Related papers: Approximate Message Passing for general non-Symmet…
Generalized Vector Approximate Message Passing (GVAMP) is an efficient iterative algorithm for approximately minimum-mean-squared-error estimation of a random vector $\mathbf{x}\sim p_{\mathbf{x}}(\mathbf{x})$ from generalized linear…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
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…
We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and…
The Message-Passing Approach (MPA) is the state-of-the-art technique to obtain quasi-analytical predictions for percolation on real complex networks. Besides being intuitive and straightforward, it has the advantage of being mathematically…
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 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…
In this paper, we investigate the joint device activity and data detection in massive machine-type communications (mMTC) with a one-phase non-coherent scheme, where data bits are embedded in the pilot sequences and the base station…
We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this…
We propose an estimator of prediction error using an approximate message passing (AMP) algorithm that can be applied to a broad range of sparse penalties. Following Stein's lemma, the estimator of the generalized degrees of freedom, which…
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…
We propose a novel algorithm for compressive imaging that exploits both the sparsity and persistence across scales found in the 2D wavelet transform coefficients of natural images. Like other recent works, we model wavelet structure using a…
Understanding efficiency in high dimensional linear models is a longstanding problem of interest. Classical work with smaller dimensional problems dating back to Huber and Bickel has illustrated the benefits of efficient loss functions.…
In integrated sensing and communication (ISAC) networks, multiple base stations (BSs) collaboratively sense a common target, leveraging diversity from multiple observation perspectives and joint signal processing to enhance sensing…
This paper introduces a random modulation technique that is decoupled from the channel matrix, allowing it to be applied to arbitrary norm-bounded and spectrally convergent channel matrices. The proposed random modulation constructs an…
Iterative information processing, either based on heuristics or analytical frameworks, has been shown to be a very powerful tool for the design of efficient, yet feasible, wireless receiver architectures. Within this context, algorithms…
We consider a class of nonlinear mappings $\mathsf{F}_{A,N}$ in $\mathbb{R}^N$ indexed by symmetric random matrices $A\in\mathbb{R}^{N\times N}$ with independent entries. Within spin glass theory, special cases of these mappings correspond…
In this work we aim to solve the compressed sensing problem for the case of a complex unknown vector by utilizing the Bayesian-optimal structured signal approximate message passing (BOSSAMP) algorithm on the jointly sparse real and…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
A unified linear algebraic approach to adaptive signal processing (ASP) is presented. Starting from just Ax=b, key ASP algorithms are derived in a simple, systematic, and integrated manner without requiring any background knowledge to the…