Neural density estimators that factor over a known Markov random field achieve dimension-independent L1 rates n^{-1/(4+r)} (and optimally n^{-1/(2+r)}), where r is the maximum clique size.
Estimating a density near an unknown manifold: a Bayesian nonparametric approach
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abstract
We study the Bayesian density estimation of data living in the offset of an unknown submanifold of the Euclidean space. In this perspective, we introduce a new notion of anisotropic H\"older for the underlying density and obtain posterior rates that are minimax optimal and adaptive to the regularity of the density, to the intrinsic dimension of the manifold, and to the size of the offset, provided that the latter is not too small -- while still allowed to go to zero. Our Bayesian procedure, based on location-scale mixtures of Gaussians, appears to be convenient to implement and yields good practical results, even for quite singular data.
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Dimension-independent rates for structured neural density estimation
Neural density estimators that factor over a known Markov random field achieve dimension-independent L1 rates n^{-1/(4+r)} (and optimally n^{-1/(2+r)}), where r is the maximum clique size.