We study a data model in which the data matrix D can be expressed as D = L + S + C, where L is a low rank matrix, S an element-wise sparse matrix and C a matrix whose non-zero columns are outlying data points. To date, robust PCA algorithms have solely considered models with either S or C, but not both. As such, existi…
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48 results for “sparse corruptions”
New methods tackle robust reinforcement learning in sparse, corrupted data.
problem Tackles robust reinforcement learning in sparse, corrupted data.
method Proposes actor-critic methods with sparse robust estimator oracles.
result First non-vacuous guarantees in high-dimensional sparse MDPs with single-policy concentrability coverage.
Robust Lasso-Zero handles missing covariates and sparse corruptions.
problem Sparse corruptions and missing covariates in sparse linear models.
method Extension of Lasso-Zero to handle sparse corruptions, with theoretical guarantees on sign recovery.
result Robust Lasso-Zero can handle missing values without specifying a parametric model.
This work presents a new robust PCA method for foreground-background separation on freely moving camera video with possible dense and sparse corruptions. Our proposed method registers the frames of the corrupted video and then encodes the varying perspective arising from camera motion as missing data in a global model.…
New algorithm robustly estimates sparse models in high dimensions with corrupted data.
problem Estimating latent variable models with arbitrarily corrupted samples in high dimensional space.
method Trimmed (Gradient) Expectation Maximization with trimming gradients and hard thresholding steps.
result The algorithm converges to near optimal statistical rate geometrically under certain conditions.
We study the problem of corrupted sensing, a generalization of compressed sensing in which one aims to recover a signal from a collection of corrupted or unreliable measurements. While an arbitrary signal cannot be recovered in the face of arbitrary corruption, tractable recovery is possible when both signal and corrup…
We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse parameters with sub-linear sample complexity, in the presence of a constant fractio…
Robust testing of sparse signals in corrupted data.
problem Testing the norm of high-dimensional sparse signals in the presence of arbitrary corruption.
method Two observation models: i.i.d. samples from and sparse linear regression model.
result The robust testing requires significantly more samples than non-robust testing.
Conventional sampling techniques fall short of drawing descriptive sketches of the data when the data is grossly corrupted as such corruptions break the low rank structure required for them to perform satisfactorily. In this paper, we present new sampling algorithms which can locate the informative columns in presence …
We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse PCA. We give the first practically viable robust estimators for these problems.…
We consider the robust phase retrieval problem of recovering the unknown signal from the magnitude-only measurements, where the measurements can be contaminated by both sparse arbitrary corruption and bounded random noise. We propose a new nonconvex algorithm for robust phase retrieval, namely Robust Wirtinger Flow to …
New method estimates sparse mean from noisy data without knowing sparsity level.
problem Sparse mean estimation under adversarial corruptions.
method Incremental learning approach to nonconvex optimization.
result Achieves optimal statistical rate under moderate signal-to-noise ratio.
This paper examines a general class of noisy matrix completion tasks where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is on settings where the matrix to be estimated is well-approximated by a product …
We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix . These may come from corrupted data, persistent experimental errors, or malicious respondents in surveys/recommender systems, etc. Such non-stochas…
New method improves deep learning models robustness to label noise.
problem Improving deep learning models' robustness to corrupted labels.
method Sparse over-parameterization and implicit regularization.
result State-of-the-art test accuracy against label noise on various datasets.
Efficiently recovers data corrupted by adversarial noise in structured settings.
problem Recovering clean data points from corrupted Gaussian data with low-rank noise and adversarial coordinate corruptions.
method Developed an efficient algorithm using a combinatorial approach to analyze Basis Pursuit (BP) method.
result Achieved nearly-optimal recovery of data points up to a error bound.
Paper tackles robust Euclidean distance estimation with sparse outliers.
problem Estimating point positions from corrupted distance measurements.
method Proposes a novel algorithm using Nyström method and robust PCA.
result Achieves accurate recovery with minimal anchors and sparse outliers.
New algorithm improves PPS for multi-object matching.
problem Efficiently synchronize partial permutations for multi-object matching.
method Proposed CEMP-Partial algorithm for partial permutation synchronization (PPS). Uses sparse matrix operations and nonconvex weighted projected power method.
result Proves CEMP-Partial can exactly classify corrupted and clean partial permutations under adversarial corruption.
We consider the problem of sparsity-constrained -estimation when both explanatory and response variables have heavy tails (bounded 4-th moments), or a fraction of arbitrary corruptions. We focus on the -sparse, high-dimensional regime where the number of variables and the sample size are related through $…
DSF improves EEG model robustness to missing channels and noise.
problem Robust learning from corrupted EEG data with missing channels.
method Dynamic Spatial Filtering (DSF) as a multi-head attention module.
result DSF achieves up to 29.4% accuracy improvement over baseline models in noisy conditions.
We improve existing results in the field of compressed sensing and matrix completion when sampled data may be grossly corrupted. We introduce three new theorems. 1) In compressed sensing, we show that if the m \times n sensing matrix has independent Gaussian entries, then one can recover a sparse signal x exactly by tr…
Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can be solved by the natural convex joint/mixed relaxations (i.e., l_{1}-norm and tr…
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 robust kernel principal component analysis (RKPCA) to decompose a partially cor…
New method tackles tensor regression with robust Kaczmarz approach.
problem Reconstructing tensor signals from corrupted measurements.
method Quantile-based randomized Kaczmarz method for tensor linear systems.
result Improved convergence and robustness to adversarial corruptions.
Robust Recovery via Implicit Bias of Discrepant Learning Rates for Double Over-parameterizationcs.LG
Gradient descent recovers low-rank matrices from corrupted measurements with double over-parameterization.
problem Robust recovery of low-rank matrices from grossly corrupted measurements.
method Gradient descent with discrepant learning rates for double over-parameterized models.
result Gradient descent with discrepant learning rates provably recovers the underlying matrix without prior knowledge on rank or sparsity.
This paper conducts a rigorous analysis for provable estimation of multidimensional arrays, in particular third-order tensors, from a random subset of its corrupted entries. Our study rests heavily on a recently proposed tensor algebraic framework in which we can obtain tensor singular value decomposition (t-SVD) that …
High-dimensional data often lie in low-dimensional subspaces corresponding to different classes they belong to. Finding sparse representations of data points in a dictionary built using the collection of data helps to uncover low-dimensional subspaces and address problems such as clustering, classification, subset sele…
New method for robust PCA with exponential family distributions.
problem Recovering low-rank structure from data matrices with outliers.
method Alternating Direction Method of Multipliers for .
result Demonstrated effectiveness in steel sheet defect detection and crime activity monitoring.
This work presents a novel approach for robust PCA with total variation regularization for foreground-background separation and denoising on noisy, moving camera video. Our proposed algorithm registers the raw (possibly corrupted) frames of a video and then jointly processes the registered frames to produce a decomposi…
New method decomposes corrupted data matrices into sparse and low-rank components.
problem Decomposing corrupted data matrices into sparse and low-rank components.
method Discrete optimization approach with alternating minimization, semidefinite relaxation, and branch-and-bound algorithm.
result High-quality solutions and meaningful bounds for SLR problems.
Class selectivity affects robustness to corruptions but not to adversarial attacks.
problem Understanding the relationship between class selectivity and robustness in neural networks.
method Investigated the impact of class selectivity on robustness to natural corruptions and adversarial attacks using Tiny ImageNetC and CIFAR10C datasets.
result Decreasing class selectivity increases robustness to both natural corruptions and adversarial attacks.
Study robust recovery of low-rank matrices from corrupted measurements without rank prior.
problem Robust recovery of low-rank matrices from corrupted Gaussian measurements with unknown rank.
method Subgradient method with diminishing stepsizes for nonconvex nonsmooth problem.
result Subgradient method converges to exact low-rank solution at sublinear rate under RDPP condition.
In presence of sparse noise we propose kernel regression for predicting output vectors which are smooth over a given graph. Sparse noise models the training outputs being corrupted either with missing samples or large perturbations. The presence of sparse noise is handled using appropriate use of -norm along-wi…
The performance of sparse signal recovery from noise corrupted, underdetermined measurements can be improved if both sparsity and correlation structure of signals are exploited. One typical correlation structure is the intra-block correlation in block sparse signals. To exploit this structure, a framework, called block…
We study the problem of robust linear regression with response variable corruptions. We consider the oblivious adversary model, where the adversary corrupts a fraction of the responses in complete ignorance of the data. We provide a nearly linear time estimator which consistently estimates the true regression vector, e…
New algorithms reduce communication for sparse mean estimation in noisy distributed systems.
problem Sparse normal means estimation with limited communication in a distributed setting.
method Two distributed algorithms for estimating a sparse mean vector with sublinear communication.
result Correct support of the sparse mean can be recovered with significantly less communication than previously required.
Robust GP model detects and corrects sparse outliers.
problem Non-Gaussian noise in real-world data.
method Relevance pursuit for data-point-specific noise levels.
result Strong concavity and approximation guarantees for subset selection.
Blind source separation (BSS) aims at recovering signals from mixtures. This problem has been extensively studied in cases where the mixtures are contaminated with additive Gaussian noise. However, it is not well suited to describe data that are corrupted with Poisson measurements such as in low photon count optics or …
Proposes a method to handle sparse multiway count data with false zeros using zero-truncated Poisson regression.
problem Handling sparse multiway count data corrupted by false zeros.
method Zero-truncated Poisson regression with tensor completion.
result Accurate estimation of multiway count data from approximately non-zero counts.
Sparse linear regression with compressed and low-precision data via concave quadratic programmingmath.OC
We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different -sparse solutions may be present in the feasible set, and the classical l1 approach may be unsuccessfu…
New algorithm learns PTFs with noisy data efficiently.
problem Learning low-degree PTFs with noisy data efficiently.
method Structural result and novel robust Chow vector estimation.
result PAC learns PTFs with nasty noise using efficient samples.
New analysis enables inversion of deep generative models with unique solutions.
problem Inverting deep generative models like GANs and VAEs.
method Sparse representation theory and layer-wise inversion pursuit algorithms.
result Invertible solutions for generative models with unique latent vectors.
This paper solves tensor robust principal component analysis via scaled gradient descent.
problem Extracting useful information from tensor data robust to corruptions and ill-conditioning.
method Directly recovers low-rank tensor factors via scaled gradient descent with adaptive thresholding.
result The proposed algorithm converges linearly to the true low-rank tensor at a constant rate independent of the condition number.
Robust estimators for Gaussian sparse tasks with optimal error under contamination.
problem Robust mean estimation, PCA, and linear regression in the presence of Huber contamination.
method Novel multidimensional filtering method for sparse regime.
result Optimal error guarantees within constant factors for Gaussian robust -sparse mean estimation.
Koopman Regularizationmath.DS
Koopman Regularization learns governing equations from sparse data.
problem Learning governing equations from sparse and corrupted data.
method Constrained optimization using Koopman Eigenfunctions.
result Restores dynamics precisely with minimal assumptions.
A simple self-supervised model for tensor RPCA using deep unfolding.
problem Tensor robust principal component analysis (RPCA) challenges in practical applications.
method Deep unfolding with only four hyperparameters.
result Competitive or superior performance compared to supervised methods, even in data-starved scenarios.
We consider the problem of robust compressed sensing whose objective is to recover a high-dimensional sparse signal from compressed measurements corrupted by outliers. A new sparse Bayesian learning method is developed for robust compressed sensing. The basic idea of the proposed method is to identify and remove the ou…
The paper analyzes how adversarial attacks affect sparse regression models.
problem Effects of adversarial attacks on sparse regression models.
method Primal-dual witness paradigm to analyze support of estimated regression parameter vector.
result Adversaries can influence sample complexity by corrupting irrelevant features.