Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Horseshoe shrinkage methods for Bayesian fusion estimation   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.

8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph