Signal Adaptive Variable Selector for the Horseshoe Prior

Ray, Pallavi; Bhattacharya, Anirban

doi:10.48550/arxiv.1810.09004

Cited by 9 publications

(37 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This paper has, in the spirit of Hahn and Carvalho (2015) and Ray and Bhattacharya (2018), proposed to conduct variable selection for continuous shrinkage priors within the Bayesian Quantile Regression by decoupling shrinkage from sparsity as derived from a Bayesian decision theoretic perspective. The resultant easy to implement SAVS procedure for the BQR selects variables on a quantile specific basis where the degree of sparsity is estimated from the data via the quantile BIC in order to allow for heterogeneous levels of penalisation across the conditional distribution.…”

Section: Discussionmentioning

confidence: 99%

“…Following Hahn and Carvalho (2015) and Ray and Bhattacharya (2018), we make three modifications to the objective function ( 22). Firstly, we make use of the 1 -norm instead of 0 -norm penalisation to obtain a convex objective function whose solution is computable with standard techniques such as the coordinate descent algorithm of Friedman et al (2010).…”

Section: Signal Adaptive Variable Selection For the Bqrmentioning

confidence: 99%

“…Lastly, Ray and Bhattacharya (2018) have observed that starting the coordinate descent algorithm with the posterior means of β|• results in convergence after the first iteration by setting φ j = 1 |β j | κ and fixing κ = 2. Hence, the solution to (24) with one iteration of the coordinate descent algorithm simplifies to:…”

Section: Signal Adaptive Variable Selection For the Bqrmentioning

confidence: 99%

“…While the original SAVS procedure proposed by Ray and Bhattacharya (2018) provides good sparsification properties by fixing κ j = 2 across all coefficients for conditional mean models, a uniform value of κ across quantiles can be inappropriate if the degree of sparsity varies across the conditional distribution. Quantile specific sparsity can arise when the coefficients β p have a quantile profile which crosses the zero line for any p ∈ (0, 1).…”

Section: Signal Adaptive Variable Selection For the Bqrmentioning

confidence: 99%

“…While the LARS algorithm (see Friedman et al (2001)) can be applied to (44), we follow Ray and Bhattacharya (2018) in making use of the efficient coordinate descent algorithm introduced by Friedman et al (2007). The coordinate descent algorithm reduces computational complexity by updating the entry in solution vector α j , conditional on all other α, which is iterated until convergence.…”

Section: A2 Derivation Of Savs-bqrmentioning

confidence: 99%

See 4 more Smart Citations

Decoupling Shrinkage and Selection for the Bayesian Quantile Regression

Kohns¹,

Szendrei²

2021

Preprint

View full text Add to dashboard Cite

This paper extends the idea of decoupling shrinkage and sparsity for continuous priors to Bayesian Quantile Regression (BQR). The procedure follows two steps: In the first step, we shrink the quantile regression posterior through state of the art continuous priors and in the second step, we sparsify the posterior through an efficient variant of the adaptive lasso, the signal adaptive variable selection (SAVS) algorithm. We propose a new variant of the SAVS which automates the choice of penalisation through quantile specific lossfunctions that are valid in high dimensions. We show in large scale simulations that our selection procedure decreases bias irrespective of the true underlying degree of sparsity in the data, compared to the un-sparsified regression posterior. We apply our two-step approach to a high dimensional growth-at-risk (GaR) exercise. The prediction accuracy of the un-sparsified posterior is retained while yielding interpretable quantile specific variable selection results. Our procedure can be used to communicate to policymakers which variables drive downside risk to the macro economy

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Signal Adaptive Variable Selection For the Bqrmentioning

confidence: 99%

Section: Signal Adaptive Variable Selection For the Bqrmentioning

confidence: 99%

Section: Signal Adaptive Variable Selection For the Bqrmentioning

confidence: 99%

Section: A2 Derivation Of Savs-bqrmentioning

confidence: 99%

See 3 more Smart Citations

Decoupling Shrinkage and Selection for the Bayesian Quantile Regression

Kohns¹,

Szendrei²

2021

Preprint

View full text Add to dashboard Cite

show abstract

Combining shrinkage and sparsity in conjugate vector autoregressive models

Hauzenberger

Huber

Onorante

2021

J of Applied Econometrics

View full text Add to dashboard Cite

Summary Conjugate priors allow for fast inference in large dimensional vector autoregressive (VAR) models. But at the same time, they introduce the restriction that each equation features the same set of explanatory variables. This paper proposes a straightforward means of postprocessing posterior estimates of a conjugate Bayesian VAR to effectively perform equation‐specific covariate selection. Compared with existing techniques using shrinkage alone, our approach combines shrinkage and sparsity in both the VAR coefficients and the error variance–covariance matrices, greatly reducing estimation uncertainty in large dimensions while maintaining computational tractability. We illustrate our approach by means of two applications. The first application uses synthetic data to investigate the properties of the model across different data‐generating processes, and the second application analyzes the predictive gains from sparsification in a forecasting exercise for U.S. data.

show abstract

Nonlinearities in macroeconomic tail risk through the lens of big data quantile regressions

Prüser,

Huber

2023

J of Applied Econometrics

View full text Add to dashboard Cite

SummaryModeling and predicting extreme movements in GDP is notoriously difficult, and the selection of appropriate covariates and/or possible forms of nonlinearities are key in obtaining precise forecasts. In this paper, our focus is on using large datasets in quantile regression models to forecast the conditional distribution of US GDP growth. To capture possible nonlinearities, we include several nonlinear specifications. The resulting models will be huge dimensional, and we thus rely on a set of shrinkage priors. Since Markov chain Monte Carlo estimation becomes slow in these dimensions, we rely on fast variational Bayes approximations to the posterior distribution of the coefficients and the latent states. We find that our proposed set of models produces precise forecasts. These gains are especially pronounced in the tails. Using Gaussian processes to approximate the nonlinear component of the model further improves the good performance, in particular in the right tail.

show abstract

Signal Adaptive Variable Selector for the Horseshoe Prior

Cited by 9 publications

References 18 publications

Decoupling Shrinkage and Selection for the Bayesian Quantile Regression

Decoupling Shrinkage and Selection for the Bayesian Quantile Regression

Combining shrinkage and sparsity in conjugate vector autoregressive models

Nonlinearities in macroeconomic tail risk through the lens of big data quantile regressions

Contact Info

Product

Resources

About