In logic, statistical inference, and supervised learning, transduction or transductive inference is reasoning from observed, specific (training) cases to specific (test) cases. In contrast, induction is reasoning from observed training cases to general rules, which are then applied to the test cases. The distinction is most interesting in cases where the predictions of the transductive model are not achievable by any inductive model. Note that this is caused by transductive inference on different test sets producing mutually inconsistent predictions. Transduction was introduced by Vladimir Vapnik in the 1990's, motivated by his view that is preferable to induction since, according to him, induction requires solving a more general problem (inferring a function) before solving a more specific problem (computing outputs for new cases): "When solving a problem of interest, do not solve a more general problem as an intermediate step. Try to get the answer that you really need but not a more general one." An example of learning which is not inductive would be in the case of binary classification, where the inputs tend to cluster in two groups. A large set of test inputs may help in finding the clusters, thus providing useful information about the classification labels. The same predictions would not be obtainable from a model which induces a function based only on the training cases. Some people may call this an example of the closely related semi-supervised learning, since Vapnik's motivation is quite different. An example of an algorithm in this category is the Transductive Support Vector Machine (TSVM). A third possible motivation which leads to transduction arises through the need to approximate. If exact inference is computationally prohibitive, one may at least try to make sure that the approximations are good at the test inputs. In this case, the test inputs could come from an arbitrary distribution (not necessarily related to the distribution of the training inputs), which wouldn't be allowed in semi-supervised learning. An example of an algorithm falling in this category is the Bayesian Committee Machine (BCM).
References
- V. N. Vapnik. Statistical learning theory. New York: Wiley, 1998. (See pages 339-371)
- V. Tresp. A Bayesian committee machine, Neural Computation, 12, 2000, pdf.
