New outlier detection method using graph Laplacian spectrum boosts performance.
problem Detecting outliers in large datasets efficiently.
method Boosted outlier detection based on graph Laplacian spectrum.
result Outperforms existing methods on synthetic datasets.
New algorithm rGMCA robustly separates sources in the presence of outliers.
problem Blind Source Separation is hampered by unknown outliers in real-world applications.
method Introduces rGMCA, a novel algorithm that estimates sources, mixing matrix, and outliers.
result Demonstrates the efficiency of rGMCA in separating sources robustly compared to standard BSS techniques.
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.
Paper improves RLS for sparse outlier detection in linear models.
problem Outliers contaminate linear regression models infrequently.
method Hierarchical-optimization recursive least squares with sparsity-inducing regularization.
result The method robustly estimates linear filters/systems with outliers.
New robust PCA algorithm for matrices with both sparse and outlying elements.
problem Simultaneous sparse and outlying corruption in matrices.
method Sparse approximation of a sparsely corrupted column to distinguish inliers from outliers.
result Robust PCA algorithm can handle both sparse and outlying corruptions.
Robust method learns nonlinear structures robustly to noise.
problem Learning nonlinear structures in noisy data.
method Robust Non-Linear Matrix Factorization (RNLMF).
result RNLMF achieves noticeable improvements in denoising and clustering.
New method detects outliers in data with subspaces using sparse representation and random walks.
problem Detecting outliers in data contaminated by subspaces.
method Combines sparse representation with random walks on a graph.
result Correct outlier detection with theoretical guarantees.
Paper explores robustness of CCS model for matrix completion.
problem Robustness of cross-concentrated sampling model against sparse outliers.
method Proposes Robust CUR Completion (RCURC) algorithm for efficient non-convex iterative matrix completion.
result Empirical validation of RCURC's efficiency and robustness in synthetic and real datasets.
RieCUR improves Robust PCA by combining Riemannian optimization and CUR decompositions.
problem Robust Principal Component Analysis (PCA) to recover low-rank and sparse matrices from their sum.
method Riemannian CUR (RieCUR) algorithm that combines Riemannian optimization and robust CUR decompositions.
result RieCUR achieves state-of-the-art performance in Robust PCA with improved robustness to outliers and comparable computational complexity.
Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix (outliers), and the goal is to recover these individual components from the observed sum. Such additive decompositions have applications in a variety of numerical problems including system identification, latent var…
Graphical Lasso detects anomalies in noisy data by splitting covariance matrix into clean and outlier parts.
problem Detecting anomalies in large, noisy data sets.
method Robust Graphical Lasso (Rglasso) using ADMM optimization.
result Rglasso outperforms standard robust methods in accuracy and speed.
HSNLD solves robust Hankel recovery efficiently and robustly.
problem Robust Hankel recovery of sparse outliers and missing entries.
method Hankel Structured Newton-Like Descent (HSNLD) algorithm.
result HSNLD achieves linear convergence independent of the condition number.
Review of robust PCA and matrix completion methods.
problem Robust Principal Component Analysis and matrix completion with outliers.
method Various provably correct, fast, and practical solutions to RPCA and matrix completion.
result Exhaustive review of recent literature on RPCA and dynamic RPCA.
New Bethe-Hessian method improves community detection in sparse networks.
problem Detect communities in sparse networks efficiently.
method Spectral clustering using the Bethe-Hessian matrix.
result Bethe-Hessian consistently estimates block number above Kesten-Stigum threshold.
Novel algorithm recovers sparse parameters in high-dimensional data with constant corruption.
problem Sparse regression with high dimensionality and constant fraction of corruptions.
method Robust Iterative Hard Thresholding, filtering algorithm for outlier removal.
result Near information-theoretically optimal error guarantee with sub-linear sample complexity.
Paper improves robust PCA for noisy, outlier, and missing data.
problem Robust PCA with noise, outliers, and missing data.
method Bridging convex and nonconvex optimization.
result Near-optimal statistical accuracy for robust PCA.
Many applications in data analysis rely on the decomposition of a data matrix into a low-rank and a sparse component. Existing methods that tackle this task use the nuclear norm and L1-cost functions as convex relaxations of the rank constraint and the sparsity measure, respectively, or employ thresholding techniques. …
This paper covers robust subspace learning and tracking methods.
problem Learning and tracking subspaces in the presence of outliers.
method Robust PCA, Robust Subspace Tracking, Robust Subspace Recovery.
result Effective methods for handling outliers in subspace learning and tracking.
New method clusters matrix-variate data with outliers.
problem Clustering matrix-variate data with outliers.
method Iterative approach using subset log-likelihoods.
result Extends OCLUST algorithm to matrix-variate normal data.
Noise statistics oblivious algorithm improves robust regression with sparse outliers.
problem Robust regression with sparse outliers in the presence of Gaussian noise.
method Developed a noise statistics oblivious algorithm called RRT-GARD by modifying GARD.
result RRT-GARD performs nearly as well as GARD with known noise statistics.
New algorithm reduces runtime for robust sparse mean estimation.
problem Efficiently estimating mean from corrupted data with sparse constraints.
method Subquadratic time algorithm using poly(k, log d, 1/ε) samples.
result First subquadratic time algorithm for robust sparse mean estimation.
Study improves robustness and sparsity in linear regression with adversarial outliers and heavy-tailed noise.
problem Outliers and heavy-tailed noise in linear regression coefficients.
method Sharp concentration inequalities and generic chaining.
result Sharper error bounds under weaker assumptions.
HARFE approximates sparse additive functions using random features and ridge regression.
problem Approximating high-dimensional sparse additive functions.
method Hard-ridge random feature expansion with sparse ridge regression and hard-thresholding pursuit.
result HARFE method converges with a given error bound and achieves lower error than other algorithms.
Proposes a new pseudo-Bayesian algorithm for robust PCA.
problem Improves robust PCA's sensitivity to outliers.
method Integrates pseudo-Bayesian approach into non-convex alternatives.
result Achieves state-of-the-art performance with theoretical support.
Develops efficient estimators for PCA and sparse regression in the presence of oblivious outliers.
problem Estimation of PCA and sparse regression in the presence of a small fraction of corrupted data.
method Designs efficient estimators using Huber loss with non-smooth regularizers like the ℓ1 norm or nuclear norm.
result Achieves consistent estimation error approaching zero as the number of observations grows.
A new method for outlier identification in Robust PCA without requiring parameter knowledge.
problem Outlier identification in Robust PCA when parameters are unknown.
method A parameter-free method for column sparse outliers in Robust PCA.
result Analytical guarantees and performance comparison with existing methods.
New method for robustly recovering sparse signals from noisy data.
problem Recovering sparse signals from corrupted measurements with outliers.
method Sparse Bayesian learning with binary indicator hyperparameters and hierarchical priors.
result The method achieves better performance than existing techniques.
Efficiently estimates sparse linear regression with heavy-tailed and outlier-contaminated data.
problem Estimating sparse linear regression coefficients with heavy-tailed and outlier-contaminated data.
method Efficient computation of estimators with sharp error bounds.
result Sharp error bounds for efficient estimators.
Robustly estimates sparse data with corrupted outliers.
problem Adversarial corruption in high-dimensional sparse data.
method Iterative filtering using spectral techniques.
result Achieves near-optimal robustness guarantees.
Efficiently estimates sparse linear regression with heavy-tailed data and outliers.
problem Sparse estimation of linear regression coefficients with heavy-tailed covariates and noises, including outliers.
method Efficient computation of robust estimator with nearly optimal error bound.
result Nearly optimal error bound for robust sparse estimation.
Paper tackles outlier detection in signals modeled by generative models with theoretical guarantees.
problem Recovering signals from linear measurements with sparse outliers.
method Proposes an iterative ADMM algorithm and gradient descent algorithm for outlier detection using ℓ1 and squared ℓ1 norm minimization. result Establishes theoretical recovery guarantees for signal reconstruction under sparse outliers.
New methods solve sparse estimation robustly, even with outliers.
problem Sparse estimation in high-dimensional data with outliers.
method Non-convex optimization formulations for robust sparse mean estimation and PCA.
result Any approximate stationary point yields near-optimal solutions.
The paper shows how to find a sparse representation of signals without strict coherence assumptions.
problem Finding a sparse representation of signals without strict coherence assumptions.
method An algorithm for the threshold correlation problem, which applies to signals with outliers.
result Approximate guarantees for dictionary learning without strict coherence assumptions.
Robust methods for high-dimensional linear learning improve performance under heavy-tailed distributions and outliers.
problem Efficient learning in high-dimensional settings with robustness to outliers and heavy-tailed data.
method Two algorithms depending on gradient-Lipschitz loss function, applied to sparse, group-sparse, and low-rank matrix recovery.
result Achieved near-optimal estimation rates under heavy-tails and outliers, with computational cost comparable to non-robust methods.
New PCA method handles multiple datasets and detects sparse patterns robustly.
problem Handling multi-source data with sparse and outlier-robust PCA.
method Developed a regularization problem with a penalty for structured sparsity and outlier resistance.
result The method detects global and local patterns across multiple data sources robustly.
Sparse R-LSSVM improves robustness and sparsity of LSSVM.
problem Robustness and sparsity issues in LSSVM.
method Interpreting robustness as a re-weighted problem, proposing a sparse R-LSSVM algorithm using low-rank approximation and entropy penalty.
result Proposed SR-LSSVM achieves sparse solutions efficiently for large-scale problems.
Paper proposes a matrix optimization model for reliable Euclidean embedding from noisy data.
problem Challenges in Euclidean embedding from noisy observations containing outliers.
method Matrix optimization based embedding model to detect and remove outliers.
result The model provides high accuracy estimators and successfully identifies outliers.
Paper proposes a generative model approach for outlier detection in signals.
problem Recovering signals from compressed measurements with sparse outliers.
method Iterative ADMM and gradient descent algorithms for ℓ1 and squared ℓ1 norm minimization. result Established recovery guarantees for generative models in the presence of outliers.
Using a Bayesian approach, we consider the problem of recovering sparse signals under additive sparse and dense noise. Typically, sparse noise models outliers, impulse bursts or data loss. To handle sparse noise, existing methods simultaneously estimate the sparse signal of interest and the sparse noise of no interest.…
A matrix factorization method detects text outliers using low rank approximations.
problem Challenges in detecting outliers in text data with mostly zero values.
method TONMF based on block coordinate descent (BCD) framework.
result Effective in distinguishing anomalies from natural variations in text data.
Paper tracks communities and anomalies in dynamic networks.
problem Tracking communities and detecting anomalies in evolving network structures.
method Dynamic factor model with sparse outlier matrix for anomaly detection.
result Efficient algorithms for online and decentralized tracking of communities and anomalies.
New method for sparse data using L1-NMF with improved sparsity control.
problem Sparse data with false zeros and heavy-tailed noise.
method Component-wise L1-NMF with weighted penalization and coordinate descent.
result Effective in handling sparse data with false zeros.
TF-OMP and TF-GARD improve sparse signal recovery without SC or noise variance knowledge.
problem Recovering sparse signals in noisy linear regression models without prior knowledge of signal sparsity or noise variance.
method Developed TF-OMP and TF-GARD, which do not require SC or noise variance knowledge.
result TF-OMP and TF-GARD achieve successful sparse recovery under RIC and mutual coherence assumptions, with competitive performance compared to algorithms requiring SC or noise variance knowledge.
RFPCA improves robustness of FPCA for matrix data.
problem Outliers in matrix data degrade the performance of FPCA.
method RFPCA uses matrix-variate t-distribution and EM algorithm for robust estimation.
result RFPCA outperforms other methods in detecting matrix-valued outliers.
Proposes a robust elastic net model for high-dimensional data.
problem High-dimensional sparse regression with outliers.
method Robust Elastic Net (REN) model with trimmed inner product.
result Performance guarantees for statistical and optimization errors.
We solve robust regression and matrix completion problems with sparse and low-rank models.
problem Adversarial contamination and noisy matrix completion in high-dimensional settings.
method Subgaussian statistical learning framework, trace-regression with matrix decomposition, novel Huber-type loss.
result Near-optimal estimation rates for robust regression and matrix completion.
A new method preserves useful information in data rows with outlying cells.
problem Preserving useful information in data rows with outlying cells.
method Cellwise robust Minimum Covariance Determinant (cellMCD) method using observed likelihood and a penalty term on cellwise outliers.
result The cellMCD method performs well in simulations and on real data.
Paper recovers multi-subspace matrices from permuted data.
problem Recovering a multi-subspace matrix from permuted data with corrupted columns.
method Four-stage algorithm pipeline: outlier identification, subspace reconstruction, outlier classification, unsupervised sensing.
result The pipeline provides theoretical guarantees for reliable multi-subspace matrix recovery.