In this paper, we study phase retrieval of spectrally sparse signal which is about reconstructing a spectrally sparse signal from a number of magnitude measurements. This is a problem that arises from the limited-feedback downlink channel state information estimation in the frequency division duplex (FDD) wireless system. Two non-convex gradient descent with alternating projection methods are proposed for this problem by exploiting the low-rank Hankel structure hidden in spectrally sparse signals. Numerical experiments have been conducted to verify the effectiveness of the methods under different initialization conditions.

In this work, we investigate the problem of simultaneous blind demixing and super-resolution. Leveraging the subspace assumption regarding unknown point spread functions, this problem can be reformulated as a low-rank matrix demixing problem. We propose a convex recovery approach that utilizes the low-rank structure of each vectorized Hankel matrix associated with the target matrix. Our analysis reveals that for achieving exact recovery, the number of samples needs to satisfy the condition n Ksr log (sn). Empirical evaluations demonstrate the recovery capabilities and the computational efficiency of the convex method.

This paper studies a policy optimization problem arising from collaborative multi-agent reinforcement learning in a decentralized setting where agents communicate with their neighbors over an undirected graph to maximize the sum of their cumulative rewards. A novel decentralized natural policy gradient method, dubbed Momentum-based Decentralized Natural Policy Gradient (MDNPG), is proposed, which incorporates natural gradient, momentum-based variance reduction, and gradient tracking into the decentralized stochastic gradient ascent framework. The $\mathcal{O}(n^{-1}\epsilon^{-3})$ sample complexity for MDNPG to converge to an $\epsilon$-stationary point has been established under standard assumptions, where $n$ is the number of agents. It indicates that MDNPG can achieve the optimal convergence rate for decentralized policy gradient methods and possesses a linear speedup in contrast to centralized optimization methods. Moreover, superior empirical performance of MDNPG over other state-of-the-art algorithms has been demonstrated by extensive numerical experiments.

This paper is concerned with the low Tucker-rank tensor completion problem, which is about reconstructing a tensor $\mathcal{T}\in\mathbb{R}^{n\times n\times n}$ of low multilinear rank from partially observed entries. Riemannian optimization algorithms are a class of efficient methods for this problem, but the theoretical convergence analysis is still lacking. In this manuscript, we establish the entrywise convergence of the vanilla Riemannian gradient method for low Tucker-rank tensor completion under the nearly optimal sampling complexity $O(n^{3/2})$. Meanwhile, the implicit regularization phenomenon of the algorithm has also been revealed. As far as we know, this is the first work that has shown the entrywise convergence and implicit regularization property of a non-convex method for low Tucker-rank tensor completion. The analysis relies on the leave-one-out technique, and some of the technical results developed in the paper might be of broader interest in investigating the properties of other non-convex methods for this problem.

Blind super-resolution can be cast as a low rank matrix recovery problem by exploiting the inherent simplicity of the signal. In this paper, we develop a simple yet efficient non-convex method for this problem based on the low rank structure of the vectorized Hankel matrix associated with the target matrix. Theoretical guarantees have been established under the similar conditions as convex approaches. Numerical experiments are also conducted to demonstrate its performance.

We consider the problem of resolving$r$point sources from$n$samples at the low end of the spectrum when point spread functions (PSFs) are not known. Assuming that the spectrum samples of the PSFs lie in low dimensional subspace (let$s$denote the dimension), we can formulate it as a matrix recovery problem, followed by location estimation. By exploiting the low rank structure of the vectorized Hankel matrix associated with the target matrix, a convex approach called Vectorized Hankel Lift is proposed for the matrix recovery. It is shown that$n\gtrsim rs\log ^{4} n$samples are sufficient for Vectorized Hankel Lift to achieve the exact recovery. For the location retrieval from the matrix, applying the single snapshot MUSIC method within the vectorized Hankel lift framework corresponds to the spatial smoothing technique proposed to improve the performance of the MMV MUSIC for the direction-of-arrival (DOA) estimation.

Context-Aware Systems (a.k.a. CASs) integrate cyber and physical space to provide context-aware adaptive functionalities. Building context-aware systems is challenging due to the uncertainty of the real physical environment. Therefore, input validation for context-aware systems plays a significant role in keeping the systems executing safely. Input validation approaches have been proposed to monitor and guard the executions of context-aware systems. However, few of these works (17%, 2 out of 12) evaluated their approaches with a real context-aware system in a real physical environment. In this paper, we study and compare the effectiveness of input validation approaches for context-aware system in both a simulated and a physical environment. We built a testing platform, RM-Testing, based on DJI RoboMaster S1 robot car. We implemented three up-to-date input validation approaches, and evaluated their effectiveness in improving the success rate of the robot car’s executions. The results show that the selected input validation approaches are effective in guarantee the safe execution of context-aware systems, which improve the success rate by 82% in the simulated environment, and 50% in the physical environment. However, the effectiveness of these approaches does vary in different environment. Thus, we believe that such CASs-based input validation works should be evaluated in the physical environment to better validate their effectiveness and usefulness.

Reusing published datasets on the Web is of great interest to researchers and developers. Their data needs may be met by submitting queries to a dataset search engine to retrieve relevant datasets. In this ongoing work towards developing a more usable dataset search engine, we characterize real data needs by annotating the semantics of 1,947 queries using a novel fine-grained scheme, to provide implications for enhancing dataset search. Based on the findings, we present a query-centered framework for dataset search, and explore the implementation of snippet generation and evaluate it with a preliminary user study.

This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of prior knowledge are available. In each case, we provide conditions (in terms of the number of measurements) for stable signal recovery from structured corruption with added unstructured noise. Our results theoretically demonstrate how to choose the regularization parameters in both partially and fully penalized recovery procedures and shed some light on the relationships among the three procedures. The key ingredient in our analysis is an extended matrix deviation inequality for isotropic sub-Gaussian matrices, which implies a tight lower bound for the restricted singular value of the extended sensing matrix. Numerical experiments are presented to verify our theoretical results.

In this letter, we characterize a data-time tradeoff for projected gradient descent (PGD) algorithms used for solving corrupted sensing problems under sub-Gaussian measurements. We also show that with a proper step size, the PGD method can achieve a linear rate of convergence when the number of measurements is sufficiently large.

This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of prior knowledge are available. In each case, we provide conditions for stable signal recovery from structured corruption with added unstructured noise. The key ingredient in our analysis is an extended matrix deviation inequality for isotropic sub-Gaussian matrices.