Singh, Vaibhav and Srijith, P K
(2018)
Convolutional Deep Gaussian Processes.
Masters thesis, Indian Institute of Technology Hyderabad.
Abstract
Deep Gaussian processes (DGPs) provide a Bayesian non-parametric alternative to
standard parametric deep learning models. A DGP is formed by stacking multiple
GPs resulting in a well-regularized composition of functions. The Bayesian framework
that equips the model with attractive properties, such as implicit capacity control and
predictive uncertainty, makes it at the same time challenging to combine with a convolutional
structure. This has hindered the application of DGPs in computer vision
tasks, an area where deep parametric models (i.e. CNNs) have made breakthroughs.
Standard kernels used in DGPs such as radial basis functions (RBFs) are insufficient
for handling pixel variability in raw images. In this paper, we build on the recent
convolutional GP to develop Convolutional DGP (CDGP) models which effectively
capture image level features through the use of convolution kernels, therefore opening
up the way for applying DGPs to computer vision tasks. Our model learns local
spatial influence and outperforms strong GP based baselines on multi-class image
classification. We also consider various constructions of convolution kernel over the
image patches, analyze the computational trade-offs and provide an efficient framework
for convolutional DGP models. The experimental results on image data such as
MNIST, rectangles-image, CIFAR10, Convex-sets and Caltech101 demonstrate the
effectiveness of the proposed approaches. We also propose a method to reduce the
computational complexity of the model. We sub-sample the number of patches and
show the efficiency of the approach on caltech101 dataset.
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