  In this thesis, I explore the possibilities of conducting Bayesian
optimization techniques in high dimensional domains. Although high dimensional
domains can be defined to be between hundreds and thousands of dimensions, we
will primarily focus on problem settings that occur between two and 20
dimensions. As such, we focus on solutions to practical problems, such as
tuning the parameters for an electron accelerator, or for even simpler tasks
that can be run and optimized just in time with a standard laptop at hand. Our
main contributions are 1.) comparing how the log-likelihood affects the
angle-difference in the real projection matrix, and the found matrix matrix,
2.) an extensive analysis of current popular methods including strengths and
shortcomings, 3.) a short analysis on how dimensionality reduction techniques
can be used for feature selection, and 4.) a novel algorithm called "BORING",
which allows for a simple fallback mechanism if the matrix identification
fails, as well as taking into consideration "passive" subspaces which provide
small perturbations of the function at hand. The main features of BORING are
1.) the possibility to identify the subspace (unlike most other optimization
algorithms), and 2.) to provide a much lower penalty to identify the subspace
if identification fails, as optimization is still the primary goal.
