Gaussian processes improve image analysis by sharing parameters across pixels and color channels
Structured Relevance Determination and Channel Additive Gaussian Processes for Image Data
Machine Learning
Summary
Gaussian processes are a way to make predictions from data, but they usually need to tune many parameters, especially with images made of many pixels and colors. The authors designed a smarter way to share tuning parameters across neighboring pixels and color channels, reducing complexity and improving prediction when data is limited. They also split image color channels into parts so the model can learn patterns from different channels together. Tests on handwritten digits and low-res satellite images show this method predicts better than older ways.
What this means in practice
- •For satellite image analysts: Improve detection of objects in low-resolution multi-channel satellite images using fewer parameters to boost reliability with limited data.
- •For machine learning engineers: Build more efficient Gaussian process models for image tasks by reducing parameter count via structured parameter sharing across pixels and color channels.
Authors
Harald Roßels, Ludovico Scarton
Abstract
We introduce radial basis function (RBF) kernels for Gaussian processes that use structured hyperparameter sharing for image-valued inputs. For high-dimensional inputs such as images, a fully anisotropic RBF kernel assigns a separate lengthscale to each input dimension, which can introduce many hyperparameters and may lead to overfitting and poorly calibrated predictive uncertainty when data are limited. We propose structured relevance determination by tying lengthscales across groups of adjacent pixels and within each colour channel. This yields patch-wise and channel-wise constrained anisotropic RBF parametrisations that reduce the number of independently learned lengthscales. We further introduce channel-additive Gaussian processes for multi-channel images and combine them with structured relevance determination, resulting in a parameter-efficient decomposition of the latent function into components defined on channel subsets, enabling some non-local generalisation. The proposed kernels are evaluated on MNIST and a compact binary aircraft-detection dataset of low-resolution RGB satellite image chips. We also show how channel-wise structured relevance determination can be incorporated into convolutional Gaussian processes. We observe improved predictive performance compared to isotropic and fully anisotropic RBF baselines.