  In this paper, we address the problem of discriminative dictionary learning
(DDL), where sparse linear representation and classification are combined in a
probabilistic framework. As such, a single discriminative dictionary and linear
binary classifiers are learned jointly. By encoding sparse representation and
discriminative classification models in a MAP setting, we propose a general
optimization framework that allows for a data-driven tradeoff between faithful
representation and accurate classification. As opposed to previous work, our
learning methodology is capable of incorporating a diverse family of
classification cost functions (including those used in popular boosting
methods), while avoiding the need for involved optimization techniques. We show
that DDL can be solved by a sequence of updates that make use of well-known and
well-studied sparse coding and dictionary learning algorithms from the
literature. To validate our DDL framework, we apply it to digit classification
and face recognition and test it on standard benchmarks.
