相关论文: Asymptotic Analysis of MAP Estimation via the Repl…

The large-system performance of MAP estimation is studied considering a general distortion function when the observation vector is received through a linear system with additive white Gaussian noise. The analysis considers the system matrix…

Compressive sensing (CS) is a new methodology to capture signals at lower rate than the Nyquist sampling rate when the signals are sparse or sparse in some domain. The performance of CS estimators is analyzed in this paper using tools from…

This manuscript goes through the fundamental connections between statistical mechanics and estimation theory by focusing on the particular problem of compressive sensing. We first show that the asymptotic analysis of a sparse recovery…

For noisy compressive sensing systems, the asymptotic distortion with respect to an arbitrary distortion function is determined when a general class of least-square based reconstruction schemes is employed. The sampling matrix is considered…

We present a randomized maximum a posteriori (rMAP) method for generating approximate samples of posteriors in high dimensional Bayesian inverse problems governed by large-scale forward problems. We derive the rMAP approach by: 1) casting…

This paper considers the fundamental limit of compressed sensing for i.i.d. signal distributions and i.i.d. Gaussian measurement matrices. Its main contribution is a rigorous characterization of the asymptotic mutual information (MI) and…

A reliable support detection is essential for a greedy algorithm to reconstruct a sparse signal accurately from compressed and noisy measurements. This paper proposes a novel support detection method for greedy algorithms, which is referred…

This paper studies the asymptotic performance of maximum-a-posteriori estimation in the presence of prior information. The problem arises in several applications such as recovery of signals with non-uniform sparsity pattern from…

The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior…

In the problem of matrix compressed sensing we aim to recover a low-rank matrix from few of its element-wise linear projections. In this contribution we analyze the asymptotic performance of a Bayes-optimal inference procedure for a model…

Maximum a posteriori (MAP) estimation, like all Bayesian methods, depends on prior assumptions. These assumptions are often chosen to promote specific features in the recovered estimate. The form of the chosen prior determines the shape of…

Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…

Transfer learning techniques aim to leverage information from multiple related datasets to enhance prediction quality against a target dataset. Such methods have been adopted in the context of high-dimensional sparse regression, and some…

Bayesian statistics has two common measures of central tendency of a posterior distribution: posterior means and Maximum A Posteriori (MAP) estimates. In this paper, we discuss a connection between MAP estimates and posterior means. We…

We study the compressed sensing (CS) signal estimation problem where an input signal is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the input signal…

Predictive mean matching imputation is popular for handling item nonresponse in survey sampling. In this article, we study the asymptotic properties of the predictive mean matching estimator of the population mean. For variance estimation,…

We present a theoretical analysis of Maximum a Posteriori (MAP) sequence estimation for binary symmetric hidden Markov processes. We reduce the MAP estimation to the energy minimization of an appropriately defined Ising spin model, and…

We consider the estimation of an i.i.d.\ random vector observed through a linear transform followed by a componentwise, probabilistic (possibly nonlinear) measurement channel. A novel algorithm, called generalized approximate message…

This paper demonstrates how new principles of compressed sensing, namely asymptotic incoherence, asymptotic sparsity and multilevel sampling, can be utilised to better understand underlying phenomena in practical compressed sensing and…

The analytic characterization of the high-dimensional behavior of optimization for Generalized Linear Models (GLMs) with Gaussian data has been a central focus in statistics and probability in recent years. While convex cases, such as the…