  We introduce a graphical framework for multiple instance learning (MIL) based
on Markov networks. This framework can be used to model the traditional MIL
definition as well as more general MIL definitions. Different levels of
ambiguity -- the portion of positive instances in a bag -- can be explored in
weakly supervised data. To train these models, we propose a discriminative
max-margin learning algorithm leveraging efficient inference for
cardinality-based cliques. The efficacy of the proposed framework is evaluated
on a variety of data sets. Experimental results verify that encoding or
learning the degree of ambiguity can improve classification performance.
