相关论文: Radio Interferometric Calibration Using a Riemanni…

We study smooth stochastic optimization problems on Riemannian manifolds. Via adapting the recently proposed SPIDER algorithm \citep{fang2018spider} (a variance reduced stochastic method) to Riemannian manifold, we can achieve faster rate…

We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two…

With the next generation of interferometric telescopes, such as the Square Kilometre Array (SKA), the need for highly computationally efficient reconstruction techniques is particularly acute. The challenge in designing learned, data-driven…

For optimization problems on Riemannian manifolds, many types of globally convergent algorithms have been proposed, and they are often equipped with the Riemannian version of the Armijo line search for global convergence. Such existing…

The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…

Precise sensor calibration is critical for autonomous vehicles as a prerequisite for perception algorithms to function properly. Rotation error of one degree can translate to position error of meters in target object detection at large…

We present an augmented Lagrangian trust-region method to efficiently solve constrained optimization problems governed by large-scale nonlinear systems with application to partial differential equation-constrained optimization. At each…

We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the…

It is often of interest to infer lower-dimensional structure underlying complex data. As a flexible class of non-linear structures, it is common to focus on Riemannian manifolds. Most existing manifold learning algorithms replace the…

Calibration is commonly evaluated by comparing model confidence with its empirical correctness, implicitly treating reliability as a function of the confidence score alone. However, this view can hide substantial structure: models may be…

We propose a Riemannian optimization approach for computing low-rank solutions of the algebraic Riccati equation. The scheme alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is on the set of…

Many astronomical questions require deep, wide-field observations at low radio frequencies. Phased arrays like LOFAR and SKA-low are designed for this, but have inherently unstable element gains, leading to time, frequency and…

Depth cameras, typically in RGB-D configurations, are common devices in mobile robotic platforms given their appealing features: high frequency and resolution, low price and power requirements, among others. These sensors may come with…

In this paper, we introduce the notion of generalized $\epsilon$-stationarity for a class of nonconvex and nonsmooth composite minimization problems on compact Riemannian submanifold embedded in Euclidean space. To find a generalized…

Consensus algorithms are popular distributed algorithms for computing aggregate quantities, such as averages, in ad-hoc wireless networks. However, existing algorithms mostly address the case where the measurements lie in a Euclidean space.…

Interpolation of data represented in curvilinear coordinates and possibly having some non-trivial, typically Riemannian or semi-Riemannian geometry is an ubiquitous task in all of physics. In this work we present a covariant generalization…

The spatial-frequency coverage of a radio interferometer is increased by combining samples acquired at different times and observing frequencies. However, astrophysical sources often contain complicated spatial structure that varies within…

Context: Radio interferometers measure frequency components of the sky brightness, modulated by the gains of the individual radio antennas. Due to atmospheric turbulence and variations in the operational conditions of the antennas these…

Low-rank optimization problems with sparse simplex constraints involve variables that must satisfy nonnegativity, sparsity, and sum-to-1 conditions, making their optimization particularly challenging due to the interplay between low-rank…

We introduce a Riemannian optimistic online learning algorithm for Hadamard manifolds based on inexact implicit updates. Unlike prior work, our method can handle in-manifold constraints, and matches the best known regret bounds in the…