Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean-Field Variational Inference for Gradient Matching with Gaussian
  Processes   Gradient matching with Gaussian processes is a promising tool for learning
parameters of ordinary differential equations (ODE's). The essence of gradient
matching is to model the prior over state variables as a Gaussian process which
implies that the joint distribution given the ODE's and GP kernels is also
Gaussian distributed. The state-derivatives are integrated out analytically
since they are modelled as latent variables. However, the state variables
themselves are also latent variables because they are contaminated by noise.
Previous work sampled the state variables since integrating them out is
\textit{not} analytically tractable. In this paper we use mean-field
approximation to establish tight variational lower bounds that decouple state
variables and are therefore, in contrast to the integral over state variables,
analytically tractable and even concave for a restricted family of ODE's,
including nonlinear and periodic ODE's. Such variational lower bounds
facilitate "hill climbing" to determine the maximum a posteriori estimate of
ODE parameters. An additional advantage of our approach over sampling methods
is the determination of a proxy to the intractable posterior distribution over
state variables given observations and the ODE's.

12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
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
1
The categories of this paper are: cs
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn