Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexity analysis of Bayesian learning of high-dimensional DAG models
  and their equivalence classes   We consider MCMC methods for learning equivalence classes of sparse Gaussian
DAG models when $p = e^{o(n)}$. The main contribution of this work is a rapid
mixing result for a random walk Metropolis-Hastings algorithm, which we prove
using a canonical path method. It reveals that the complexity of Bayesian
learning of sparse equivalence classes grows only polynomially in $n$ and $p$,
under some common high-dimensional assumptions. Further, a series of
high-dimensional consistency results is obtained by the path method, including
the strong selection consistency of an empirical Bayes model for structure
learning and the consistency of a greedy local search on the restricted search
space. Rapid mixing and slow mixing results for other structure-learning MCMC
methods are also derived. Our path method and mixing time results yield crucial
insights into the computational aspects of high-dimensional structure learning,
which may be used to develop more efficient MCMC algorithms.

33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph