  We propose a Multi-Instance-Learning (MIL) approach for weakly-supervised
learning problems, where a training set is formed by bags (sets of feature
vectors or instances) and only labels at bag-level are provided. Specifically,
we consider the Multi-Instance Dynamic-Ordinal-Regression (MI-DOR) setting,
where the instance labels are naturally represented as ordinal variables and
bags are structured as temporal sequences. To this end, we propose
Multi-Instance Dynamic Ordinal Random Fields (MI-DORF). In this framework, we
treat instance-labels as temporally-dependent latent variables in an Undirected
Graphical Model. Different MIL assumptions are modelled via newly introduced
high-order potentials relating bag and instance-labels within the energy
function of the model. We also extend our framework to address the
Partially-Observed MI-DOR problems, where a subset of instance labels are
available during training. We show on the tasks of weakly-supervised facial
behavior analysis, Facial Action Unit (DISFA dataset) and Pain (UNBC dataset)
Intensity estimation, that the proposed framework outperforms alternative
learning approaches. Furthermore, we show that MIDORF can be employed to reduce
the data annotation efforts in this context by large-scale.
