Related papers: Estimation in Rotationally Invariant Generalized L…
Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…
This paper proposes a fast approximate message-passing (AMP) algorithm for solving compressed sensing (CS) recovery problems with 1D-finite-difference sparsity in term of MMSE estimation. The proposed algorithm, named ssAMP-BGFD, is…
We consider matrix factorization (MF) with certain constraints, which finds wide applications in various areas. Leveraging variational inference (VI) and unitary approximate message passing (UAMP), we develop a Bayesian approach to MF with…
Decentralized generalized approximate message-passing (GAMP) is proposed for compressed sensing from distributed generalized linear measurements in a tree-structured network. Consensus propagation is used to realize average consensus…
For the problem of multi-class linear classification and feature selection, we propose approximate message passing approaches to sparse multinomial logistic regression (MLR). First, we propose two algorithms based on the Hybrid Generalized…
Signal recovery under generative neural network priors has emerged as a promising direction in statistical inference and computational imaging. Theoretical analysis of reconstruction algorithms under generative priors is, however,…
We study estimation in the linear model $y=A\beta^\star+\epsilon$, in a Bayesian setting where $\beta^\star$ has an entrywise i.i.d. prior and the design $A$ is rotationally-invariant in law. In the large system limit as dimension and…
This paper studies asynchronous message passing (AMP), a new paradigm for applying neural network based learning to graphs. Existing graph neural networks use the synchronous distributed computing model and aggregate their neighbors in each…
Phase retrieval refers to the problem of recovering a high-dimensional vector $\boldsymbol{x} \in \mathbb{C}^N$ from the magnitude of its linear transform $\boldsymbol{z} = A \boldsymbol{x}$, observed through a noisy channel. To improve the…
We consider compressive imaging problems, where images are reconstructed from a reduced number of linear measurements. Our objective is to improve over existing compressive imaging algorithms in terms of both reconstruction error and…
Often, large, high dimensional datasets collected across multiple modalities can be organized as a higher order tensor. Low-rank tensor decomposition then arises as a powerful and widely used tool to discover simple low dimensional…
Computing maximum a posteriori (MAP) estimation in graphical models is an important inference problem with many applications. We present message-passing algorithms for quadratic programming (QP) formulations of MAP estimation for pairwise…
Maximum a posteriori (MAP) inference is a fundamental computational paradigm for statistical inference. In the setting of graphical models, MAP inference entails solving a combinatorial optimization problem to find the most likely…
Gradient-descent-based algorithms and their stochastic versions have widespread applications in machine learning and statistical inference. In this work we perform an analytic study of the performances of one of them, the Langevin…
The ubiquity of approximately sparse data has led a variety of com- munities to great interest in compressed sensing algorithms. Although these are very successful and well understood for linear measurements with additive noise, applying…
Maximum a posteriori (MAP) inference in discrete-valued Markov random fields is a fundamental problem in machine learning that involves identifying the most likely configuration of random variables given a distribution. Due to the…
In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…
Reconstruction of images from noisy linear measurements is a core problem in image processing, for which convex optimization methods based on total variation (TV) minimization have been the long-standing state-of-the-art. We present an…
Quantitative Acoustic Microscopy (QAM) is an imaging technology utilising high frequency ultrasound to produce quantitative two-dimensional (2D) maps of acoustical and mechanical properties of biological tissue at microscopy scale.…
We analyse a linear regression problem with nonconvex regularization called smoothly clipped absolute deviation (SCAD) under an overcomplete Gaussian basis for Gaussian random data. We propose an approximate message passing (AMP) algorithm…