Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast Doubly-Adaptive MCMC to Estimate the Gibbs Partition Function with
  Weak Mixing Time Bounds   We present a novel method for reducing the computational complexity of
rigorously estimating the partition functions (normalizing constants) of Gibbs
(Boltzmann) distributions, which arise ubiquitously in probabilistic graphical
models. A major obstacle to practical applications of Gibbs distributions is
the need to estimate their partition functions. The state of the art in
addressing this problem is multi-stage algorithms, which consist of a cooling
schedule, and a mean estimator in each step of the schedule. While the cooling
schedule in these algorithms is adaptive, the mean estimation computations use
MCMC as a black-box to draw approximate samples. We develop a doubly adaptive
approach, combining the adaptive cooling schedule with an adaptive MCMC mean
estimator, whose number of Markov chain steps adapts dynamically to the
underlying chain. Through rigorous theoretical analysis, we prove that our
method outperforms the state of the art algorithms in several factors: (1) The
computational complexity of our method is smaller; (2) Our method is less
sensitive to loose bounds on mixing times, an inherent component in these
algorithms; and (3) The improvement obtained by our method is particularly
significant in the most challenging regime of high-precision estimation. We
demonstrate the advantage of our method in experiments run on classic factor
graphs, such as voting models and Ising models.

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The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
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The categories of this paper are: econ
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th