The horseshoe estimator for sparse signals

By Carlos M. Carvalho, Nicholas G. Polson, James G. Scott. 2010

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Citations in the corpus

Efficient and Scalable Bayesian Neural Nets with Rank-1 Factors (2020, background): “However, the exploration of heavy-tailed priors has been mostly limited to half-Cauchy (Carvalho et al., 2010) and log-uniform priors (Kingma et al., 2015) on the scale parameters.”
Bayesian Compression for Deep Learning (2017, methodology): “It should be mentioned that the improper log-uniform prior is the limiting case of the horseshoe prior when the shapes of the (inverse) Gamma hyperpriors on α̃i, β̃i go to zero [8].”
Bayesian group factor analysis with structured sparsity (2016, methodology): “…scale mixtures of normal priors have been proposed as a computationally efficient alternative to the two component spike-and-slab prior (West, 1987; Carvalho et al., 2010; Polson and Scott, 2011; Armagan et al., 2013, 2011; Bhattacharya et al., 2014): such priors generally assume normal…”
Penalized Wavelets: Embedding Wavelets into Semiparametric Regression (2011, methodology): “The Horseshoe and NormalExponential-Gamma density functions correspond to non-convex penalization and have been proposed in the wide data regression literature by, respectively, Carvalho, Polson and Scott [12] and Griffin and Brown [32].”
Regularization and confounding in linear regression for treatment effect estimation (2016, methodology): “For additional details concerning how these attributes are defined and where they were obtained, see the original paper (Donohue III and Levitt, 2001).”
Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects (with Discussion) (2020, positive): “We evaluated three variants of BART, the causal random forest model of Athey et al. (2019) (using the default specification in the grf package), and a regularized linear model (LM), using the horseshoe prior (HR) of Carvalho et al. (2010), with up to three way interactions.”
Foundations of Linear and Generalized Linear Models (2015, methodology): “7 Binary and multinomial GLMs: For Bayesian modeling of binary data, see Christensen et al. (2010, Chapter 8), Hosmer et al. (2013, Section 10.6), Gelman et al. (2013, Chapter 16), Ntzoufras (2009, Sections 7.5 and 9.3), O’Hagan and Forster (2004, Chapter 12), and Zellner and Rossi (1984). For Bayes”
Adaptive posterior contraction rates for the horseshoe (2017, methodology): “In the present paper we study the Bayesian method based on the horseshoe prior [7, 6, 28, 23, 24].”
On the half-cauchy prior for a global scale parameter (2011, methodology): “We then used Markov Chain Monte Carlo to compute the marginal likelihood of the data as a function of λ , assuming that each βi has a horseshoe prior (Carvalho et al., 2010).”
The Horseshoe Estimator: Posterior Concentration around Nearly Black Vectors (2014, methodology): “By approximating the posterior distribution of τ 2 given κ = ( κ 1 , . . . , κ n ) in case a prior on τ is used, Carvalho, Polson and Scott (2010) show that if most observations are shrunk near zero, τ will be very small with high probability.”
Dirichlet-Laplace priors for optimal shrinkage (2014, methodology): “Ca(0;1). These traditional choices lead to a kernel which is bounded in a neighborhood of zero. However, if one instead uses a half Cauchy prior 1=2 j ˘Ca +(0;1), then the resulting horseshoe kernel [6, 7] is unbounded with a singularity at zero. This phenomenon coupled with tail robustness properti”
Shrink Globally, Act Locally: Sparse Bayesian Regularization and Prediction (2012, background): “a bound proven in Carvalho et al. [2010]. This second integral is easily computed and of order .”
Sparse Multi-Output Gaussian Processes for Medical Time Series Prediction (2017, methodology): “(22) For our results, we set α = β = γ = d = 0.5 to recapitulate two layers of the horseshoe prior, using a statistically equivalent prior represented by a hierarchical gamma with four layers (Carvalho et al., 2010; Armagan et al., 2011; Gao et al., 2013; Zhao et al., 2016).”
Time-varying sparsity in dynamic regression models (2014, neutral): “An alternative class of methods is Bayesian regularisation methods which use absolutely continuous priors and encourage small regression effects to be aggressively shrunk towards zero under the posterior (see Carvalho et al. (2010), and Polson and Scott (2011)).”
BAYESIAN LINEAR REGRESSION WITH SPARSE PRIORS (2014, background): “, [14, 23, 24]) can cope with somewhat higher dimensions, but truly high-dimensional models are out of reach of fully Bayesian methods at the present time.”
The Graphical Horseshoe Estimator for Inverse Covariance Matrices (2017, methodology): “Both of these properties are inherited from the horseshoe prior of Carvalho, Polson, and Scott (2010) for the sparse normal means model.”