Related papers: A Combinatorial Approach to Robust PCA

This work studies the recursive robust principal components' analysis (PCA) problem. Here, "robust" refers to robustness to both independent and correlated sparse outliers, although we focus on the latter. A key application where this…

Second-order information -- such as curvature or data covariance -- is critical for optimisation, diagnostics, and robustness. However, in many modern settings, only the gradients are observable. We show that the gradients alone can reveal…

In this paper we present a linear programming solution for sign pattern recovery of a sparse signal from noisy random projections of the signal. We consider two types of noise models, input noise, where noise enters before the random…

We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle…

We give a polynomial-time algorithm for the problem of robustly estimating a mixture of $k$ arbitrary Gaussians in $\mathbb{R}^d$, for any fixed $k$, in the presence of a constant fraction of arbitrary corruptions. This resolves the main…

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…

Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…

Deep neural networks achieve high prediction accuracy when the train and test distributions coincide. In practice though, various types of corruptions occur which deviate from this setup and cause severe performance degradations. Few…

Recovery from linear measurements under sparse adversarial corruption is typically formulated as an exact-recovery problem: one seeks structural conditions on $A$ (e.g., the restricted isometry property) that guarantee unique recovery of…

Recovering linear subspaces from data is a fundamental and important task in statistics and machine learning. Motivated by heterogeneity in Federated Learning settings, we study a basic formulation of this problem: the principal component…

We develop two methods for the following fundamental statistical task: given an $\epsilon$-corrupted set of $n$ samples from a $d$-dimensional sub-Gaussian distribution, return an approximate top eigenvector of the covariance matrix. Our…

The problem of Non-Gaussian Component Analysis (NGCA) is about finding a maximal low-dimensional subspace $E$ in $\mathbb{R}^n$ so that data points projected onto $E$ follow a non-gaussian distribution. Although this is an appropriate model…

Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…

Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called…

We consider the high-dimensional inference problem where the signal is a low-rank symmetric matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large…

Recovering a low-rank matrix from highly corrupted measurements arises in compressed sensing of structured high-dimensional signals (e.g., videos and hyperspectral images among others). Robust principal component analysis (RPCA), solved via…

We consider the problem of estimating a rank-one matrix in Gaussian noise under a probabilistic model for the left and right factors of the matrix. The probabilistic model can impose constraints on the factors including sparsity and…

This work studies the recursive robust principal components analysis (PCA) problem. If the outlier is the signal-of-interest, this problem can be interpreted as one of recursively recovering a time sequence of sparse vectors, $S_t$, in the…

The problem of recovering a low-rank matrix from a set of observations corrupted with gross sparse error is known as the robust principal component analysis (RPCA) and has many applications in computer vision, image processing and web data…

We develop theoretically guaranteed stochastic methods for outlier-robust PCA. Outlier-robust PCA seeks an underlying low-dimensional linear subspace from a dataset that is corrupted with outliers. We are able to show that our methods,…