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Concept
Transduction (machine learning)
Summary
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 1990s, motivated by
his view that transduction 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." A similar
observation had been made earlier by Bertrand Russell:
"we shall reach the conclusion that Socrates is mortal with a greater approach to
certainty if we make our argument purely inductive than if we go by way of 'all men are mortal' and then use
deduction" (Russell 1912, chap VII).
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.
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