Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: MM Algorithms for Distance Covariance based Sufficient Dimension
  Reduction and Sufficient Variable Selection   Sufficient dimension reduction (SDR) using distance covariance (DCOV) was
recently proposed as an approach to dimension-reduction problems. Compared with
other SDR methods, it is model-free without estimating link function and does
not require any particular distributions on predictors (see Sheng and Yin,
2013, 2016). However, the DCOV-based SDR method involves optimizing a nonsmooth
and nonconvex objective function over the Stiefel manifold. To tackle the
numerical challenge, we novelly formulate the original objective function
equivalently into a DC (Difference of Convex functions) program and construct
an iterative algorithm based on the majorization-minimization (MM) principle.
At each step of the MM algorithm, we inexactly solve the quadratic subproblem
on the Stiefel manifold by taking one iteration of Riemannian Newton's method.
The algorithm can also be readily extended to sufficient variable selection
(SVS) using distance covariance. We establish the convergence property of the
proposed algorithm under some regularity conditions. Simulation studies show
our algorithm drastically improves the computation efficiency and is robust
across various settings compared with the existing method. Supplemental
materials for this article are available.

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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ