A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Unified framework improves PCA for outliers and distributed data.
We develop efficient algorithms for robust PCA that handle outliers.
PCA++ improves robustness to background noise in contrastive learning.
Principal Component Analysis (PCA) has wide applications in machine learning, text mining and computer vision. Classical PCA based on a Gaussian noise model is fragile to noise of large magnitude. Laplace noise assumption based PCA methods cannot deal with dense noise effectively. In this paper, we propose Cauchy Princ…
Robust PCA has drawn significant attention in the last decade due to its success in numerous application domains, ranging from bio-informatics, statistics, and machine learning to image and video processing in computer vision. Robust PCA and its variants such as sparse PCA and stable PCA can be formulated as optimizati…
A new robust PCA estimator combining M-estimators and minimum divergence estimators.
RieCUR improves Robust PCA by combining Riemannian optimization and CUR decompositions.
Anchor PCA improves robustness in multi-domain PCA.
Proposes AE for robust PCA, improving robustness to outliers.
New algorithm solves fair PCA, robust PCA, and sparse PCA problems efficiently.
It is well known that Principal Component Analysis (PCA) is strongly affected by outliers and a lot of effort has been put into robustification of PCA. In this paper we present a new algorithm for robust PCA minimizing the trimmed reconstruction error. By directly minimizing over the Stiefel manifold, we avoid deflatio…
Proposes MPCA for robust PCA using mode estimation.
Unified PCA framework on flag manifolds for robust data analysis.
Robust PCA detects anomalies and fills gaps in seasonal time series data.
Robust PCA, the problem of PCA in the presence of outliers has been extensively investigated in the last few years. Here we focus on Robust PCA in the column sparse outlier model. The existing methods for column sparse outlier model assumes either the knowledge of the dimension of the lower dimensional subspace or the …
Revisits PCA with new formulations and insights.
New PCA method handles multiple datasets and detects sparse patterns robustly.
Tuning-free OR-PCA improves scalability for large datasets.
A new robust PCA method uses Innovation Search and Leverage Scores.
A new PCA method using T-norm outperforms existing methods.
RFPCA improves robustness of FPCA for matrix data.
Robust PCA, the problem of PCA in the presence of outliers has been extensively investigated in the last few years. Here we focus on Robust PCA in the outlier model where each column of the data matrix is either an inlier or an outlier. Most of the existing methods for this model assumes either the knowledge of the dim…
Fast robust subspace tracking in sparse data-dependent noise with near-optimal delay.
A method to remove mean-shift noise from PCA using knockoffs.
Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In this context, the fresh look advocated here permeates benefits from variable sele…
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…
Many machine learning systems are vulnerable to small perturbations made to inputs either at test time or at training time. This has received much recent interest on the empirical front due to applications where reliability and security are critical. However, theoretical understanding of algorithms that are robust to a…
We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the distributions are multivariate Gaussian. COCA improves upon PCA and sparse PCA in three as…
AdvPCA uses robust optimization to achieve sparse PCA without tuning.
Robust PCA is a widely used statistical procedure to recover a underlying low-rank matrix with grossly corrupted observations. This work considers the problem of robust PCA as a nonconvex optimization problem on the manifold of low-rank matrices, and proposes two algorithms (for two versions of retractions) based on ma…
Develops PRPCA for smooth image recovery combining low-rank and smoothness.
We consider principal component analysis for contaminated data-set in the high dimensional regime, where the dimensionality of each observation is comparable or even more than the number of observations. We propose a deterministic high-dimensional robust PCA algorithm which inherits all theoretical properties of its ra…
Principal Components Analysis (PCA) is one of the most widely used dimension reduction techniques. Robust PCA (RPCA) refers to the problem of PCA when the data may be corrupted by outliers. Recent work by Cand{è}s, Wright, Li, and Ma defined RPCA as a problem of decomposing a given data matrix into the sum of a low-ran…
GT-PCA improves PCA for image and time series data.
New methods solve sparse estimation robustly, even with outliers.
Paper extends KPCA using dualization for faster, more robust algorithms.
Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian samples and/or outliers often makes it unreliable in practice. To this end, a robust…
A new PCA method robust to outliers using Median of Means.
Dynamic robust PCA refers to the dynamic (time-varying) extension of robust PCA (RPCA). It assumes that the true (uncorrupted) data lies in a low-dimensional subspace that can change with time, albeit slowly. The goal is to track this changing subspace over time in the presence of sparse outliers. We develop and study …
Kernel PCA explains self-attention mechanisms in deep learning models.
PCA-Triage optimizes sensor data sampling for IoT networks.
We propose a new method for robust PCA -- the task of recovering a low-rank matrix from sparse corruptions that are of unknown value and support. Our method involves alternating between projecting appropriate residuals onto the set of low-rank matrices, and the set of sparse matrices; each projection is {\em non-convex…
This work obtains novel finite sample guarantees for Principal Component Analysis (PCA). These hold even when the corrupting noise is non-isotropic, and a part (or all of it) is data-dependent. Because of the latter, in general, the noise and the true data are correlated. The results in this work are a significant impr…
Two new algorithms improve robust PCA and Schatten packing.
New method improves PCA robustness using Wasserstein distances.
PCA is a classical statistical technique whose simplicity and maturity has seen it find widespread use as an anomaly detection technique. However, it is limited in this regard by being sensitive to gross perturbations of the input, and by seeking a linear subspace that captures normal behaviour. The first issue has bee…
SPCA improves PCA by learning from simple to complex samples.
A novel unsupervised outlier detection method using Randomized PCA Forest.