Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximations of conditional probability density functions in Lebesgue
  spaces via mixture of experts models   Mixture of experts (MoE) models are widely applied for conditional
probability density estimation problems. We demonstrate the richness of the
class of MoE models by proving denseness results in Lebesgue spaces, when
inputs and outputs variables are both compactly supported. We further prove an
almost uniform convergence result when the input is univariate. Auxiliary
lemmas are proved regarding the richness of the soft-max gating function class,
and their relationships to the class of Gaussian gating functions.

10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga