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A Mean Field Approach to Empirical Bayes Estimation in High-dimensional Linear Regression
Sumit Mukherjee, Bodhisattva Sen, Subhabrata Sen
We study empirical Bayes estimation in high-dimensional linear regression. To facilitate computationally efficient estimation of the underlying prior, we adopt a variational empiri…
Wasserstein-Cramér-Rao Theory of Unbiased Estimation
Nicolás GarcÃa Trillos, Adam Quinn Jaffe, Bodhisattva Sen
The quantity of interest in the classical Cramér-Rao theory of unbiased estimation (e.g., the Cramér-Rao lower bound, its exact attainment for exponential families, and asymptoti…
Estimation of Algebraic Sets: Extending PCA Beyond Linearity
Alberto González-Sanz, Gilles Mordant, Ãlvaro Samperio +1
An algebraic set is defined as the zero locus of a system of real polynomial equations. In this paper we address the problem of recovering an unknown algebraic set fr…
Variational Inference for Latent Variable Models in High Dimensions
Chenyang Zhong, Sumit Mukherjee, Bodhisattva Sen
Variational inference (VI) is a popular method for approximating intractable posterior distributions in Bayesian inference and probabilistic machine learning. In this paper, we int…