Manifold Scaffold Sampling


When data points exhibit salient geometric structure, density estimation and generative modeling can be more efficient by exploiting the data manifold. Here we propose Manifold Scaffold, a generative model for data concentrated near a manifold. First we estimate the data manifold using subspace-constrained accelerated mean shift (SAMS). Then we estimate the probability density on the estimated manifold using Riemannian kernel (RK), which can be sampled using a SAMS-based second-order retraction. Conditional distributions on normal spaces of the estimated manifold can be estimated discretely by normal-bundle bootstrap or continuously using Gaussian kernels. Combining the marginal and conditional models gives a joint generative model. We give benchmark results of Manifold Scaffold against KDE, manifold Parzen windows, and the PLoM method by Soize and Ghanem (2016).