  Analogical reasoning depends fundamentally on the ability to learn and
generalize about relations between objects. We develop an approach to
relational learning which, given a set of pairs of objects
$\mathbf{S}=\{A^{(1)}:B^{(1)},A^{(2)}:B^{(2)},\ldots,A^{(N)}:B ^{(N)}\}$,
measures how well other pairs A:B fit in with the set $\mathbf{S}$. Our work
addresses the following question: is the relation between objects A and B
analogous to those relations found in $\mathbf{S}$? Such questions are
particularly relevant in information retrieval, where an investigator might
want to search for analogous pairs of objects that match the query set of
interest. There are many ways in which objects can be related, making the task
of measuring analogies very challenging. Our approach combines a similarity
measure on function spaces with Bayesian analysis to produce a ranking. It
requires data containing features of the objects of interest and a link matrix
specifying which relationships exist; no further attributes of such
relationships are necessary. We illustrate the potential of our method on text
analysis and information networks. An application on discovering functional
interactions between pairs of proteins is discussed in detail, where we show
that our approach can work in practice even if a small set of protein pairs is
provided.
