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In this paper, we propose a gradient boosting algorithm for large-scale regression problems called textit{Gradient Boosted Binary Histogram Ensemble} (GBBHE) based on binary histogram partition and ensemble learning. From the theoretical perspective, by assuming the H{o}lder continuity of the target function, we establish the statistical convergence rate of GBBHE in the space $C^{0,alpha}$ and $C^{1,0}$, where a lower bound of the convergence rate for the base learner demonstrates the advantage of boosting. Moreover, in the space $C^{1,0}$, we prove that the number of iterations to achieve the fast convergence rate can be reduced by using ensemble regressor as the base learner, which improves the computational efficiency. In the experiments, compared with other state-of-the-art algorithms such as gradient boosted regression tree (GBRT), Breimans forest, and kernel-based methods, our GBBHE algorithm shows promising performance with less running time on large-scale datasets.
We propose a novel algorithm for large-scale regression problems named histogram transform ensembles (HTE), composed of random rotations, stretchings, and translations. First of all, we investigate the theoretical properties of HTE when the regressio
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 unsupervise
We propose a novel method designed for large-scale regression problems, namely the two-stage best-scored random forest (TBRF). Best-scored means to select one regression tree with the best empirical performance out of a certain number of purely rando
Gradient Boosting Machines (GBM) are hugely popular for solving tabular data problems. However, practitioners are not only interested in point predictions, but also in probabilistic predictions in order to quantify the uncertainty of the predictions.
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal processing.