Related papers: Optimal Quantized Compressed Sensing via Projected…
We study the problem of recovering Gaussian data under adversarial corruptions when the noises are low-rank and the corruptions are on the coordinate level. Concretely, we assume that the Gaussian noises lie in an unknown $k$-dimensional…
Autoencoders are a prominent model in many empirical branches of machine learning and lossy data compression. However, basic theoretical questions remain unanswered even in a shallow two-layer setting. In particular, to what degree does a…
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)…
Compressed sensing is a technique for recovering a high-dimensional signal from lower-dimensional data, whose components represent partial information about the signal, utilizing prior knowledge on the sparsity of the signal. For further…
Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the…
Correcting scan-positional errors is critical in achieving electron ptychography with both high resolution and high precision. This is a demanding and challenging task due to the sheer number of parameters that need to be optimized. For…
This paper considers the problem of decentralized optimization on compact submanifolds, where a finite sum of smooth (possibly non-convex) local functions is minimized by $n$ agents forming an undirected and connected graph. However, the…
In this paper, we propose a uniformly dithered 1-bit quantization scheme for high-dimensional statistical estimation. The scheme contains truncation, dithering, and quantization as typical steps. As canonical examples, the quantization…
Stochastic gradient descent (SGD) is the main algorithm behind a large body of work in machine learning. In many cases, constraints are enforced via projections, leading to projected stochastic gradient algorithms. In recent years, a large…
Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection…
Parameterized mathematical models play a central role in understanding and design of complex information systems. However, they often cannot take into account the intricate interactions innate to such systems. On the contrary, purely…
Compressed Sensing (CS) is a novel technique for simultaneous signal sampling and compression based on the existence of a sparse representation of signal and a projected dictionary $PD$, where $P\in\mathbb{R}^{m\times d}$ is the projection…
We introduce two quantum algorithms for solving structured prediction problems. We first show that a stochastic gradient descent that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the…
Compressive phase retrieval is a popular variant of the standard compressive sensing problem in which the measurements only contain magnitude information. In this paper, motivated by recent advances in deep generative models, we provide…
While it is well known that the restricted isometry property (RIP) guarantees uniform sparse recovery from noisy linear measurements, uniform recovery of structured signals from nonlinear observations remains much less understood. This…
Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…
Gaussian Process Regression (GPR) is a nonparametric supervised learning method, widely valued for its ability to quantify uncertainty. Despite its advantages and broad applications, classical GPR implementations face significant…
We present a technique for performing quantum detector tomography (QDT) of phase insensitive quantum detectors, a category under which many detectors of interest fall under, using gradient descent-based optimization to learn the positive…
We consider the general problem of recovering a high-dimensional signal from noisy quantized measurements. Quantization, especially coarse quantization such as 1-bit sign measurements, leads to severe information loss and thus a good prior…
We study high-probability (HP) convergence guarantees in decentralized stochastic optimization, where multiple agents collaborate to jointly train a model over a network. Existing HP results in decentralized settings almost exclusively…