Related papers: Phase Diagram and Approximate Message Passing for …
We extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear case, which enables its…
Accurate quantification of uncertainty is crucial for real-world applications of machine learning. However, modern deep neural networks still produce unreliable predictive uncertainty, often yielding over-confident predictions. In this…
For certain sensing matrices, the Approximate Message Passing (AMP) algorithm efficiently reconstructs undersampled signals. However, in Magnetic Resonance Imaging (MRI), where Fourier coefficients of a natural image are sampled with…
We consider the problem of reconstructing a signal from multi-layered (possibly) non-linear measurements. Using non-rigorous but standard methods from statistical physics we present the Multi-Layer Approximate Message Passing (ML-AMP)…
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,…
Recovering an unknown complex signal from the magnitude of linear combinations of the signal is referred to as phase retrieval. We present an exact performance analysis of a recently proposed convex-optimization-formulation for this…
The classical Kaczmarz iteration and its randomized variants are popular tools for fast inversion of linear overdetermined systems. This method extends naturally to the setting of the phase retrieval problem via substituting at each…
Approximate Message Passing (AMP) algorithms are a class of iterative procedures for computationally-efficient estimation in high-dimensional inference and estimation tasks. Due to the presence of an 'Onsager' correction term in its…
Various alignment problems arising in cryo-electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as Z/L, U(1), or…
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…
We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access.…
Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…
In this paper we consider Basis Pursuit De-Noising (BPDN) problems in which the sparse original signal is drawn from a finite alphabet. To solve this problem we propose an iterative message passing algorithm, which capitalises not only on…
Experimental quantum simulators have become large and complex enough that discovering new physics from the huge amount of measurement data can be quite challenging, especially when little theoretical understanding of the simulated model is…
This paper studies transfer learning for estimating the mean of random functions based on discretely sampled data, where, in addition to observations from the target distribution, auxiliary samples from similar but distinct source…
This paper addresses the problem of simultaneous signal recovery and dictionary learning based on compressive measurements. Multiple signals are analyzed jointly, with multiple sensing matrices, under the assumption that the unknown signals…
We consider the problem of localizing change points in a generalized linear model (GLM), a model that covers many widely studied problems in statistical learning including linear, logistic, and rectified linear regression. We propose a…
In the recent literature on machine learning and decision making, calibration has emerged as a desirable and widely-studied statistical property of the outputs of binary prediction models. However, the algorithmic aspects of measuring model…
When recorded in an enclosed room, a sound signal will most certainly get affected by reverberation. This not only undermines audio quality, but also poses a problem for many human-machine interaction technologies that use speech as their…
An improved inference method for densely connected systems is presented. The approach is based on passing condensed messages between variables, representing macroscopic averages of microscopic messages. We extend previous work that showed…