Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Posterior convergence rates in non-linear latent variable models   Non-linear latent variable models have become increasingly popular in a
variety of applications. However, there has been little study on theoretical
properties of these models. In this article, we study rates of posterior
contraction in univariate density estimation for a class of non-linear latent
variable models where unobserved U(0,1) latent variables are related to the
response variables via a random non-linear regression with an additive error.
Our approach relies on characterizing the space of densities induced by the
above model as kernel convolutions with a general class of continuous mixing
measures. The literature on posterior rates of contraction in density
estimation almost entirely focuses on finite or countably infinite mixture
models. We develop approximation results for our class of continuous mixing
measures. Using an appropriate Gaussian process prior on the unknown regression
function, we obtain the optimal frequentist rate up to a logarithmic factor
under standard regularity conditions on the true density.

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The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
3
The categories of this paper are: physics
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The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an