  In this paper, we propose a density estimation algorithm called
\textit{Gradient Boosting Histogram Transform} (GBHT), where we adopt the
\textit{Negative Log Likelihood} as the loss function to make the boosting
procedure available for the unsupervised tasks. From a learning theory
viewpoint, we first prove fast convergence rates for GBHT with the smoothness
assumption that the underlying density function lies in the space
$C^{0,\alpha}$. Then when the target density function lies in spaces
$C^{1,\alpha}$, we present an upper bound for GBHT which is smaller than the
lower bound of its corresponding base learner, in the sense of convergence
rates. To the best of our knowledge, we make the first attempt to theoretically
explain why boosting can enhance the performance of its base learners for
density estimation problems. In experiments, we not only conduct performance
comparisons with the widely used KDE, but also apply GBHT to anomaly detection
to showcase a further application of GBHT.
