Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Empirical priors for prediction in sparse high-dimensional linear
  regression   In this paper we adopt the familiar sparse, high-dimensional linear
regression model and focus on the important but often overlooked task of
prediction. In particular, we consider a new empirical Bayes framework that
incorporates data in the prior in two ways: one is to center the prior for the
non-zero regression coefficients and the other is to provide some additional
regularization. We show that, in certain settings, the asymptotic concentration
of the proposed empirical Bayes posterior predictive distribution is very fast,
and we establish a Bernstein--von Mises theorem which ensures that the derived
empirical Bayes prediction intervals achieve the targeted frequentist coverage
probability. The empirical prior has a convenient conjugate form, so posterior
computations are relatively simple and fast. Finally, our numerical results
demonstrate the proposed method's strong finite-sample performance in terms of
prediction accuracy, uncertainty quantification, and computation time compared
to existing Bayesian methods.

30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex