifically. Transductive learning has a narrower, sometimes easier goal: you're given a fixed, specific set of unlabeled points at training time and only need to correctly label those particular points — you never claim, and don't need, a rule that generalizes beyond them.

$$\text{Inductive: learn } f \text{ such that } f(x) \approx y \text{ for } x \text{ drawn from the population.}$$ $$\text{Transductive: label } \{x_1, \dots, x_m\} \text{ correctly, using both labeled and these specific unlabeled points.}$$

In plain English: an inductive model has to work on data it has never seen at training time, so it must generalize; a transductive method gets to look at the exact unlabeled points it will be judged on while still training, so it can exploit their specific structure instead of having to generalize to the whole population.

Worked example

A hedge fund needs to classify 500 specific unlabeled news articles from last week as "market-moving" or not, and has 2,000 labeled historical articles to learn from. An inductive approach trains a classifier on the 2,000 labeled articles alone and applies it to the 500 new ones as unseen data. A transductive approach instead includes the 500 unlabeled articles' text features (without their labels) directly in the learning process, letting the algorithm exploit patterns in how those specific 500 articles cluster relative to the labeled ones — often producing a more accurate labeling of exactly those 500, at the cost of producing no reusable general-purpose classifier for next week's news.