Paper proposes a method for estimating sparse and low-rank tensors from sketchings.
problem Estimating sparse and low-rank tensors from limited data.
method Two-stage non-convex implementation using sparse tensor decomposition and thresholded gradient descent.
result Exact and stable recovery of tensors in noisy and noiseless cases with high probability.
Paper proposes a new method to separate low rank and sparse matrices without bias.
problem Recovering low rank and sparse matrices from measurements.
method Uses nonconvex regularizers and alternating proximal gradient descent.
result Error bounds for the algorithm applied to sparse optimization, matrix completion, and robust PCA.
New algorithm speeds up LVGGM estimation by solving nonconvex optimization.
problem Estimating the latent variable Gaussian graphical model with sparse and low-rank components.
method Sparsity constrained maximum likelihood estimator with alternating gradient descent and hard thresholding.
result Our algorithm converges linearly to the optimal components up to statistical precision.
This work tackles sparse coding in DLRA for interpretable multiway data.
problem Sparse coding in DLRA for interpretable multiway data.
method Proposes a new sparse-coding subproblem (MSC) and several algorithms to solve it.
result DLRA extends low-rank approximations, reducing variance and enhancing interpretability.
Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse components becomes possible. This fundamental identifiability issue arises with tra…
This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices. We first benefit from a convex optimization which develops l1-norm penalty to encourage the sparsity and nuclear norm to favor the low-rank property. For the proposed estimator, we then p…
Proposes a model to relate a tensor feature to a univariate outcome using sparse and low-rank components.
problem Relating a univariate outcome to a feature tensor with sparse and low-rank components.
method Divide-and-conquer strategy, stagewise estimation procedure for unit-rank tensor regression.
result The stagewise solution paths converge to those of regularized regression as step size goes to zero.
HERA improves PLL by integrating heterogeneous loss and sparse-low-rank regularization.
problem Learning from data with partial labels.
method Combines heterogeneous loss and sparse-low-rank regularization.
result Achieves superior performance on artificial and real-world data.
Survey on nonconvex penalties for sparse and low-rank recovery in various fields.
problem Achieving sparsity and low-rankness in signal processing, statistics, and machine learning.
method Analysis of nonconvex penalties and their applications.
result Nonconvex penalties can significantly improve performance in various applications.
ReFACTor improves low-rank matrix recovery from noisy data.
problem Recovering low-rank matrices from noisy column-sparse data.
method A simple variation of TSVD, leveraging column-sparsity.
result ReFACTor outperforms TSVD and PCA in various scenarios.
Low-rank framework for task-specific LLM ranking from sparse comparisons.
problem Challenges in reliable task-specific ranking of LLMs under sparse, imbalanced comparisons.
method Low-rank modeling of task-by-model ability matrix, max-norm accurate estimator, task-wise top-K recovery guarantees, uncertainty quantification framework.
result Improves sample efficiency and produces tighter, better-calibrated ranking certificates.
We address the problem of estimating a sparse low-rank matrix from its noisy observation. We propose an objective function consisting of a data-fidelity term and two parameterized non-convex penalty functions. Further, we show how to set the parameters of the non-convex penalty functions, in order to ensure that the ob…
Efficiently estimates high-dimensional varying index coefficient models without link function estimation.
problem Parameter estimation in high-dimensional varying index coefficient models.
method Stein's identity for computationally efficient estimators of sparse or low-rank parameters.
result Optimal statistical rates of convergence for estimators in both sparse and low-rank settings.
Improved Frank-Wolfe method tackles nonsmooth functions.
problem Efficiently solving large nonsmooth problems with sparse structures.
method Optimizes for approximation quality over all affine approximations.
result Overcomes issues with existing nonsmooth methods in low-rank matrix estimation.
LASSI models improve dynamic imaging from sparse data.
problem Efficiently reconstruct dynamic images from limited data.
method Data-adaptive decomposition of dynamic signals into low-rank and sparse components.
result LASSI models outperform existing methods in dynamic MRI reconstruction.
New method for separating foreground from background in noisy, moving camera video.
problem Foreground-background separation in noisy, free-moving camera video.
method Registers frames, encodes perspective as missing data, uses OptShrink for low-rank estimation, and weighted total variation for smooth foreground.
result Panoramic background component that stitches together corrupted data from overlapping frames.
The paper tackles transfer learning for growing matrix representations, improving estimation accuracy.
problem Structured matrix estimation under growing ambient dimensions and latent representations.
method Proposes a general transfer framework decomposing target parameters into embedded source components, low-rank innovations, and sparse edits. Develops an anchored alternating projection estimator.
result Establishes deterministic error bounds that separate target noise, representation growth, and source estimation error, yielding improved rates.
Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of methods have been developed for this recovery problem. However, a principled meth…
LORIS model estimates main and interaction effects in large data frames.
problem Handling large data frames with missing values and explicit modeling of main effects.
method Low-rank interaction and sparse additive effects (LORIS) model with mixed coordinate gradient descent (MCGD).
result LORIS method provides statistical guarantees and converges efficiently for large data sets.
Paper tackles matrix estimation under arbitrary noise, achieving minimax optimality.
problem Noisy low-rank-plus-sparse matrix recovery under arbitrary dependence.
method Incoherent-constrained least-square estimator, novel energy spreading result.
result Achieves minimax optimality in estimating structured Markov transition kernels.
Unified model for tensor completion using low-rank and sparse Tucker decomposition.
problem Estimating missing data from incomplete tensor measurements.
method Unified low-rank and sparse enhanced Tucker decomposition model with ADMM.
result Our model achieves higher recovery accuracy on various real-world data sets.
A new method models user-specific parameters as a low-rank plus sparse component for efficient personalization.
problem Efficient personalization of machine learning models for individual users.
method Meta-learning approach that models network weights as a sum of low-rank and sparse components.
result The proposed method, AMHT-LRS, achieves nearly optimal sample complexity for estimating the low-rank and sparse components.
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.
Paper proposes a single task optimization for endmembers' number estimation and unmixing.
problem Endmembers' number estimation and unmixing in hyperspectral images.
method Low-rank and sparse nonnegative matrix factorization with alternating proximal algorithm.
result Effectiveness of the proposed approach verified by experiments.
Algorithm recovers sparse and low rank matrix components efficiently.
problem Recovery of sparse and low rank components of matrices.
method Iterative method with adaptive thresholding.
result Algorithm performs well with low run-time and suitable for non-sparse noise.
Enhances VAR model estimation using transfer learning.
problem Estimating high-dimensional VAR models with temporal dependencies.
method Transfer learning for VAR models with low-rank and sparse structures.
result Theoretical guarantees for model parameter consistency and informative set selection.
We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation X of the sum of an approximately) low rank matrix Θ⋆ with a second matrix Γ⋆ endowed with a complementary …
New method for factor analysis using nuclear and ℓ0 norms.
problem Finding a low-rank plus sparse decomposition from noisy covariance matrix.
method Formulated an optimization problem with nuclear norm, ℓ0 norm, and KL divergence. Used alternating minimization algorithm. result Algorithm effectively decomposes covariance matrices in synthetic and real datasets.
We introduce a two step algorithm with theoretical guarantees to recover a jointly sparse and low-rank matrix from undersampled measurements of its columns. The algorithm first estimates the row subspace of the matrix using a set of common measurements of the columns. In the second step, the subspace aware recovery of …
The paper introduces a penalized matrix estimation procedure aiming at solutions which are sparse and low-rank at the same time. Such structures arise in the context of social networks or protein interactions where underlying graphs have adjacency matrices which are block-diagonal in the appropriate basis. We introduce…
Unified framework for solving low-rank plus sparse matrix recovery problems.
problem Solving general low-rank plus sparse matrix recovery problems.
method Unified framework based on matrix factorization, projected gradient descent, and double thresholding operator.
result Our algorithm converges to the unknown low-rank and sparse matrices at a locally linear rate, matching robustness guarantees.
In a plethora of applications dealing with inverse problems, e.g. in image processing, social networks, compressive sensing, biological data processing etc., the signal of interest is known to be structured in several ways at the same time. This premise has recently guided the research to the innovative and meaningful …
Improved GCNs for non-sparse graphs with low-rank filters.
problem Training and evaluation of GCNs on large non-sparse graphs is computationally expensive.
method Introduced low-rank filters and a reduced-order GCN architecture.
result Significant runtime acceleration and improved accuracy achieved.
Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. This paper introduces a penalized approximation framework to recover such model structures from large covariance matrix estimation. We propos…
New nonconvex regularizers improve low-rank matrix recovery efficiency and accuracy.
problem Efficiently recover low-rank matrices from incomplete data.
method Factor group-sparse regularization, related to Schatten-p norms.
result Improved generalization error bounds for Schatten-p norms as p decreases.
We consider the problem of modeling multivariate time series with parsimonious dynamical models which can be represented as sparse dynamic Bayesian networks with few latent nodes. This structure translates into a sparse plus low rank model. In this paper, we propose a Gaussian regression approach to identify such a mod…
New method improves robust low-rank matrix completion for computer vision.
problem Robust low-rank matrix completion for partially observed data.
method Formulated as a nonsmooth Riemannian optimization problem over Grassmann manifold, solved with an alternating manifold proximal gradient continuation method.
result Demonstrated advantages over existing approaches in background extraction from surveillance videos.
Improved Frank-Wolfe for sparse/low-rank problems.
problem Sparse/low-rank optimization problems.
method Primal-Dual Block Frank-Wolfe algorithm.
result Empirically outperforms state-of-the-art methods in classification tasks.
Improved matrix completion for non-uniformly sampled data.
problem Estimating unobserved entries in a matrix with varying sampling probabilities.
method Developed entry-specific bounds for low-rank matrix completion under structured non-uniform sampling.
result Error bounds for each entry match minimax lower bounds under certain conditions.
ScaledGD algorithm estimates low-rank tensors efficiently from corrupted data.
problem Estimating meaningful information from corrupted tensor data.
method Scaled gradient descent (ScaledGD) algorithm with tailored spectral initializations.
result ScaledGD achieves linear convergence at a constant rate independent of condition number.
iRRR integrates multi-view data for faster prediction.
problem Predicting from multi-view data with high dimensions and sparse relevant views.
method Integrative reduced-rank regression with convex composite nuclear norm penalization.
result iRRR achieves faster convergence and recovers oracle bounds.
Paper identifies sparse structures and communities in heterogeneous graphical models.
problem Detecting community structures in graphical models.
method Novel decomposition into sparse and low-rank parts, three-stage estimation procedure.
result Consistent model selection for adaptive ℓ1 penalized estimator. The article develops a method to learn sparse and low rank PARAFAC decomposition robust to noise.
problem Learning sparse and low rank PARAFAC decomposition for tensors with missing values.
method Bayesian model with elastic net regularization, efficient algorithms for large scale problems.
result The method finds true rank and sparse factor matrix robust to noise.
The paper proposes a method to estimate tensor regression parameters using low-rank and sparse Tucker decompositions.
problem Estimating tensor regression parameters from limited data.
method Low-rank and sparse Tucker decompositions, non-convex optimization, projected gradient descent.
result The method can linearly converge to an appropriate solution under certain conditions.
3BASiL-TM decomposes LLMs into sparse and low-rank matrices for efficient compression.
problem Efficiently compressing large language models without significant performance loss.
method 3-Block ADMM method and transformer-matching refinement step for sparse plus low-rank decomposition.
result 3BASiL-TM reduces perplexity gap by over 30% and speeds up compression by 2.5x.
RNNs solve modular addition tasks using low rank and sparse Fourier structures.
problem Solving modular addition tasks with recurrent neural networks.
method Identified low rank structures and sparse Fourier representations in RNN weights.
result RNNs robust to removing individual frequencies but degrade with more ablation.
Sparse LR-LSSVM improves kernel machine performance.
problem Improving kernel machine performance with controlled model size.
method Introduces LR-LSSVM with low rank kernels and a two-step optimization algorithm.
result Proposed algorithm's performance is comparable or superior to existing kernel machines.
SILVar models latent variables in complex systems.
problem Estimating latent variables in complex, networked systems.
method Semi-parametric, non-linear regression model with regularized empirical risk minimization.
result Joint estimation of non-linearities, direct interactions, and unmodeled elements.