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 -reg…
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48 results for “Support union recovery”
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.
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 -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.
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.
Estimates multiple related causal graphs with shared causal order.
problem Discovering multiple related Gaussian DAGs with shared causal order.
method Proposes a -regularized MLE for joint estimation of linear structural equation models.
result Joint estimator achieves better sample complexity and consistency in causal order recovery.
We sharply characterize the performance of different penalization schemes for the problem of selecting the relevant variables in the multi-task setting. Previous work focuses on the regression problem where conditions on the design matrix complicate the analysis. A clearer and simpler picture emerges by studying the No…
In multivariate regression, a -dimensional response vector is regressed upon a common set of covariates, with a matrix of regression coefficients. We study the behavior of the multivariate group Lasso, in which block regularization based on the norm is used for supp…
In applications ranging from communications to genetics, signals can be modeled as lying in a union of subspaces. Under this model, signal coefficients that lie in certain subspaces are active or inactive together. The potential subspaces are known in advance, but the particular set of subspaces that are active (i.e., …
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.
Unions of subspaces provide a powerful generalization to linear subspace models for collections of high-dimensional data. To learn a union of subspaces from a collection of data, sets of signals in the collection that belong to the same subspace must be identified in order to obtain accurate estimates of the subspace s…
New method recovers matrices with nonlinear structures using optimization on Grassmann manifold.
problem Recovering high-rank matrices with nonlinear structures like subspaces or clusters.
method Formulated as rank minimization of a nonlinear feature map, approximated by constrained non-convex optimization on the Grassmann manifold, using Riemannian and alternating minimization schemes.
result Global convergence and worst-case complexity bounds for alternating minimization scheme, leading to unique limit point.
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.
In this paper, we present multi-task structure learning for Gaussian graphical models. We analyze the sufficient number of samples for the correct recovery of the support union and edge signs. We also analyze the necessary number of samples for any conceivable method by providing information-theoretic lowe…
Feature interactions can contribute to a large proportion of variation in many prediction models. In the era of big data, the coexistence of high dimensionality in both responses and covariates poses unprecedented challenges in identifying important interactions. In this paper, we suggest a two-stage interaction identi…
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.
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 measurements, improving to 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 -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.
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.
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.
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.
Examines insurance market development and similarity post-2004 EU enlargement.
problem Comparing insurance markets of EU old and new members post-enlargement.
method Analyzes data from 2004 to present to compare insurance markets.
result Identifies similarities and differences in insurance markets post-2004 enlargement.
Algorithm recovers sparse PCA support from incomplete data.
problem Sparse PCA with incomplete and noisy data.
method Semidefinite program (SDP) relaxation of non-convex -regularized PCA.
result SDP enables exact recovery of true support of sparse leading eigenvector.
New method fuses audio and magnetic data to identify underlying subspaces.
problem Identifying complex trends in multi-modality data.
method Robust Group Subspace Recovery (RoGSuRe) algorithm based on group sparsity and bi-sparsity pursuit.
result Competitive performance in clustering and classification of multi-modal 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.
It is known that for a certain class of single index models (SIMs) , support recovery is impossible when 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 penalty.
method Data-driven line search rule for adaptive step size determination.
result Proves error bound without restrictions on cost functional.
In this short note we extend some of the recent results on matrix completion under the assumption that the columns of the matrix can be grouped (clustered) into subspaces (not necessarily disjoint or independent). This model deviates from the typical assumption prevalent in the literature dealing with compression and r…
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.
Average case analysis of Lasso under ultra-sparse conditionscond-mat.dis-nn
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.
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…
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.
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…
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.
We demonstrate that the primal-dual witness proof method may be used to establish variable selection consistency and -bounds for sparse regression problems, even when the loss function and/or regularizer are nonconvex. Using this method, we derive two theorems concerning support recovery and -…
The non-negative solution to an underdetermined linear system can be uniquely recovered sometimes, even without imposing any additional sparsity constraints. In this paper, we derive conditions under which a unique non-negative solution for such a system can exist, based on the theory of polytopes. Furthermore, we deve…
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 -regularized PCA problem.
result Support of the sparse leading eigenvector can be recovered with high probability.
Compressed sensing is a powerful tool in applications such as magnetic resonance imaging (MRI). It enables accurate recovery of images from highly undersampled measurements by exploiting the sparsity of the images or image patches in a transform domain or dictionary. In this work, we focus on blind compressed sensing (…
New techniques for compressive sensing without noise or signal statistics.
problem Support recovery in underdetermined linear regression models without prior noise and signal statistics.
method Proposes RRM and RRTA to operate OMP algorithm without noise variance or signal sparsity knowledge.
result Establishes high SNR consistency for OMP without prior noise and signal statistics.
High-dimensional data often lie in low-dimensional subspaces corresponding to different classes they belong to. Finding sparse representations of data points in a dictionary built using the collection of data helps to uncover low-dimensional subspaces and address problems such as clustering, classification, subset sele…
Paper tackles distributed high-dimensional regression with quantile loss, overcoming heavy-tailed noise challenges.
problem High-dimensional linear regression with heavy-tailed noise.
method Adopting quantile regression loss, transforming response variable, and using gradient information for distributed estimation.
result Proposed distributed estimator achieves near-oracle convergence rate and supports recovery without machine number restrictions.
We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix . These may come from corrupted data, persistent experimental errors, or malicious respondents in surveys/recommender systems, etc. Such non-stochas…
Let (M, g) be a simple, real analytic, Riemannian manifold with boundary and of dimension n>=3. In this work, we prove a support theorem for the transverse ray transform of tensor fields of rank 2 defined over such manifolds. More specifically, given a symmetric tensor field f of rank 2, we show that if the transverse …