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.…
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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.
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48 results for “sparse noise”
Study on signal recovery from low-rank matrix with sparse noise.
problem Inference of a rank-one signal in the presence of sparse noise.
method Replica method from statistical physics, recursive distributional equations, population dynamics algorithm.
result Critical signal strength for recovery via top eigenvector identified.
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.
Linear regression models contaminated by Gaussian noise (inlier) and possibly unbounded sparse outliers are common in many signal processing applications. Sparse recovery inspired robust regression (SRIRR) techniques are shown to deliver high quality estimation performance in such regression models. Unfortunately, most…
Study improves model robustness in noisy datasets.
problem Instance-specific label noise in robust classification tasks.
method Coordinated Sparse Recovery (CSR) method introduces a collaboration matrix and confidence weights to reduce generalization error.
result CSR and CSR+ significantly reduce generalization error compared to existing methods.
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.
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…
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 distribution, alternative approximations like Genera…
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.
Many data-driven approaches exist to extract neural representations of functional magnetic resonance imaging (fMRI) data, but most of them lack a proper probabilistic formulation. We propose a group level scalable probabilistic sparse factor analysis (psFA) allowing spatially sparse maps, component pruning using automa…
Sparse Linear Regression when Noises and Covariates are Heavy-Tailed and Contaminated by Outliersstat.ML
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.
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual square and scaling the penalty in proportion to the estimated noise level. The iterat…
A new method for joint noise removal and trend estimation from sparse signals.
problem Jointly removing noise and estimating trends from sparse signals.
method PENDANTSS combines SOOT/SPOQ penalties with BEADS algorithm in a Trust-Region block alternating variable metric forward-backward approach.
result Outperforms comparable methods in deconvolving analytical chemistry signals.
Additive asynchronous and cyclostationary impulsive noise limits communication performance in OFDM powerline communication (PLC) systems. Conventional OFDM receivers assume additive white Gaussian noise and hence experience degradation in communication performance in impulsive noise. Alternate designs assume a parametr…
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 handles structural uncertainty in graphs better than existing models.
problem Handling heterophily and structural noise in semi-supervised learning on graphs.
method Sparse signed message passing network that models a posterior distribution over signed adjacency matrices.
result Our method outperforms strong baseline models on heterophilic benchmarks under both synthetic and real-world structural noise.
Noise in SGD affects overparameterized models, favoring sparse solutions.
problem Understanding and mitigating implicit bias in SGD with parameter-dependent noise.
method Theoretical analysis of a quadratically-parameterized model with label noise and Gaussian noise.
result SGD with label noise recovers sparse ground-truth solutions, while SGD with Gaussian noise overfits dense solutions.
Proposes a robust similarity measure for sparse time series data.
problem Sparse time course data in biological settings.
method Gaussian processes (GP) similarity measure based on log-likelihood ratio.
result Enhanced robustness to noise compared to Euclidean distance.
The paper tackles tensor factorization and completion from noisy data.
problem Sparse nonnegative tensor factorization and completion from partial and noisy observations.
method Minimizes the sum of maximum likelihood estimation and tensor norm with nonnegativity constraints.
result Error bounds and minimax lower bounds are established for the proposed model.
The ability to detect sparse signals from noisy high-dimensional data is a top priority in modern science and engineering. A sparse solution of the linear system can be found efficiently with an -norm minimization approach if the data is noiseless. Detection of the signal's support from data corrupted b…
Most artificial networks today rely on dense representations, whereas biological networks rely on sparse representations. In this paper we show how sparse representations can be more robust to noise and interference, as long as the underlying dimensionality is sufficiently high. A key intuition that we develop is that …
Fast robust subspace tracking in sparse data-dependent noise with near-optimal delay.
problem Robustly tracking time-varying subspaces in the presence of sparse outliers.
method Introduces a fast mini-batch robust ST solution under mild assumptions.
result Provably correct subspace tracking with near-optimal delay and same time complexity as simple PCA.
Sparse Max-Affine Regressionstat.ML
Paper proposes Sp-GD for sparse max-affine regression with theoretical guarantees.
problem Sparse max-affine regression model selection and estimation.
method Sparse Gradient Descent (Sp-GD) initialization using sparse PCA and covering search.
result Sp-GD provides ε-accurate estimates with optimal number of observations.
Simultaneous orthogonal matching pursuit (SOMP) and block OMP (BOMP) are two widely used techniques for sparse support recovery in multiple measurement vector (MMV) and block sparse (BS) models respectively. For optimal performance, both SOMP and BOMP require \textit{a priori} knowledge of signal sparsity or noise vari…
Inference of Sparse Networks with Unobserved Variables. Application to Gene Regulatory Networksstat.ML
Networks are a unifying framework for modeling complex systems and network inference problems are frequently encountered in many fields. Here, I develop and apply a generative approach to network inference (RCweb) for the case when the network is sparse and the latent (not observed) variables affect the observed ones. …
Improved SINDy autoencoder for identifying noisy dynamical systems.
problem Robust identification of noisy dynamical systems from data.
method Incorporates noise-separating neural network structures into SINDy autoencoder architecture.
result Accurately recovers latent dynamics and estimates measurement noise from noisy observations.
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 …
Rotation invariant algorithms fail on sparse problems even with noise.
problem Rotation invariant algorithms' suboptimality in sparse linear problems with noise.
method Lower bounds and trajectory analysis of optimization algorithms.
result Rotation invariant algorithms are suboptimal even with noise and many examples.
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…
Study on sparse recovery with mixed-quality data, establishing sample-size conditions.
problem Sparse recovery with heterogeneous noise from high- and low-quality sources.
method Establishes linear trade-off for sufficient conditions, analyzes LASSO algorithm.
result Linear trade-off for sufficient conditions, robustness of LASSO to data heterogeneity.
This paper proposes an exploration method for deep reinforcement learning based on parameter space noise. Recent studies have experimentally shown that parameter space noise results in better exploration than the commonly used action space noise. Previous methods devised a way to update the diagonal covariance matrix o…
Many models for sparse regression typically assume that the covariates are known completely, and without noise. Particularly in high-dimensional applications, this is often not the case. This paper develops efficient OMP-like algorithms to deal with precisely this setting. Our algorithms are as efficient as OMP, and im…
This paper examines fundamental error characteristics for a general class of matrix completion problems, where the matrix of interest is a product of two a priori unknown matrices, one of which is sparse, and the observations are noisy. Our main contributions come in the form of minimax lower bounds for the expected pe…
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.
New algorithms recover sparse tensor principal components efficiently.
problem Recovering sparse tensor principal components from noisy data.
method Family of algorithms interpolating between polynomial-time and exhaustive search, tailored for sparse and highly sparse regimes.
result Our algorithms recover sparse vectors for signal-to-noise ratios beyond previous limits, with time complexity .
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.
This research develops an evolutionary approach to discover non-Gaussian stochastic dynamical systems.
problem Discovering explicit governing equations of stochastic dynamical systems with Lévy noise from data.
method ESSR approach using genetic programming, sparse regression, and nonlocal Kramers-Moyal formulas.
result The approach effectively extracts non-Gaussian stochastic dynamical systems from sample path data.
This work optimizes signal estimation for sparse MRA with collision-free signals.
problem Recovering an unknown signal from repeated observations under cyclic isometries with high noise.
method Investigates minimax optimality for collision-free signals in the MRA model.
result The minimax optimal rate of estimation is \( \sigma^2/\sqrt{n} \) for sparse MRA.
Sparse Identification of Nonlinear Dynamical Systems via Reweighted -regularized Least Squaresstat.ML
Method improves SINDy for noisy nonlinear systems.
problem Recover nonlinear dynamical systems from noisy data.
method Reweighted -regularized least squares.
result Improved accuracy and robustness in noisy conditions.
New auto-encoder handles varying noise levels without retraining.
problem Auto-encoders degrade in noisy conditions.
method Formalized auto-encoders as transform learning, derived new architecture.
result Models generalize well to different noise levels.
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…
Jointly learns feature and sample relevancies for robust sparse recovery.
problem Sparse recovery sensitivity to data contaminants like outliers or misspecified noise.
method Jointly learns feature and sample relevancies via marginal likelihood optimization.
result Consistent sparse and robust prediction models across diverse tasks.
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.
New insights into statistical and computational limits for mixed sparse linear regression.
problem Recovering two sparse signals from noisy linear measurements.
method Analysis of low-degree polynomials and a simple thresholding algorithm.
result Identification of a smooth information-computation tradeoff and order-optimality of the thresholding algorithm.
In compressed sensing, we wish to reconstruct a sparse signal from observed data . In sparse coding, on the other hand, we wish to find a representation of an observed signal as a sparse linear combination, with coefficients , of elements from an overcomplete dictionary. While many algorithms are competit…
Paper finds sparse representation of functions using inverse scale space flow.
problem Finding sparse representation of functions.
method Inverse scale space flow to minimize loss.
result Convergence to optimal solution in ideal and noisy cases.
This paper considers the problem of subspace clustering under noise. Specifically, we study the behavior of Sparse Subspace Clustering (SSC) when either adversarial or random noise is added to the unlabelled input data points, which are assumed to be in a union of low-dimensional subspaces. We show that a modified vers…
New algorithms recover signals robustly against outliers and heavy-tailed noise.
problem Estimating signals in the presence of heavy-tailed noise and outliers.
method Sum-of-squares relaxations for robust estimation.
result Recovery of signals in polynomial/quasipolynomial time for specific problems.