Statistical physics of inference: Thresholds and algorithms
L Zdeborová, F Krzakala - Advances in Physics, 2016 - Taylor & Francis
Many questions of fundamental interest in today's science can be formulated as inference
problems: some partial, or noisy, observations are performed over a set of variables and the …
problems: some partial, or noisy, observations are performed over a set of variables and the …
Scaling limits of wide neural networks with weight sharing: Gaussian process behavior, gradient independence, and neural tangent kernel derivation
G Yang - arXiv preprint arXiv:1902.04760, 2019 - arxiv.org
Several recent trends in machine learning theory and practice, from the design of state-of-
the-art Gaussian Process to the convergence analysis of deep neural nets (DNNs) under …
the-art Gaussian Process to the convergence analysis of deep neural nets (DNNs) under …
Phase retrieval via Wirtinger flow: Theory and algorithms
We study the problem of recovering the phase from magnitude measurements; specifically,
we wish to reconstruct a complex-valued signal about which we have phaseless samples of …
we wish to reconstruct a complex-valued signal about which we have phaseless samples of …
AMP-inspired deep networks for sparse linear inverse problems
M Borgerding, P Schniter… - IEEE Transactions on …, 2017 - ieeexplore.ieee.org
Deep learning has gained great popularity due to its widespread success on many inference
problems. We consider the application of deep learning to the sparse linear inverse …
problems. We consider the application of deep learning to the sparse linear inverse …
A unifying tutorial on approximate message passing
Over the last decade or so, Approximate Message Passing (AMP) algorithms have become
extremely popular in various structured high-dimensional statistical problems. Although the …
extremely popular in various structured high-dimensional statistical problems. Although the …
Implicit regularization in nonconvex statistical estimation: Gradient descent converges linearly for phase retrieval and matrix completion
Recent years have seen a flurry of activities in designing provably efficient nonconvex
optimization procedures for solving statistical estimation problems. For various problems like …
optimization procedures for solving statistical estimation problems. For various problems like …
Joint channel estimation and signal recovery for RIS-empowered multiuser communications
Reconfigurable intelligent surfaces (RISs) have been recently considered as a promising
candidate for energy-efficient solutions in future wireless networks. Their dynamic and low …
candidate for energy-efficient solutions in future wireless networks. Their dynamic and low …
Optimal errors and phase transitions in high-dimensional generalized linear models
Generalized linear models (GLMs) are used in high-dimensional machine learning,
statistics, communications, and signal processing. In this paper we analyze GLMs when the …
statistics, communications, and signal processing. In this paper we analyze GLMs when the …
Solving random quadratic systems of equations is nearly as easy as solving linear systems
This paper is concerned with finding a solution x to a quadratic system of equations yi=|< ai,
x>|^ 2, i= 1, 2,..., m. We prove that it is possible to solve unstructured quadratic systems in n …
x>|^ 2, i= 1, 2,..., m. We prove that it is possible to solve unstructured quadratic systems in n …
Phasemax: Convex phase retrieval via basis pursuit
T Goldstein, C Studer - IEEE Transactions on Information …, 2018 - ieeexplore.ieee.org
We consider the recovery of a (real-or complex-valued) signal from magnitude-only
measurements, known as phase retrieval. We formulate phase retrieval as a convex …
measurements, known as phase retrieval. We formulate phase retrieval as a convex …