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This paper presents a brand new nonparametric density estimation strategy named the best-scored random forest density estimation whose effectiveness is supported by both solid theoretical analysis and significant experimental performance. The terminology best-scored stands for selecting one density tree with the best estimation performance out of a certain number of purely random density tree candidates and we then name the selected one the best-scored random density tree. In this manner, the ensemble of these selected trees that is the best-scored random density forest can achieve even better estimation results than simply integrating trees without selection. From the theoretical perspective, by decomposing the error term into two, we are able to carry out the following analysis: First of all, we establish the consistency of the best-scored random density trees under $L_1$-norm. Secondly, we provide the convergence rates of them under $L_1$-norm concerning with three different tail assumptions, respectively. Thirdly, the convergence rates under $L_{infty}$-norm is presented. Last but not least, we also achieve the above convergence rates analysis for the best-scored random density forest. When conducting comparative experiments with other state-of-the-art density estimation approaches on both synthetic and real data sets, it turns out that our algorithm has not only significant advantages in terms of estimation accuracy over other methods, but also stronger resistance to the curse of dimensionality.
Single-level density-based approach has long been widely acknowledged to be a conceptually and mathematically convincing clustering method. In this paper, we propose an algorithm called best-scored clustering forest that can obtain the optimal level
We propose an algorithm named best-scored random forest for binary classification problems. The terminology best-scored means to select the one with the best empirical performance out of a certain number of purely random tree candidates as each singl
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
Given a set of empirical observations, conditional density estimation aims to capture the statistical relationship between a conditional variable $mathbf{x}$ and a dependent variable $mathbf{y}$ by modeling their conditional probability $p(mathbf{y}|
Random forests is a common non-parametric regression technique which performs well for mixed-type data and irrelevant covariates, while being robust to monotonic variable transformations. Existing random forest implementations target regression or cl