Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nearest Neighbor Dirichlet Mixtures   There is a rich literature on Bayesian methods for density estimation, which
characterize the unknown density as a mixture of kernels. Such methods have
advantages in terms of providing uncertainty quantification in estimation,
while being adaptive to a rich variety of densities. However, relative to
frequentist locally adaptive kernel methods, Bayesian approaches can be slow
and unstable to implement in relying on Markov chain Monte Carlo algorithms. To
maintain most of the strengths of Bayesian approaches without the computational
disadvantages, we propose a class of nearest neighbor-Dirichlet mixtures. The
approach starts by grouping the data into neighborhoods based on standard
algorithms. Within each neighborhood, the density is characterized via a
Bayesian parametric model, such as a Gaussian with unknown parameters.
Assigning a Dirichlet prior to the weights on these local kernels, we obtain a
pseudo-posterior for the weights and kernel parameters. A simple and
embarrassingly parallel Monte Carlo algorithm is proposed to sample from the
resulting pseudo-posterior for the unknown density. Desirable asymptotic
properties are shown, and the methods are evaluated in simulation studies and
applied to a motivating data set in the context of classification.

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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex