Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithm   We propose a Markov chain Monte Carlo (MCMC) algorithm based on third-order
Langevin dynamics for sampling from distributions with log-concave and smooth
densities. The higher-order dynamics allow for more flexible discretization
schemes, and we develop a specific method that combines splitting with more
accurate integration. For a broad class of $d$-dimensional distributions
arising from generalized linear models, we prove that the resulting third-order
algorithm produces samples from a distribution that is at most $\varepsilon >
0$ in Wasserstein distance from the target distribution in
$O\left(\frac{d^{1/4}}{ \varepsilon^{1/2}} \right)$ steps. This result requires
only Lipschitz conditions on the gradient. For general strongly convex
potentials with $\alpha$-th order smoothness, we prove that the mixing time
scales as $O \left(\frac{d^{1/4}}{\varepsilon^{1/2}} +
\frac{d^{1/2}}{\varepsilon^{1/(\alpha - 1)}} \right)$.

20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph