  Some real-world problems revolve to solve the optimization problem
\max_{x\in\mathcal{X}}f\left(x\right) where f\left(.\right) is a black-box
function and X might be the set of non-vectorial objects (e.g., distributions)
where we can only define a symmetric and non-negative similarity score on it.
This setting requires a novel view for the standard framework of Bayesian
Optimization that generalizes the core insightful spirit of this framework.
With this spirit, in this paper, we propose Analogical-based Bayesian
Optimization that can maximize black-box function over a domain where only a
similarity score can be defined. Our pathway is as follows: we first base on
the geometric view of Gaussian Processes (GP) to define the concept of
influence level that allows us to analytically represent predictive means and
variances of GP posteriors and base on that view to enable replacing kernel
similarity by a more genetic similarity score. Furthermore, we also propose two
strategies to find a batch of query points that can efficiently handle high
dimensional data.
