  Ordinal learning (OL) is a type of machine learning models with broad utility
in health care applications such as diagnosis of different grades of a disease
(e.g., mild, modest, severe) and prediction of the speed of disease progression
(e.g., very fast, fast, moderate, slow). This paper aims to tackle a situation
when precisely labeled samples are limited in the training set due to cost or
availability constraints, whereas there could be an abundance of samples with
imprecise labels. We focus on imprecise labels that are intervals, i.e., one
can know that a sample belongs to an interval of labels but cannot know which
unique label it has. This situation is quite common in health care datasets due
to limitations of the diagnostic instrument, sparse clinical visits, or/and
patient dropout. Limited research has been done to develop OL models with
imprecise/interval labels. We propose a new Hybrid Ordinal Learner (HOL) to
integrate samples with both precise and interval labels to train a robust OL
model. We also develop a tractable and efficient optimization algorithm to
solve the HOL formulation. We compare HOL with several recently developed OL
methods on four benchmarking datasets, which demonstrate the superior
performance of HOL. Finally, we apply HOL to a real-world dataset for
predicting the speed of progressing to Alzheimer's Disease (AD) for individuals
with Mild Cognitive Impairment (MCI) based on a combination of multi-modality
neuroimaging and demographic/clinical datasets. HOL achieves high accuracy in
the prediction and outperforms existing methods. The capability of accurately
predicting the speed of progression to AD for each individual with MCI has the
potential for helping facilitate more individually-optimized interventional
strategies.
