  In today's data driven world, storing, processing, and gleaning insights from
large-scale data are major challenges. Data compression is often required in
order to store large amounts of high-dimensional data, and thus, efficient
inference methods for analyzing compressed data are necessary. Building on a
recently designed simple framework for classification using binary data, we
demonstrate that one can improve classification accuracy of this approach
through iterative applications whose output serves as input to the next
application. As a side consequence, we show that the original framework can be
used as a data preprocessing step to improve the performance of other methods,
such as support vector machines. For several simple settings, we showcase the
ability to obtain theoretical guarantees for the accuracy of the iterative
classification method. The simplicity of the underlying classification
framework makes it amenable to theoretical analysis and studying this approach
will hopefully serve as a step toward developing theory for more sophisticated
deep learning technologies.
