  In this paper, we propose a gradient boosting algorithm called
\textit{adaptive boosting histogram transform} (\textit{ABHT}) for regression
to illustrate the local adaptivity of gradient boosting algorithms in histogram
transform ensemble learning. From the theoretical perspective, when the target
function lies in a locally H\"older continuous space, we show that our ABHT can
filter out the regions with different orders of smoothness. Consequently, we
are able to prove that the upper bound of the convergence rates of ABHT is
strictly smaller than the lower bound of \textit{parallel ensemble histogram
transform} (\textit{PEHT}). In the experiments, both synthetic and real-world
data experiments empirically validate the theoretical results, which
demonstrates the advantageous performance and local adaptivity of our ABHT.
