紀建名博士學術專題演講111/03/14

  • 2022-03-08
  • 楊 文敏

國立政治大學統計學系
     
主講人:紀建名博士(Postdoctoral researcher, Data Sciences and Operations
                Department, Marshall School of Business, USC)

題   目:Asymptotic Properties of High-Dimensional Random Forests
時     間:民國111314 (星期一) 下午130 
地   點:國立政治大學逸仙樓050101教室
        要:
                As a flexible nonparametric learning tool, random forests has been widely applied to various real applications with appealing empirical performance, even in the presence of high-dimensional feature space. Unveiling the underlying mechanisms has led to some important recent theoretical results on the consistency of the random forests algorithm and its variants. However, to our knowledge, all existing works concerning random forests consistency under the setting of high dimensionality were done for various modified random forests models where the splitting rules are independent of the response. In light of this, in this paper we derive the consistency rates for the random forests algorithm associated with the sample CART splitting criterion, which is the one used in the original version of the algorithm in Breiman (2001), in a general high-dimensional nonparametric regression setting through a bias-variance decomposition analysis. Our new theoretical results show that random forests can indeed adapt to high dimensionality and allow for discontinuous regression function. Our bias analysis characterizes explicitly how the random forests bias depends on the sample size, tree height, and column subsampling parameter. Some limitations of our current results are also discussed.