Related papers: An Overview of Robust Subspace Recovery

Recoverable robust optimization is a multi-stage approach, where it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed. We analyze this approach for a class of selection problems. The aim is to choose…

This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…

This work analyzes the subspace-constrained Tyler's estimator (STE), a method designed to recover a low-dimensional subspace from a dataset that may be heavily corrupted by outliers. The STE has previously been shown to be competitive for…

Given pointwise samples of an unknown function belonging to a certain model set, one seeks in Optimal Recovery to recover this function in a way that minimizes the worst-case error of the recovery procedure. While it is often known that…

Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called…

Robust low-rank approximation under row-wise adversarial corruption can be achieved with a single pass, randomized procedure that detects and removes outlier rows by thresholding their projected norms. We propose a scalable, non-iterative…

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…

Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…

Learning in the presence of outliers is a fundamental problem in statistics. Until recently, all known efficient unsupervised learning algorithms were very sensitive to outliers in high dimensions. In particular, even for the task of robust…

This work studies the problem of sequentially recovering a sparse vector $x_t$ and a vector from a low-dimensional subspace $l_t$ from knowledge of their sum $m_t = x_t + l_t$. If the primary goal is to recover the low-dimensional subspace…

We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…

In many linear inverse problems, we want to estimate an unknown vector belonging to a high-dimensional (or infinite-dimensional) space from few linear measurements. To overcome the ill-posed nature of such problems, we use a low-dimension…

In this paper, we study the problem of matrix recovery, which aims to restore a target matrix of authentic samples from grossly corrupted observations. Most of the existing methods, such as the well-known Robust Principal Component Analysis…

Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…

This paper deals with robust regression and subspace estimation and more precisely with the problem of minimizing a saturated loss function. In particular, we focus on computational complexity issues and show that an exact algorithm with…

We consider the case in which a robot has to navigate in an unknown environment but does not have enough on-board power or payload to carry a traditional depth sensor (e.g., a 3D lidar) and thus can only acquire a few (point-wise) depth…

Subspace clustering is to find underlying low-dimensional subspaces and cluster the data points correctly. In this paper, we propose a novel multi-view subspace clustering method. Most existing methods suffer from two critical issues.…

Spatial perception is the backbone of many robotics applications, and spans a broad range of research problems, including localization and mapping, point cloud alignment, and relative pose estimation from camera images. Robust spatial…

We derive a convex optimization problem for the task of segmenting sequential data, which explicitly treats presence of outliers. We describe two algorithms for solving this problem, one exact and one a top-down novel approach, and we…

In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…