8,661 research outputs found
Sparsity-Promoting Bayesian Dynamic Linear Models
Sparsity-promoting priors have become increasingly popular over recent years
due to an increased number of regression and classification applications
involving a large number of predictors. In time series applications where
observations are collected over time, it is often unrealistic to assume that
the underlying sparsity pattern is fixed. We propose here an original class of
flexible Bayesian linear models for dynamic sparsity modelling. The proposed
class of models expands upon the existing Bayesian literature on sparse
regression using generalized multivariate hyperbolic distributions. The
properties of the models are explored through both analytic results and
simulation studies. We demonstrate the model on a financial application where
it is shown that it accurately represents the patterns seen in the analysis of
stock and derivative data, and is able to detect major events by filtering an
artificial portfolio of assets
A Hierarchical Bayesian Framework for Constructing Sparsity-inducing Priors
Variable selection techniques have become increasingly popular amongst
statisticians due to an increased number of regression and classification
applications involving high-dimensional data where we expect some predictors to
be unimportant. In this context, Bayesian variable selection techniques
involving Markov chain Monte Carlo exploration of the posterior distribution
over models can be prohibitively computationally expensive and so there has
been attention paid to quasi-Bayesian approaches such as maximum a posteriori
(MAP) estimation using priors that induce sparsity in such estimates. We focus
on this latter approach, expanding on the hierarchies proposed to date to
provide a Bayesian interpretation and generalization of state-of-the-art
penalized optimization approaches and providing simultaneously a natural way to
include prior information about parameters within this framework. We give
examples of how to use this hierarchy to compute MAP estimates for linear and
logistic regression as well as sparse precision-matrix estimates in Gaussian
graphical models. In addition, an adaptive group lasso method is derived using
the framework.Comment: Submitted for publication; corrected typo
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