# Empirical Bayes Estimation with Side Information: A Nonparametric Integrative Tweedie Approach

arXiv: https://arxiv.org/abs/2308.05883 · HTML: https://mlsanity.com/paper/2308.05883/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 53 references that are in the map.
- First posted on arXiv 11 Aug 2023.

## Builds on (most cited first, 15 of 15)

- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Control functionals for Monte Carlo integration](https://mlsanity.com/paper/1410.2392/) (2014)
- [On the nonparametric maximum likelihood estimator for Gaussian location mixture densities with application to Gaussian denoising](https://mlsanity.com/paper/1712.02009/) (2017)
- [Testing Goodness of Fit of Conditional Density Models with Kernels](https://mlsanity.com/paper/2002.10271/) (2020)
- [AdaPT: An interactive procedure for multiple testing with side information](https://mlsanity.com/paper/1609.06035/) (2016)
- [Multiple testing with the structure adaptive Benjamini-Hochberg algorithm](https://mlsanity.com/paper/1606.07926/) (2016)
- [Covariate powered cross-weighted multiple testing](https://mlsanity.com/paper/1701.05179/) (2017)
- [Group-Linear Empirical Bayes Estimates for a Heteroscedastic Normal Mean](https://mlsanity.com/paper/1503.08503/) (2015)
- [Covariate-Powered Empirical Bayes Estimation](https://mlsanity.com/paper/1906.01611/) (2019)
- [Optimal shrinkage estimation in heteroscedastic hierarchical linear models](https://mlsanity.com/paper/1503.06262/) (2015)
- [Adaptive Sparse Estimation with Side Information](https://mlsanity.com/paper/1811.11930/) (2018)
- [Empirical Bayes mean estimation with nonparametric errors via order statistic regression on replicated data](https://mlsanity.com/paper/1911.05970/) (2019)
- [A General Framework for Empirical Bayes Estimation in Discrete Linear Exponential Family](https://mlsanity.com/paper/1910.08997/) (2019)

## Abstract (arXiv)

We investigate the problem of compound estimation of normal means while accounting for the presence of side information. Leveraging the empirical Bayes framework, we develop a nonparametric integrative Tweedie (NIT) approach that incorporates structural knowledge encoded in multivariate auxiliary data to enhance the precision of compound estimation. Our approach employs convex optimization tools to estimate the gradient of the log-density directly, enabling the incorporation of structural constraints. We conduct theoretical analyses of the asymptotic risk of NIT and establish the rate at which NIT converges to the oracle estimator. As the dimension of the auxiliary data increases, we accurately quantify the improvements in estimation risk and the associated deterioration in convergence rate. The numerical performance of NIT is illustrated through the analysis of both simulated and real data, demonstrating its superiority over existing methods.