  Building highly non-linear and non-parametric models is central to several
state-of-the-art machine learning systems. Kernel methods form an important
class of techniques that induce a reproducing kernel Hilbert space (RKHS) for
inferring non-linear models through the construction of similarity functions
from data. These methods are particularly preferred in cases where the training
data sizes are limited and when prior knowledge of the data similarities is
available. Despite their usefulness, they are limited by the computational
complexity and their inability to support end-to-end learning with a
task-specific objective. On the other hand, deep neural networks have become
the de facto solution for end-to-end inference in several learning paradigms.
In this article, we explore the idea of using deep architectures to perform
kernel machine optimization, for both computational efficiency and end-to-end
inferencing. To this end, we develop the DKMO (Deep Kernel Machine
Optimization) framework, that creates an ensemble of dense embeddings using
Nystrom kernel approximations and utilizes deep learning to generate
task-specific representations through the fusion of the embeddings.
Intuitively, the filters of the network are trained to fuse information from an
ensemble of linear subspaces in the RKHS. Furthermore, we introduce the kernel
dropout regularization to enable improved training convergence. Finally, we
extend this framework to the multiple kernel case, by coupling a global fusion
layer with pre-trained deep kernel machines for each of the constituent
kernels. Using case studies with limited training data, and lack of explicit
feature sources, we demonstrate the effectiveness of our framework over
conventional model inferencing techniques.
