Investigating deep learning through the lens of adaptive kernels.

There is no denying that deep neural networks have had a profound impact on research across statistics, data science and machine learning, as well as  significantly altered the analytical landscape in many application areas, including bioinformatics and systems biology.

While previous research efforts were focused on the then surprisingly excellent performance of deep neural networks, the field is now shifting toward trying to explain this performance through connections to classical statistical methodologies, specifically through kernel learning, where models are generated via first principles by borrowing predictive strength across similar sets of observations.In this project, we explore the connection between deep and kernel learning in multiple directions.

First, we recast the kernel learning through regression approximations of gradient descent.

This provides a transparent framework through which we can gain a better understanding on how we can extend classical statistical methods to be more flexible, and thus mimic the properties of deep learners.

Secondly, we propose to train deep and kernel learners in a coupled fashion, to enable the classical methods to reach the performance levels of the deep learners.

Thirdly, we propose to explore how these methods can be used for flexible, yet interpretable and robust modeling of large-scale biobank and cancer genomic data.