# Horseshoe shrinkage methods for Bayesian fusion estimation

arXiv: https://arxiv.org/abs/2102.07378 · HTML: https://mlsanity.com/paper/2102.07378/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2021.

## Built on by (most cited first, 1 of 1)

- [T-LoHo: A Bayesian Regularization Model for Structured Sparsity and Smoothness on Graphs](https://mlsanity.com/paper/2107.02510/) (2021)

## Abstract (arXiv)

We consider the problem of estimation and structure learning of high dimensional signals via a normal sequence model, where the underlying parameter vector is piecewise constant, or has a block structure. We develop a Bayesian fusion estimation method by using the Horseshoe prior to induce a strong shrinkage effect on successive differences in the mean parameters, simultaneously imposing sufficient prior concentration for non-zero values of the same. The proposed method thus facilitates consistent estimation and structure recovery of the signal pieces. We provide theoretical justifications of our approach by deriving posterior convergence rates and establishing selection consistency under suitable assumptions. We also extend our proposed method to signal de-noising over arbitrary graphs and develop efficient computational methods along with providing theoretical guarantees. We demonstrate the superior performance of the Horseshoe based Bayesian fusion estimation method through extensive simulations and two real-life examples on signal de-noising in biological and geophysical applications. We also demonstrate the estimation performance of our method on a real-world large network for the graph signal de-noising problem.