Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On polynomial-time computation of high-dimensional posterior measures by
  Langevin-type algorithms   The problem of generating random samples of high-dimensional posterior
distributions is considered. The main results consist of non-asymptotic
computational guarantees for Langevin-type MCMC algorithms which scale
polynomially in key quantities such as the dimension of the model, the desired
precision level, and the number of available statistical measurements. As a
direct consequence, it is shown that posterior mean vectors as well as
optimisation based maximum a posteriori (MAP) estimates are computable in
polynomial time, with high probability under the distribution of the data.
These results are complemented by statistical guarantees for recovery of the
ground truth parameter generating the data.
  Our results are derived in a general high-dimensional non-linear regression
setting (with Gaussian process priors) where posterior measures are not
necessarily log-concave, employing a set of local `geometric' assumptions on
the parameter space, and assuming that a good initialiser of the algorithm is
available. The theory is applied to a representative non-linear example from
PDEs involving a steady-state Schr\"odinger equation.

22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph