  Many objects in the real world are difficult to describe by a single
numerical vector of a fixed length, whereas describing them by a set of vectors
is more natural. Therefore, Multiple instance learning (MIL) techniques have
been constantly gaining on importance throughout last years. MIL formalism
represents each object (sample) by a set (bag) of feature vectors (instances)
of fixed length where knowledge about objects (e.g., class label) is available
on bag level but not necessarily on instance level. Many standard tools
including supervised classifiers have been already adapted to MIL setting since
the problem got formalized in late nineties. In this work we propose a neural
network (NN) based formalism that intuitively bridges the gap between MIL
problem definition and the vast existing knowledge-base of standard models and
classifiers. We show that the proposed NN formalism is effectively optimizable
by a modified back-propagation algorithm and can reveal unknown patterns inside
bags. Comparison to eight types of classifiers from the prior art on a set of
14 publicly available benchmark datasets confirms the advantages and accuracy
of the proposed solution.
