A piece-wise constant approximation for non-conjugate Gaussian Process models
This work addresses a computational bottleneck for researchers using Gaussian Processes with non-conjugate likelihoods, offering an incremental improvement in efficiency.
The paper tackles the challenge of applying Gaussian Processes to non-Gaussian data by approximating the inverse-link function with a piece-wise constant function, resulting in a closed-form solution for Sparse Variational Gaussian Processes and enabling optimization of the function from data.
Gaussian Processes (GPs) are a versatile and popular method in Bayesian Machine Learning. A common modification are Sparse Variational Gaussian Processes (SVGPs) which are well suited to deal with large datasets. While GPs allow to elegantly deal with Gaussian-distributed target variables in closed form, their applicability can be extended to non-Gaussian data as well. These extensions are usually impossible to treat in closed form and hence require approximate solutions. This paper proposes to approximate the inverse-link function, which is necessary when working with non-Gaussian likelihoods, by a piece-wise constant function. It will be shown that this yields a closed form solution for the corresponding SVGP lower bound. In addition, it is demonstrated how the piece-wise constant function itself can be optimized, resulting in an inverse-link function that can be learnt from the data at hand.