arXiv research

Sign-RIP improves robust low-rank matrix recovery by preserving norms even with corrupted measurements.

HSNLD solves robust Hankel recovery efficiently and robustly.

Study robust recovery of low-rank matrices from corrupted measurements without rank prior.

Efficient algorithm for robust recovery in stochastic block models.

This paper will serve as an introduction to the body of work on robust subspace recovery. Robust subspace recovery involves finding an underlying low-dimensional subspace in a dataset that is possibly corrupted with outliers. While this problem is easy to state, it has been difficult to develop optimal algorithms due t…

Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study the problem of robust low-rank tensor recovery in a convex optimization framework,…

This paper investigates the problem of sparse signal recovery in the presence of additive impulsive noise. The heavytailed impulsive noise is well modelled with stable distributions. Since there is no explicit formulation for the probability density function of $SαS$ distribution, alternative approximations like Genera…

Deep RL trains a robust humanoid push-recovery policy.

Develops PRPCA for smooth image recovery combining low-rank and smoothness.

In this paper we introduce a new optimization formulation for sparse regression and compressed sensing, called CLOT (Combined L-One and Two), wherein the regularizer is a convex combination of the $\ell_1$- and $\ell_2$-norms. This formulation differs from the Elastic Net (EN) formulation, in which the regularizer is a…

WPCA improves subspace recovery robustness to outliers.

Paper proves IRLS converges to subspace from any start, with practical benefits.

New method improves traffic data recovery for streaming data.

Paper proposes a new method for exact recovery in robust tensor principal component analysis.

This paper considers the problem of robust subspace recovery: given a set of $N$ points in $\mathbb{R}^D$, if many lie in a $d$-dimensional subspace, then can we recover the underlying subspace? We show that Tyler's M-estimator can be used to recover the underlying subspace, if the percentage of the inliers is larger t…

Study iterative regularization for linear models with convex bias, improving robust sparse recovery.

Gradient descent recovers low-rank matrices from corrupted measurements with double over-parameterization.

New method robust to semi-random sparse recovery, nearly-linear time.

Paper develops efficient AltMin algorithm for SRPCP robust matrix recovery.

Theoretical guarantees for STE, a robust subspace recovery method.

Low-degree method fails to predict robust subspace recovery problem.

Jointly learns feature and sample relevancies for robust sparse recovery.

We consider the problem of signal recovery on graphs as graphs model data with complex structure as signals on a graph. Graph signal recovery implies recovery of one or multiple smooth graph signals from noisy, corrupted, or incomplete measurements. We propose a graph signal model and formulate signal recovery as a cor…

Study improves model robustness in noisy datasets.

Compressed sensing (CS) is an important theory for sub-Nyquist sampling and recovery of compressible data. Recently, it has been extended by Pham and Venkatesh to cope with the case where corruption to the CS data is modeled as impulsive noise. The new formulation, termed as robust CS, combines robust statistics and CS…

Study optimal portfolio selection with Recovery Average Value at Risk, showing better control over liabilities.

Paper offers robust recovery for 1-bit sensing with partial Gaussian circulant matrices.

We study the problem of robust subspace recovery (RSR) in the presence of adversarial outliers. That is, we seek a subspace that contains a large portion of a dataset when some fraction of the data points are arbitrarily corrupted. We first examine a theoretical estimator that is intractable to calculate and use it to …

Paper proposes robust compressed sensing using generative models.

In this paper, we generalize Huber's criterion to multichannel sparse recovery problem of complex-valued measurements where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known elementary vec…

C-kNN-LSH identifies similar patient histories for causal inference in longitudinal data.

Robust Lasso-Zero handles missing covariates and sparse corruptions.

Robust score matching improves parameter estimation in contaminated data.

We study the basic problem of robust subspace recovery. That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed underlying subspace. We first estimate "robust inverse sample covariance" by solvi…

Improved algorithm for partial recovery of tree-structured graphs with noisy data.

Paper proposes fast, robust methods for low-rank matrix recovery.

Develops a robust GMM estimator for outlier-tolerant inference.

Tyler's M-estimator's phase transition at DS-SNR = 1 is resolved.

PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The problem of subspace learning or PCA in the presence of outliers is called robust su…

Develops a two-stage approach for robust tensor completion of visual data.

Flat minima lead to better generalization in low-rank matrix recovery models.

This work provides a guaranteed tensor recovery method by combining low-rankness and smoothness priors.

Global convergence for robust regression problems via IRLS with enhancements.

In this paper, we consider the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is based on the recently proposed tensor-tensor product (or t-product). Induced by the t-product, we first rigorously deduce the tensor sp…

Paper analyzes adaptive Lasso for high-dimensional diffusion processes, improving support recovery and bias.

RTC-GTNLN model recovers traffic data from missing values and noise.

This paper explores robust recovery of a superposition of $R$ distinct complex exponential functions from a few random Gaussian projections. We assume that the signal of interest is of $2N-1$ dimensional and $R<<2N-1$. This framework covers a large class of signals arising from real applications in biology, automation,…

Robust methods for high-dimensional linear learning improve performance under heavy-tailed distributions and outliers.