Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probabilistic Curve Learning: Coulomb Repulsion and the Electrostatic
  Gaussian Process   Learning of low dimensional structure in multidimensional data is a canonical
problem in machine learning. One common approach is to suppose that the
observed data are close to a lower-dimensional smooth manifold. There are a
rich variety of manifold learning methods available, which allow mapping of
data points to the manifold. However, there is a clear lack of probabilistic
methods that allow learning of the manifold along with the generative
distribution of the observed data. The best attempt is the Gaussian process
latent variable model (GP-LVM), but identifiability issues lead to poor
performance. We solve these issues by proposing a novel Coulomb repulsive
process (Corp) for locations of points on the manifold, inspired by physical
models of electrostatic interactions among particles. Combining this process
with a GP prior for the mapping function yields a novel electrostatic GP
(electroGP) process. Focusing on the simple case of a one-dimensional manifold,
we develop efficient inference algorithms, and illustrate substantially
improved performance in a variety of experiments including filling in missing
frames in video.

2
The categories of this paper are: math
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an