Algorithm recovers sparse PCA support from incomplete data.
problem Sparse PCA with incomplete and noisy data.
method Semidefinite program (SDP) relaxation of non-convex l1-regularized PCA. result SDP enables exact recovery of true support of sparse leading eigenvector.
The paper improves support recovery in high-dimensional precision matrix estimation using meta learning.
problem Support recovery in high-dimensional precision matrix estimation with reduced sample complexity.
method Pooling samples from different tasks and using an improper ℓ1-regularized log-determinant Bregman divergence to estimate a single precision matrix. result The support of the improperly estimated single precision matrix is equal to the true support union with high probability.
A new online learning framework selects features and improves convergence.
problem Online learning's limitations in convergence and feature selection.
method A novel online learning framework based on running averages with feature selection.
result The framework achieves high true support recovery and faster convergence.
The Lasso performs well in ultra-sparse linear models with finite support size.
problem Performance analysis of Lasso in ultra-sparse linear models.
method Novel application of replica method from statistical physics, rigorous analysis of average case performance.
result Average performance of Lasso assessed without scaling assumptions, offering sample complexity bounds.
A new method enhances signal recovery with FDR control.
problem Challenging signal recovery in compressive sensing.
method Knockoff-guided compressive sensing framework with FDR control.
result Guaranteed FDR control leads to more accurate signal reconstruction.
Meta-learning improves support recovery in high-dimensional PCA.
problem Support recovery in high-dimensional Principal Component Analysis.
method Meta-learning approach to reduce sample complexity and support recovery.
result Support recovery can be achieved with significantly fewer samples than traditional methods.
Study supports recovery of PDEs from noisy data using a specific regularization method.
problem Support recovery of PDEs from a single noisy trajectory.
method Applying ℓ1-regularized Pseudo-Least Squares model to a given data set.
result Support of ℓ1-c coefficients asymptotically converges to the true signed-support of the PDE.
In this note we compare two recently proposed semidefinite relaxations for the sparse linear regression problem by Pilanci, Wainwright and El Ghaoui (Sparse learning via boolean relaxations, 2015) and Dong, Chen and Linderoth (Relaxation vs. Regularization A conic optimization perspective of statistical variable select…
Lasso-Zero improves support recovery in high-dimensional linear models.
problem Support recovery in high-dimensional linear models with sparse β0. method Lasso-Zero uses an 'overfit, then threshold' approach with noise dictionaries.
result Lasso-Zero outperforms competitors in support recovery and trade-off between true positives and false discoveries.
The paper analyzes sparse PCA for incomplete data and proves support recovery conditions.
problem Support recovery in sparse PCA with non-random missing data.
method Semidefinite relaxation of the ℓ1-regularized PCA problem. result Support of the sparse leading eigenvector can be recovered with high probability.
Paper proposes estimators for sparse PCA with oracle property.
problem Estimating sparse principal subspace in high-dimensional settings.
method Semidefinite relaxation with novel regularizations.
result One estimator achieves exact support recovery and statistical rate.
We consider the Orthogonal Least-Squares (OLS) algorithm for the recovery of a m-dimensional k-sparse signal from a low number of noisy linear measurements. The Exact Recovery Condition (ERC) in bounded noisy scenario is established for OLS under certain condition on nonzero elements of the signal. The new result a…
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous theoretical analysis. We show that the proposed algorithms enjoy linear convergence a…
Posterior sampling estimator achieves near-optimal recovery guarantees for signals from any prior distribution.
problem Characterizing measurement complexity for signals from any prior distribution, including the entire space.
method Characterization of measurement complexity using posterior sampling estimator for Gaussian measurements and any prior distribution.
result Posterior sampling estimator achieves near-optimal recovery guarantees for signals from any prior distribution, robust to model mismatch.
Paper proposes an algorithm for automatically selecting latent dimensions in NMF.
problem Automatic model selection for NMF with theoretical guarantees.
method Empirical second-order moment and support union recovery.
result The algorithm provably detects the true latent dimensionality.
Gradient descent with specific initialization and step size achieves optimal sparse signal recovery.
problem Reconstructing a sparse signal from underdetermined linear measurements.
method Gradient descent with specific initialization, step size, and stopping time.
result Achieves the minimax rate with poly-logarithmic factors and adapts to instance difficulty.
Unfolded ISTA achieves linear convergence for sparse signal recovery.
problem Understanding and improving convergence of iterative algorithms in sparse signal recovery.
method Introducing weight structure and incorporating thresholding in the network.
result Unfolded ISTA can achieve linear convergence, better than sublinear convergence of ISTA/FISTA.
We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix X. These may come from corrupted data, persistent experimental errors, or malicious respondents in surveys/recommender systems, etc. Such non-stochas…
This paper improves support recovery in universal one-bit compressed sensing.
problem Support recovery in one-bit compressed sensing for sparse signals.
method Proposes approximate support recovery and superset recovery algorithms with polynomial-time complexity.
result Achieves improved support recovery with fewer measurements compared to existing methods.
New algorithm recovers model coefficients and supports from noisy data.
problem Simultaneous estimation and support recovery in linear models with Gaussian noise.
method Projection-based algorithm for STG regularized minimization problem, proving convergence and support recovery guarantees.
result New algorithm outperforms existing methods in support recovery for various data setups.
KSS method converges and recovers correct clustering under certain conditions.
problem Subspace clustering for semi-randomly sampled data.
method Local convergence analysis and recovery guarantee for KSS method.
result KSS method converges superlinearly and finds correct clustering within loglog N iterations.
SCOPE iteratively optimizes sparsity-constrained problems without tuning hyperparameters.
problem Optimizing sparsity-constrained problems in signal processing, statistics, and machine learning.
method SCOPE (Sparsity-Constrained Optimization via sPlicing itEration) replaces gradient steps with a splicing operation guided by the objective value.
result SCOPE achieves linear convergence and superior support recovery performance.
This paper improves support recovery in universal one-bit compressed sensing with fewer measurements.
problem Support recovery in universal one-bit compressed sensing.
method Developed algorithms to recover the support of sparse signals with a small number of false positives.
result Support recovery with ildeO(k3/2) measurements, improving to ildeO(k) with known dynamic range. Efficient algorithms for sparse parameter recovery in mixture models.
problem Support recovery of high-dimensional sparse latent vectors in mixture models.
method Efficient algorithms with logarithmic sample complexity dependence on dimensionality.
result First guarantees on support recovery for various mixture models.
IRKSN algorithm achieves sparse recovery with wider applicability conditions.
problem Sparse recovery challenges due to NP-hard nature and restrictive conditions.
method IRKSN algorithm based on k-support norm regularizer. result Achieves sparse recovery with explicit constants and standard linear rate.
Paper analyzes adaptive Lasso for high-dimensional diffusion processes, improving support recovery and bias.
problem Support recovery for high-dimensional diffusion processes under sparsity constraints.
method Adaptive Lasso estimator for d-dimensional ergodic diffusion process, focusing on linear models.
result Adaptive Lasso achieves support recovery and asymptotic normality for drift parameter under certain conditions.
Sign-RIP improves robust low-rank matrix recovery by preserving norms even with corrupted measurements.
problem Robust low-rank matrix recovery in the presence of corrupted measurements.
method Proposed Sign-RIP, a robust restricted isometry property.
result Sign-RIP guarantees uniform convergence of subdifferentials in robust low-rank matrix recovery.
Study on limits of recovering sparse variables from phaseless measurements.
problem Support recovery in phase retrieval model with noisy phaseless measurements.
method Information-theoretic analysis, considering discrete and Gaussian models, Gaussian measurement matrices.
result Sharp thresholds with near-matching constant factors for sparsity and signal-to-noise ratio in various scaling regimes.
This letter presents a novel Block Bayesian Hypothesis Testing Algorithm (Block-BHTA) for reconstructing block sparse signals with unknown block structures. The Block-BHTA comprises the detection and recovery of the supports, and the estimation of the amplitudes of the block sparse signal. The support detection and rec…
Paper tackles distributed quantile regression with improved efficiency and support recovery.
problem Challenges in distributed estimation and support recovery for high-dimensional linear quantile regression.
method Transformed quantile regression into least-squares optimization, applied double-smoothing approach, developed efficient algorithm.
result Achieved near-oracle convergence rate and high support recovery accuracy.
A tuning-free method recovers jointly sparse signals in MMV using implicit regularization.
problem Recovering jointly sparse signals in MMV with minimal tuning or prior knowledge.
method Reparameterizes MMV estimation matrix into decoupled factors and applies gradient descent to a least-squares objective.
result Gradient descent dynamics exhibit a momentum-like effect, converging towards an idealized row-sparse solution.
New algorithm converges to optimal phase retrieval estimator with misspecified link functions.
problem High-dimensional sparse phase retrieval with incorrect model specification.
method Simple variant of thresholded Wirtinger flow algorithm, linear convergence for optimal accuracy.
result Linear convergence to optimal estimator for a broad family of unknown link functions.
Study identifies key differences in convex relaxations for combinatorial penalties.
problem Understanding which structures are preserved by convex relaxations for combinatorial penalties.
method Examined homogeneous and non-homogeneous convex relaxations, introduced lower combinatorial envelope, and proposed adaptive estimator.
result Identified new necessary and sufficient conditions for support recovery in convex monotone regularizers.
In this paper, we investigate a multivariate multi-response (MVMR) linear regression problem, which contains multiple linear regression models with differently distributed design matrices, and different regression and output vectors. The goal is to recover the support union of all regression vectors using l1/l2-reg…
It is known that for a certain class of single index models (SIMs) Y=f(Xp×1⊺β0,ε), support recovery is impossible when X∼N(0,Ip×p) and a model complexity adjusted sample size is below a critical threshold. Recen…
Study on recovering supports of multiple sparse vectors from mixed linear measurements.
problem Recovering supports of multiple sparse vectors from a mixture of linear measurements.
method Developed algorithms to identify the support of all component vectors using polynomial and quasi-polynomial number of measurements.
result Polynomial and quasi-polynomial number of measurements sufficient for recovering the supports of all component vectors.
Enhanced Elastic-Net with box-constraint improves support recovery in noisy measurements.
problem Support recovery of sparse signals from noisy measurements.
method Box-Elastic Net (Box-EN) method with mean squared error and probability of support recovery analysis.
result The Box-Elastic Net outperforms the standard Elastic-Net in support recovery.
A new line search rule improves support recovery in high-dimensional data.
problem Support recovery in high-dimensional data analysis with ℓ0 penalty. method Data-driven line search rule for adaptive step size determination.
result Proves ℓ2 error bound without restrictions on cost functional. New algorithm improves signal recovery from noisy measurements with theoretical guarantees.
problem Recovering signals from noisy measurements in inverse problems.
method Wasserstein-based projections (WP) replacing analytic regularization with data-driven denoising.
result WP approximates true projection with high probability, providing theoretical guarantees.
We consider the mixed regression problem with two components, under adversarial and stochastic noise. We give a convex optimization formulation that provably recovers the true solution, and provide upper bounds on the recovery errors for both arbitrary noise and stochastic noise settings. We also give matching minimax …
Federated learning supports exact support recovery with minimal communication.
problem Learning the exact support of sparse linear regression in federated learning.
method One-shot communication algorithm for exact support recovery without optimization.
result Polynomial sample complexity and logarithmic number of clients required.
iFlow improves latent representation recovery by directly maximizing marginal likelihood.
problem Recovering true latent representations from observed data.
method Flow-based model (iFlow) that directly maximizes the marginal likelihood, providing theoretical guarantees on identifiability.
result iFlow delivers optimal solutions in both theory and practice, outperforming variational autoencoders.
GRRT recovers sparse signals without prior sparsity or noise variance knowledge.
problem Recovering sparse signals without prior sparsity or noise variance knowledge.
method Generalized residual ratio thresholding (GRRT) for SOMP and BOMP.
result Finite sample and finite SNR guarantees for exact support recovery.
In this correspondence, we obtain exact recovery conditions for regularized modified basis pursuit (reg-mod-BP) and discuss when the obtained conditions are weaker than those for modified-CS or for basis pursuit (BP). The discussion is also supported by simulation comparisons. Reg-mod-BP provides a solution to the spar…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in regression, and group testing. In this paper, we take a unified approach to supp…
The paper analyzes error bounds and KL properties for noisy matrix recovery problems.
problem Noisy low-rank matrix recovery problems.
method Squared F-norm regularization, accelerated alternating minimization method.
result Established error bounds and KL properties for critical points and global minimizers.
New method selects variables in groups with few nonzeros, improving support recovery.
problem Structured variable selection with sparse patterns across groups.
method Composite norm and proximal algorithm for exclusive group sparsity.
result Asymptotic consistency in signed support recovery under conventional assumptions.
Auto-Encoders are unsupervised models that aim to learn patterns from observed data by minimizing a reconstruction cost. The useful representations learned are often found to be sparse and distributed. On the other hand, compressed sensing and sparse coding assume a data generating process, where the observed data is g…