Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adaptive Concentration of Regression Trees, with Application to Random
  Forests   We study the convergence of the predictive surface of regression trees and
forests. To support our analysis we introduce a notion of adaptive
concentration for regression trees. This approach breaks tree training into a
model selection phase in which we pick the tree splits, followed by a model
fitting phase where we find the best regression model consistent with these
splits. We then show that the fitted regression tree concentrates around the
optimal predictor with the same splits: as d and n get large, the discrepancy
is with high probability bounded on the order of sqrt(log(d) log(n)/k)
uniformly over the whole regression surface, where d is the dimension of the
feature space, n is the number of training examples, and k is the minimum leaf
size for each tree. We also provide rate-matching lower bounds for this
adaptive concentration statement. From a practical perspective, our result
enables us to prove consistency results for adaptively grown forests in high
dimensions, and to carry out valid post-selection inference in the sense of
Berk et al. [2013] for subgroups defined by tree leaves.

20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th