Diffusion driven empirical Bayes estimation of high-dimensional normal means vectors

In this work we consider the problem of estimating independent and possibly high-dimensional normal means vectors in a sparse empirical Bayes framework that glues together a recent manifold-modeling technique called diffusion maps, with a more classical concept of sparsity based on the assumption that most of the unknown coordinates of model parameter are actually 0. More specifically, for the vector valued parameter of interest, we adopt a mixture prior composed by an atom at zero and a completely unspecified density for the non-zero component. The novelty of the proposed method is the way we use the data to implicitly drive the prior specification through a (weighted/iterative) quantized diffusion density estimator of the marginal distribution. In this way, depending on the actual structure of the data at hand, we are able to reach a balance between the two complementary approaches to sparsity mentioned above.