Related papers: Local Convergence of an AMP Variant to the LASSO S…
We propose a minimum distance estimation method for robust regression in sparse high-dimensional settings. The traditional likelihood-based estimators lack resilience against outliers, a critical issue when dealing with high-dimensional…
This paper proposes a sparse regression method that continuously interpolates between Forward Stepwise selection (FS) and the LASSO. When tuned appropriately, our solutions are much sparser than typical LASSO fits but, unlike FS fits,…
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…
This paper is concerned with the problem of reconstructing an unknown rank-one matrix with prior structural information from noisy observations. While computing the Bayes-optimal estimator seems intractable in general due to its nonconvex…
Generalised approximate message passing (GAMP) is an approximate Bayesian estimation algorithm for signals observed through a linear transform with a possibly non-linear subsequent measurement model. By leveraging prior information about…
This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Numerous renowned algorithms for tackling the compressed sensing problem…
We study sparse linear regression over a network of agents, modeled as an undirected graph and no server node. The estimation of the $s$-sparse parameter is formulated as a constrained LASSO problem wherein each agent owns a subset of the…
We establish non-asymptotic bounds on the finite-sample behavior of generalized first-order iterative algorithms -- including gradient-based optimization methods and approximate message passing (AMP) -- with Gaussian data matrices and…
Approximate message passing (AMP) algorithms break a (high-dimensional) statistical problem into parts then repeatedly solve each part in turn, akin to alternating projections. A distinguishing feature is their asymptotic behaviours can be…
High-dimensional linear regression model is the most popular statistical model for high-dimensional data, but it is quite a challenging task to achieve a sparse set of regression coefficients. In this paper, we propose a simple heuristic…
Approximate-message passing (AMP) algorithms have become an important element of high-dimensional statistical inference, mostly due to their adaptability and concentration properties, the state evolution (SE) equations. This is demonstrated…
We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the…
The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the…
This paper addresses the reconstruction of an unknown signal vector with sublinear sparsity from generalized linear measurements. Generalized approximate message-passing (GAMP) is proposed via state evolution in the sublinear sparsity…
In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional generalized bilinear regression, to the multi-layer case for the handling of cascaded problem such as…
We consider a distributed learning setup where a sparse signal is estimated over a network. Our main interest is to save communication resource for information exchange over the network and reduce processing time. Each node of the network…
Approximate message passing (AMP) is an effective iterative sparse recovery algorithm for linear system models. Its performance is characterized by the state evolution (SE) which is a simple scalar recursion. However, depending on a…
The goal of Sparse Convex Optimization is to optimize a convex function $f$ under a sparsity constraint $s\leq s^*\gamma$, where $s^*$ is the target number of non-zero entries in a feasible solution (sparsity) and $\gamma\geq 1$ is an…
Shrinkage estimators that possess the ability to produce sparse solutions have become increasingly important to the analysis of today's complex datasets. Examples include the LASSO, the Elastic-Net and their adaptive counterparts.…
This paper considers the massive connectivity problem in an asynchronous grant-free random access system, where a huge number of devices sporadically transmit data to a base station (BS) with imperfect synchronization. The goal is to design…