Kernel density estimation on Riemannian manifolds

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Geodesic Finite Mixture Models (2014, background): “This is in contrast to existing non-parametric approaches [22] whose complexity grows with the training set size.”
Empirical graph Laplacian approximation of Laplace–Beltrami operators: Large sample results (2006, unknown): “…bounded derivatives sup p∈M sup f∈F ∣ ∣ ∣ ∆hn,pf(p) − 1 |µ| ∆Mf(p) ∣ ∣ ∣ = O ( √ log(1/hn) nhd+2n ) a.s. as soon as nhd+2n / log h −1 n → ∞ and nh d+4 n / log h −1 n → 0, and also prove asymptotic normality of ∆hn,pf(p) − 1 |µ| ∆M f(p) (functional CLT) for a fixed p ∈ M and uniformly in f.”
Normalizing Flows on Riemannian Manifolds (2016, background): “The induced Riemannian metric Gφ allows for well-defined notions of curvature, volume, gradients of functions and divergence of vector fields [21, 22, 23].”
Statistical topology via Morse theory, persistence and nonparametric estimation (2009, background): “Considerable progress has been achieved in terms of optimal estimation [14, 12, 16, 26, 27, 19, 17].”
Non-parametric regression estimation on closed Riemannian manifolds (2006, methodology): “More specifically, we have the following result [20].”