时间相关过程的随机森林

Pub Date : 2020-01-01 DOI:10.1051/PS/2020015
Benjamin Goehry
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引用次数: 16

摘要

布雷曼在2001年引入了随机森林。我们研究了原始布雷曼随机森林和简化版本的中心随机森林的理论方面。在独立同分布假设下,Scornet、Biau和Vert证明了Breiman随机森林的一致性,Biau研究了简化版本,得到了稀疏情况下的收敛率。然而,通常不满足i.i.d假设,例如在处理时间序列时。我们将先前的结果扩展到观测值弱依赖的情况,更准确地说,当序列是平稳的β -混合时。
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Random forests for time-dependent processes
Random forests were introduced by Breiman in 2001. We study theoretical aspects of both original Breiman’s random forests and a simplified version, the centred random forests. Under the independent and identically distributed hypothesis, Scornet, Biau and Vert proved the consistency of Breiman’s random forest, while Biau studied the simplified version and obtained a rate of convergence in the sparse case. However, the i.i.d hypothesis is generally not satisfied for example when dealing with time series. We extend the previous results to the case where observations are weakly dependent, more precisely when the sequences are stationary β−mixing.
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