Holistic Deep Learning

There is much interest in deep learning to solve challenges that arise in applying neural network models in real-world environments. In particular, three areas have received considerable attention: adversarial robustness, parameter sparsity, and output stability. Despite numerous attempts on solving these problems independently, there is very little work addressing the challenges simultaneously. In this paper, we address this problem of constructing holistic deep learning models by proposing a novel formulation that solves these issues in combination. Real-world experiments on both tabular and MNIST dataset show that our formulation is able to simultaneously improve the accuracy, robustness, stability, and sparsity over traditional deep learning models among many others.

Learning High Order Feature Interactions with Fine Control Kernels

We provide a methodology for learning sparse statistical models that use as features all possible multiplicative interactions among an underlying atomic set of features. While the resulting optimization problems are exponentially sized, our methodology leads to algorithms that can often solve these problems exactly or provide approximate solutions based on combining highly correlated features. We also introduce an algorithmic paradigm, the Fine Control Kernel framework, so named because it is based on Fenchel Duality and is reminiscent of kernel methods. Its theory is tailored to large sparse learning problems, and it leads to efficient feature screening rules for interactions. These rules are inspired by the Apriori algorithm for market basket analysis -- which also falls under the purview of Fine Control Kernels, and can be applied to a plurality of learning problems including the Lasso and sparse matrix estimation. Experiments on biomedical datasets demonstrate the efficacy of our methodology in deriving algorithms that efficiently produce interactions models which achieve state-of-the-art accuracy and are interpretable.