Related papers: Empirical Bayes Estimators for High-Dimensional Sp…
We investigate the problem of recovering a structured sparse signal from a linear observation model with an uncertain dynamic grid in the sensing matrix. The state-of-the-art expectation maximization based compressed sensing (EM-CS)…
Shrinkage estimation is a fundamental tool of modern statistics, pioneered by Charles Stein upon his discovery of the famous paradox involving the multivariate Gaussian. A large portion of the subsequent literature only considers the…
It is a challenging task to select correlated variables in a high dimensional space. To address this challenge, the elastic net has been developed and successfully applied to many applications. Despite its great success, the elastic net…
We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of…
Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…
We consider the classical problem of estimating a vector $\bolds{\mu}=(\mu_1,...,\mu_n)$ based on independent observations $Y_i\sim N(\mu_i,1)$, $i=1,...,n$. Suppose $\mu_i$, $i=1,...,n$ are independent realizations from a completely…
We introduce a flexible empirical Bayes approach for fitting Bayesian generalized linear models. Specifically, we adopt a novel mean-field variational inference (VI) method and the prior is estimated within the VI algorithm, making the…
Bayesian estimation is a vital tool in robotics as it allows systems to update the robot state belief using incomplete information from noisy sensors. To render the state estimation problem tractable, many systems assume that the motion and…
In this paper, the sparse sensor placement problem for least-squares estimation is considered, and the previous novel approach of the sparse sensor selection algorithm is extended. The maximization of the determinant of the matrix which…
Consider a situation of analyzing high-dimensional count data containing an excess of near-zero counts with a small number of moderate or large counts. Assuming that the observations are modeled by a Poisson distribution, we are interested…
We propose a family of novel hierarchical Bayesian deep auto-encoder models capable of identifying disentangled factors of variability in data. While many recent attempts at factor disentanglement have focused on sophisticated learning…
Predictive inference in the sparse Gaussian sequence model has received considerably less attention than its non-sparse, finite-sample counterpart. Existing work has largely been confined to discrete mixture priors. In this paper, we study…
We revisit the theoretical properties of Hamiltonian stochastic differential equations (SDES) for Bayesian posterior sampling, and we study the two types of errors that arise from numerical SDE simulation: the discretization error and the…
We study methods for simultaneous analysis of many noisy and biased estimates, each paired with an even noisier estimate of its own bias. The analyst's goal is to construct short calibrated intervals for each parameter. The standard…
Conjugate priors allow for fast inference in large dimensional vector autoregressive (VAR) models but, at the same time, introduce the restriction that each equation features the same set of explanatory variables. This paper proposes a…
We propose an empirical Bayes framework for aggregating estimators obtained from several identification functionals associated to the same causal parameter. The central object is a posterior mean that pools a collection of asymptotically…
Accurate and precise covariance matrices will be important in enabling planned cosmological surveys to detect new physics. Standard methods imply either the need for many N-body simulations in order to obtain an accurate estimate, or a…
We develop machinery to design efficiently computable and consistent estimators, achieving estimation error approaching zero as the number of observations grows, when facing an oblivious adversary that may corrupt responses in all but an…
We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…
Fine stratification is a popular design as it permits the stratification to be carried out to the fullest possible extent. Some examples include the Current Population Survey and National Crime Victimization Survey both conducted by the…