相关论文: Equivalence of Approximate Message Passing and Low…
This paper considers a discrete-valued signal estimation scheme based on a low-complexity Bayesian optimal message passing algorithm (MPA) for solving massive linear inverse problems under highly correlated measurements. Gaussian belief…
Mean-field characterizations of first-order iterative algorithms -- including Approximate Message Passing (AMP), stochastic and proximal gradient descent, and Langevin diffusions -- have enabled a precise understanding of learning dynamics…
The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of…
In a recent paper, the authors proposed a new class of low-complexity iterative thresholding algorithms for reconstructing sparse signals from a small set of linear measurements \cite{DMM}. The new algorithms are broadly referred to as AMP,…
Approximate Message Passing (AMP) algorithms enable precise characterization of certain classes of random objects in the high-dimensional limit, and have found widespread applications in fields such as signal processing, statistics, and…
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…
Given a redundant dictionary $\Phi$, represented by an $M \times N$ matrix ($\Phi \in \mathbb{R}^{M \times N}$) and a target signal $y \in \mathbb{R}^M$, the \emph{sparse approximation problem} asks to find an approximate representation of…
Consider a set of agents that wish to estimate a vector of parameters of their mutual interest. For this estimation goal, agents can sense and communicate. When sensing, an agent measures (in additive gaussian noise) linear combinations of…
Generalized approximate message passing (GAMP) is a promising technique for unknown signal reconstruction of generalized linear models (GLM). However, it requires that the transformation matrix has independent and identically distributed…
Recently we extended Approximate message passing (AMP) algorithm to be able to handle general invariant matrix ensembles. In this contribution we extend our S-AMP approach to non-linear observation models. We obtain generalized AMP (GAMP)…
In this paper, we present a wideband subspace estimation method that characterizes the signal subspace through its orthogonal projection matrix at each frequency. Fundamentally, the method models this projection matrix as a function of…
We propose a scheme to estimate the parameters $b_i$ and $c_j$ of the bilinear form $z_m=\sum_{i,j} b_i z_m^{(i,j)} c_j$ from noisy measurements $\{y_m\}_{m=1}^M$, where $y_m$ and $z_m$ are related through an arbitrary likelihood function…
We consider the algorithmic problem of finding a near ground state (near optimal solution) of a $p$-spin model. We show that for a class of algorithms broadly defined as Approximate Message Passing (AMP), the presence of the Overlap Gap…
SLOPE is a relatively new convex optimization procedure for high-dimensional linear regression via the sorted l1 penalty: the larger the rank of the fitted coefficient, the larger the penalty. This non-separable penalty renders many…
Sparse Principal Component Analysis (PCA) is a dimensionality reduction technique wherein one seeks a low-rank representation of a data matrix with additional sparsity constraints on the obtained representation. We consider two…
The generalized approximate message passing (GAMP) algorithm under the Bayesian setting shows advantage in recovering under-sampled sparse signals from corrupted observations. Compared to conventional convex optimization methods, it has a…
In this paper, the `Approximate Message Passing' (AMP) algorithm, initially developed for compressed sensing of signals under i.i.d. Gaussian measurement matrices, has been extended to a multi-terminal setting (MAMP algorithm). It has been…
The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…
Purpose: For quantitative susceptibility mapping (QSM), the lack of ground-truth in clinical settings makes it challenging to determine suitable parameters for the dipole inversion. We propose a probabilistic Bayesian approach for QSM with…
In monotone classification, the input is a multi-set $P$ of points in $\mathbb{R}^d$, each associated with a hidden label from $\{-1, 1\}$. The goal is to identify a monotone function $h$, which acts as a classifier, mapping from…