Proposes a new sparse recovery method using generalized error function.
problem Sparse recovery in signal processing and imaging.
method Introduces a penalty function with shape and scale parameters for sparse recovery.
result The method improves MRI reconstruction and is theoretically sound.
This paper considers the recovery of a low-rank matrix from an observed version that simultaneously contains both (a) erasures: most entries are not observed, and (b) errors: values at a constant fraction of (unknown) locations are arbitrarily corrupted. We provide a new unified performance guarantee on when the natura…
We introduce a general framework to handle structured models (sparse and block-sparse with possibly overlapping blocks). We discuss new methods for their recovery from incomplete observation, corrupted with deterministic and stochastic noise, using block-ℓ1 regularization. While the current theory provides promis…
Optimal recovery framework for non-IID data in Hilbert spaces.
problem Generalization in non-IID data scenarios.
method Optimal recovery perspective, semidefinite programming, kernel ridgeless regression.
result Optimal recovery formula coincides with kernel ridgeless regression in some cases.
A new method for gradient recovery on manifold data without tangent spaces.
problem Gradient recovery schemes for data on discretized manifolds.
method Parametric Polynomial Preserving Recovery (PPPR) on manifolds.
result Superconvergence and high curvature stability of PPPR.
This paper tackles tensor recovery from noisy and multi-level quantized measurements.
problem Tensors from multi-level quantized measurements.
method Nonconvex optimization problem with alternating proximal gradient descent.
result The recovery error diminishes to zero with increasing tensor dimensions.
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 …
New method recovers signals from saturated data using linear loss and nonconvex penalties.
problem Signal recovery from saturated measurements with sign information loss.
method Linear loss and nonconvex penalties (e.g., minimax concave penalty, sorted ℓ1 norm).
result Estimation error is bounded and recovery performance improved.
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 insights into variable selection with different model assumptions.
problem Sparse recovery with ℓ∞ error guarantees in variable selection. method Separation between oblivious and adaptive models of ℓ∞ sparse recovery. result Proves a surprising contrast between oblivious and adaptive models in ℓ∞ sparse recovery. Paper develops TLoc framework to improve Telco outdoor position recovery.
problem High data collection cost and poor accuracy in Telco outdoor position recovery.
method Transfer learning applied to Telco outdoor position recovery.
result TLoc framework improves accuracy by 27.58% and 26.12% on 2G GSM and 4G LTE MR datasets.
Study recovers community structure from coarse graph measurements.
problem Community recovery from low-resolution graph measurements.
method Formalized coarsening process of graph measurements, developed conditions for perfect recovery.
result Simple and closed-form asymptotic conditions for perfect recovery of coarse graph communities.
We discuss a general notion of "sparsity structure" and associated recoveries of a sparse signal from its linear image of reduced dimension possibly corrupted with noise. Our approach allows for unified treatment of (a) the "usual sparsity" and "usual ℓ1 recovery," (b) block-sparsity with possibly overlapping blo…
Paper provides conditions for local recovery of tensor data's Kronecker-structured dictionaries.
problem Local recovery of Kronecker-structured dictionaries for tensor data.
method Derives sufficient conditions for local recovery of coordinate dictionaries.
result Sufficient conditions guarantee recovery of individual coordinate dictionaries up to specified error.
A framework for discrete structure recovery using iterative algorithms.
problem Recovering various discrete structures from data.
method General iterative algorithm for discrete structure recovery.
result Linear convergence of the proposed algorithm under certain conditions.
Study exact partition recovery with same-cluster oracle, bounded error.
problem Exact recovery of partitions with same-cluster oracle in adversarial error.
method Novel connection to correlation clustering, Rényi-Ulam framework, upper and lower bounds, randomized algorithm analysis, adaptivity-query complexity study.
result Upper and lower bounds on worst-case query complexity, expected performance bounds of randomized algorithm.
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.
Paper develops a new algorithm for sparse signal recovery.
problem Sparse signal recovery from noisy observations.
method Iterative Stochastic Optimization using Stochastic Mirror Descent.
result Linear convergence during preliminary phase of the routine.
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.
Faster convergence in inverse problems with minimal additional error.
problem Balancing convergence speed and reconstruction accuracy in iterative algorithms.
method Using a coarse estimate of the set to modify iterative algorithms for faster convergence.
result It is possible to achieve faster convergence without significantly increasing computational cost.
Paper reconciles minimax rates and optimal recovery rates for noisy observations.
problem Estimating a function from noisy observations.
method Develops NLA minimax rates for Besov classes in Lq-norms. result NLA minimax rates continuously depend on noise level and match optimal recovery rates as noise decreases.
Small initialization improves tensor recovery from noisy data.
problem Recovering low-tubal-rank tensors from noisy measurements.
method Factorized gradient descent with small initialization.
result Achieves nearly minimax optimal recovery error.
Hybrid QML model improves recovery rate prediction accuracy.
problem Complex nonlinear dependencies, high-dimensional feature spaces, and limited sample sizes in recovery rate forecasting.
method Hybrid Quantum Machine Learning (QML) with Amplitude Encoding, leveraging PQC and qubit data compression.
result Significantly lower RMSE (0.228) compared to classical models.
Linear reconstruction works for MRI compression without prior signal knowledge.
problem Compressive MRI reconstruction without signal structure knowledge.
method Learn sub-sampling pattern from training data, use linear reconstruction.
result Theoretical and experimental validation of linear reconstruction effectiveness.
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.
In this paper, we develop a relative error bound for nuclear norm regularized matrix completion, with the focus on the completion of full-rank matrices. Under the assumption that the top eigenspaces of the target matrix are incoherent, we derive a relative upper bound for recovering the best low-rank approximation of t…
Paper tackles robust sparse recovery in impulsive noise, using CMN and ADMM.
problem Sparse signal recovery in the presence of heavy-tailed impulsive noise.
method Exploits Continuous Mixed Norm (CMN) and Alternating Direction Method of Multipliers (ADMM).
result CMN leads to near optimal recovery in blind conditions.
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.
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.
New CSIM index improves image patch recovery from missing data.
problem Recovering missing image samples using sparse representation.
method Proposes a new convex similarity index (CSIM) and an iterative sparse recovery method.
result Proves the convergence of the algorithm to the globally optimal solution.
A new model for dynamic covariance recovery in neuroimaging data.
problem Estimating time-varying covariances in high-dimensional neuroimaging data.
method Nonconvex factorization into sparse spatial and smooth temporal components, combined with spectral initialization and gradient descent.
result The proposed method achieves linear convergence and superior performance compared to existing approaches.
SDP achieves exponential error rate in cluster estimation for Stochastic Block Model.
problem Cluster estimation in Stochastic Block Model.
method Semidefinite Programming (SDP) formulation.
result SDP achieves exponential error rate in signal-to-noise ratio.
Improved subspace recovery algorithm with dimension-independent error and polynomial time.
problem Efficiently recover a covariance matrix from a mix of inliers and adversarial outliers.
method List-decodable subspace recovery algorithm with faster fixed-polynomial time and less restrictive distributional assumptions.
result Achieved dimension-independent error guarantee of O(1/α) with poly(1/α d^O(1)) time complexity.
The paper analyzes prediction and recovery bounds for noisy ordinal embedding.
problem Predicting and recovering embeddings from noisy distance comparisons.
method Derives prediction error bounds, investigates Maximum Likelihood estimator, proposes new algorithms.
result Relates prediction errors to embedding accuracy through a nonlinear map.
New algorithm clusters networks with outliers, achieving exact recovery.
problem Clustering networks with outliers and degree corrections.
method Convex optimization with a penalization term for positive deviations.
result Achieves exact recovery of clusters under mild conditions.
New algorithm recovers matrices that are both low rank and sparse in rows and columns.
problem Recovering matrices that are simultaneously low rank and row/column sparse.
method Gradient Descent with hard Thresholding (GDT) algorithm to minimize a bi-convex function over a nonconvex set of constraints.
result GDT achieves linear convergence to near optimal solutions with statistical error.
Consider the recovery of an unknown signal x from quantized linear measurements. In the one-bit compressive sensing setting, one typically assumes that x is sparse, and that the measurements are of the form sign(⟨ai,x⟩)∈{±1}. Since such measurements give no informati…
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 findings on computational limits for estimating hidden structures.
problem Estimating hidden structures in noisy data.
method Use of low-degree polynomials as a restricted model of computation.
result Established low-degree hardness of recovery problems for easy detection problems.
The paper provides entrywise bounds for Sparse PCA, improving upon previous results.
problem Sparse Principal Component Analysis (PCA) recovery error characterization in spectral or Frobenius norms.
method Entrywise ℓ2,∞ bounds for Sparse PCA under general high-dimensional subgaussian design, using sparsistent algorithms. result Improved entrywise bounds for Sparse PCA, finer characterization of estimation error.
Paper connects neural network hyperparameter optimization and NAS to structured sparse recovery.
problem Hyperparameter optimization and neural architecture search in neural networks.
method Structured sparse recovery methods applied to HPO and NAS.
result Improvements in hyperparameter optimization and discovery of novel neural architectures.
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.
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation matrix completion in various fields such as the financial market and the low-ra…
Study iterative regularization for linear models with convex bias, improving robust sparse recovery.
problem Improving robust sparse recovery with iterative regularization for linear models.
method Primal-dual gradient approach, analyzing convergence in presence of noise, combining regularization and optimization.
result Theoretical results show state-of-the-art performances with computational speed-ups.
Convex optimization with expander matrices improves sparse recovery efficiency.
problem Sparse recovery from linear measurements using expander matrices.
method Use of expander matrices for linear sketches in convex optimization to recover block-sparse matrices.
result The recovery error can be expressed in terms of the model-based norm, ensuring the solution is within the model.
These notes review six lectures given by Prof. Andrea Montanari on the topic of statistical estimation for linear models. The first two lectures cover the principles of signal recovery from linear measurements in terms of minimax risk. Subsequent lectures demonstrate the application of these principles to several pract…
Geometric framework links clustering accuracy to structural recovery.
problem Understanding the trade-off between robustness and sensitivity in clustering.
method Develops a clustering condition number to compare within-cluster scale to the minimum loss increase required to move a point across a cluster boundary.
result Sharp phase transitions for exact recovery under different objectives, providing geometric principle for interpreting low objective values.
AMP with Gaussian initialization shows weak-recovery threshold for phase retrieval.
problem Phase retrieval with noiseless data.
method Approximate message passing with random initialization.
result Random initialization attains weak-recovery threshold \( \delta_{ ext{weak}} = 1/2 \).