Related papers: Double shrinkage priors for a normal mean matrix
This paper discusses regularized estimators in the multivariate statistical model as tools naturally arising within a Bayesian framework. First, a link is established between Bayesian estimation and inference under parameter rounding…
Low-rank matrix estimation from incomplete measurements recently received increased attention due to the emergence of several challenging applications, such as recommender systems; see in particular the famous Netflix challenge. While the…
Scale-mixture shrinkage priors have recently been shown to possess robust empirical performance and excellent theoretical properties such as model selection consistency and (near) minimax posterior contraction rates. In this paper, the…
In the value-added literature, it is often claimed that regressing on empirical Bayes shrinkage estimates corrects for the measurement error problem in linear regression. We clarify the conditions needed; we argue that these conditions are…
We study the problem of matrix estimation and matrix completion under a general framework. This framework includes several important models as special cases such as the gaussian mixture model, mixed membership model, bi-clustering model and…
We study Bayesian inference in statistical linear inverse problems with Gaussian noise and priors in Hilbert space. We focus our interest on the posterior contraction rate in the small noise limit. Existing results suffer from a certain…
We investigate shrinkage priors on power spectral densities for complex-valued circular-symmetric autoregressive processes. We construct shrinkage predictive power spectral densities, which asymptotically dominate (i) the Bayesian…
We consider the problem of estimating the error variance in a general linear model when the error distribution is assumed to be spherically symmetric, but not necessary Gaussian. In particular we study the case of a scale mixture of…
We consider the problem of learning the structure of a high dimensional precision matrix under sparsity assumptions. We propose to use a shrinkage prior, called the DL-graphical prior based on the Dirichlet-Laplace prior used for the…
Standard Bayesian analyses can be difficult to perform when the full likelihood, and consequently the full posterior distribution, is too complex and difficult to specify or if robustness with respect to data or to model misspecifications…
In this work, we address the problem of Hessian inversion bias in distributed second-order optimization algorithms. We introduce a novel shrinkage-based estimator for the resolvent of gram matrices which is asymptotically unbiased, and…
Fitted probabilities from widely used Bayesian multinomial probit models can depend strongly on the choice of a base category, which is used to uniquely identify the parameters of the model. This paper proposes a novel identification…
Wavelet shrinkage estimators are widely applied in several fields of science for denoising data in wavelet domain by reducing the magnitudes of empirical coefficients. In nonparametric regression problem, most of the shrinkage rules are…
This is the second part of a two-paper series on generalized inverses that minimize matrix norms. In Part II we focus on generalized inverses that are minimizers of entrywise p norms whose main representative is the sparse pseudoinverse for…
We develop an empirical Bayes (EB) algorithm for the matrix completion problems. The EB algorithm is motivated from the singular value shrinkage estimator for matrix means by Efron and Morris (1972). Since the EB algorithm is essentially…
The present paper proposes a bayesian approach for wavelet shrinkage with the use of a shrinkage prior based on the generalized secant hyperbolic distribution symmetric around zero in a nonparemetric regression problem. This shrinkage prior…
We consider the Bayesian analysis of a few complex, high-dimensional models and show that intuitive priors, which are not tailored to the fine details of the model and the estimated parameters, produce estimators which perform poorly in…
The problem of estimating a mean matrix of a multivariate complex normal distribution with an unknown covariance matrix is considered under an invariant loss function. By using complex versions of the Stein identity, the Stein-Haff…
We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of…
We give a sufficient condition for admissibility of generalized Bayes estimators of the location vector of spherically symmetric distribution under squared error loss. Compared to the known results for the multivariate normal case, our…