Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimax Rates for High-Dimensional Random Tessellation Forests   Random forests are a popular class of algorithms used for regression and
classification. The algorithm introduced by Breiman in 2001 and many of its
variants are ensembles of randomized decision trees built from axis-aligned
partitions of the feature space. One such variant, called Mondrian forests, was
proposed to handle the online setting and is the first class of random forests
for which minimax rates were obtained in arbitrary dimension. However, the
restriction to axis-aligned splits fails to capture dependencies between
features, and random forests that use oblique splits have shown improved
empirical performance for many tasks. In this work, we show that a large class
of random forests with general split directions also achieve minimax rates in
arbitrary dimension. This class includes STIT forests, a generalization of
Mondrian forests to arbitrary split directions, as well as random forests
derived from Poisson hyperplane tessellations. These are the first results
showing that random forest variants with oblique splits can obtain minimax
optimality in arbitrary dimension. Our proof technique relies on the novel
application of the theory of stationary random tessellations in stochastic
geometry to statistical learning theory.

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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph