Paper tackles graph estimation with approximate recovery criteria, matching exact recovery bounds in many cases.
problem Estimating the graph of an Ising model with approximate recovery criteria.
method Adopting approximate recovery criterion, using Fano's inequality and graph ensembles to derive lower bounds.
result Lower bounds on sample complexity match exact recovery bounds in many cases, indicating similar difficulty.
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.
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.
We study signal recovery on graphs based on two sampling strategies: random sampling and experimentally designed sampling. We propose a new class of smooth graph signals, called approximately bandlimited, which generalizes the bandlimited class and is similar to the globally smooth class. We then propose two recovery s…
WARPd method solves inverse problems with approximate sharpness conditions.
problem Reconstruction of signals from undersampled and noisy measurements.
method First-order method based on primal-dual iterations with restart-reweight scheme.
result WARPd achieves stable linear convergence under generic approximate sharpness condition.
Greedy method improves low rank matrix estimation with new approximation guarantees.
problem Low rank matrix estimation under restricted strong convexity and smoothness.
method Novel greedy algorithm analysis linking to combinatorial optimization.
result Improved approximation guarantees and statistical recovery.
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. Paper proposes a new method for recovering missing samples in images.
problem Missing sample recovery in image signals.
method Iterative sparse recovery algorithm using constrained l1-norm minimization with a new CSIM fidelity metric. result Simulation results demonstrate the efficiency of the proposed method.
DeepInverse learns to invert signals faster than traditional methods.
problem Slow convergence and non-sparse real-world data in compressive sensing.
method Develops a deep convolutional network to learn the inverse signal transformation.
result DeepInverse network approximates state-of-the-art CS recovery algorithms but is significantly faster.
Paper extends tensor recovery method for low CP-rank tensors.
problem Recovery of low-rank tensors from few measurements.
method Iterative Hard Thresholding with tensor version of RIP.
result Exact recovery of tensors with low CP-rank is guaranteed.
Symmetry helps VI recover certain statistics.
problem Understanding how symmetry in variational inference affects the recovery of statistics.
method Developed a general theory of symmetry-induced statistic recovery in variational inference.
result Symmetry can force the recovery of certain statistics in VI, even under model misspecification.
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.
Neural networks can approximate positive homogeneous functions, especially with multiple hidden layers.
problem Approximating positive homogeneous functions with neural networks.
method Using scale-invariant ReLU networks with multiple hidden layers.
result Approximation of positive homogeneous functions is possible with neural networks, especially with two hidden layers.
This paper improves diffusion models for low-dimensional data.
problem Theoretical foundations of diffusion models are lacking for low-dimensional data.
method Score approximation, estimation, and distribution recovery of diffusion models on low-dimensional data.
result Sample complexity bounds for distribution estimation using diffusion models are provided.
Develops PRPCA for smooth image recovery combining low-rank and smoothness.
problem Image matrix recovery under low-rank and smoothness assumptions.
method Projected Robust PCA (PRPCA) framework combining low-rank and smoothness.
result Explicit statistical guarantees for PRPCA, reducing matrix dimensionality.
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 \( \delta_{ ext{weak}} = 1/2 \).
Paper proposes a new method for MRI data recovery using bi-linear modeling.
problem Recovering high-fidelity MRI data from dynamic sequences.
method Bi-linear modeling framework for manifold learning and sparse approximation.
result The method improves MRI data recovery over existing techniques.
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.
New algorithms recover differential equations from short bursts of data.
problem Locally recover unknown governing differential equations from measurement data.
method Approximate governing equations using standard basis functions and short bursts of trajectory data.
result Effective numerical algorithms recover accurate governing equations from short bursts of data.
Simplifies solving noisy SDPs for low rank matrix recovery problems.
problem Solving SDPs with noisy data for low rank matrix recovery problems.
method Identifies conditions called simplicity to limit error in noisy SDP solutions.
result Simple SDPs can be efficiently solved and their approximate solutions trusted.
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.
Empirical observations of CNN invertibility explained with a mathematical model.
problem Understanding why Convolutional Neural Networks (CNNs) are approximately invertible.
method Developed a mathematical model of sparse signal recovery consistent with random-weight CNNs, connecting to model-based compressive sensing.
result CNNs trained with random weights are consistent with the mathematical model and can be used for reasonable image reconstruction.
Study generalizes matrix completion with side info in low noise settings.
problem Matrix completion with side information in low noise conditions.
method Inductive matrix completion with i.i.d. subgaussian noise, uniform sampling, and side information.
result Generalization bounds with noise scaling, convergence to zero, and logarithmic dependence on matrix size.
Auto-encoders can recover true signals under certain conditions.
problem Signal recovery from auto-encoders.
method Highly incoherent weight matrices and unit ℓ2 row length, negative bias vectors equal to data mean. result True hidden representation can be approximately recovered with increasing sparsity.
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.
New definition of joint stationarity improves process recovery over graphs.
problem Regression tasks with high-dimensional multivariate processes dependent on graph topology.
method Introduces joint stationarity, a new definition that reduces estimation variance and complexity.
result One reliably learns covariance structure from a single realization and solves MMSE problems nearly linearly in time.
This paper explores how random sampling and coding can speed up approximate matrix multiplication.
problem Efficiently computing large-scale matrix multiplications in distributed systems.
method Proposes two schemes: coding for recovery and random sampling for approximation.
result Investigates tradeoffs between recovery threshold and approximation error.
Paper shows moderate RIP is insufficient for avoiding spurious local minima in matrix recovery.
problem The need for moderate RIP to avoid spurious local minima in matrix recovery.
method Analyzes the necessity of RIP constants and provides counterexamples.
result Counterexamples show spurious local minima exist even with moderate RIP.
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.
New method recovers matrix column space with active sampling for better results.
problem Recovering column space of partially observed matrices with limited data.
method Alternating minimization with active sampling strategy.
result Active sampling improves convergence to true column space with higher probability.
New method solves sparse approximation problem using trimmed lasso and generalized soft-min penalties.
problem Sparse approximation or best subset selection problem.
method Regularized approach with trimmed lasso and generalized soft-min penalties.
result The trimmed lasso provides sparse recovery guarantees and a practical optimization algorithm.
Study reveals efficient recovery of multi-modal signals via Bayesian methods and sequential learning.
problem Recovering multiple high-dimensional signals from correlated modalities.
method Bayesian Approximate Message Passing and Sequential Curriculum Learning.
result Sequential learning strategy optimally recovers weak signals in multi-modal settings.
Optimizes sparse signal recovery using nonlinear approximations.
problem Recovering sparse stochastic signals efficiently.
method Probabilistic approach with linear and nonlinear estimators.
result Structured estimator outperforms linear in MSE.
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.
Combines VAMP with EM for joint signal and parameter recovery.
problem Recovering signals from noisy linear measurements with unknown parameters.
method Vector approximate message passing (VAMP) combined with Expectation-Maximization (EM).
result EM-VAMP algorithm yields stationary points of a free-energy, providing a variational interpretation.
High precision analytical approximation is proposed for variance-covariance based risk allocation in a portfolio of risky assets. A general case of a single-period multi-factor Merton-type model with stochastic recovery is considered. The accuracy of the approximation as well as its speed are compared to and shown to b…
Optimal spectral estimators and AMP combine for efficient weak recovery in orthogonally invariant GLMs.
problem Parameter estimation from generalized linear models with complex correlation structures.
method Spectral initialization and approximate message passing (AMP) algorithm.
result Established rigorous performance guarantees for spectral initialization and AMP.
Algorithm finds a subspace minimizing distances to inliers with outliers.
problem Finding a k-dimensional subspace minimizing distances to inliers with outliers. method Extends dimension reduction techniques and bi-criteria approximations based on sampling.
result Efficient algorithm for multiplicative (1+ε)-approximation of optimal solution. The paper develops a new framework for managing asymmetric volatility.
problem Managing asymmetric volatility to improve recovery and participation.
method Path-dependent framework for asymmetric volatility management.
result Skew engineering reduces harmful downside participation more than productive upside participation.
New method recovers clean data from corrupted samples.
problem Recovering clean data from corrupted samples with uncertainty.
method Probabilistic Tomographic Auto-Encoder method that derives reduced entropy condition approximate inference.
result Superior performance in imputation and de-noising compared to existing methods.
Paper provides recovery guarantees for weighted low-rank approximation via alternating minimization.
problem Recovering a low-rank matrix from noisy observations.
method Simple alternating minimization algorithm with clipping step.
result Bounding the spectral norm of the difference between recovered and ground truth matrices.
New algorithms recover low-rank matrices from few noisy projections.
problem Estimating low-rank matrices from rank-one projections with noise.
method Two fast, non-convex algorithms for matrix recovery.
result Proposed algorithms achieve linear convergence and independent sample complexity of condition number.
Paper develops DLTF to learn optimized dictionaries for efficient thresholded feature recovery.
problem Efficiently recover sparse code support from time-consuming sparse coding.
method Formulates DLTF model to learn optimized dictionary for thresholded feature, derives log-linear time proximal operator.
result DLTF model demonstrates remarkable efficiency, effectiveness, and robustness in various tasks.
It is a well known fact that recovery rates tend to go down when the number of defaults goes up in economic downturns. We demonstrate how the loss given default model with the default and recovery dependent via the latent systematic risk factor can be estimated using Bayesian inference methodology and Markov chain Mont…
This paper considers compressed sensing and affine rank minimization in both noiseless and noisy cases and establishes sharp restricted isometry conditions for sparse signal and low-rank matrix recovery. The analysis relies on a key technical tool which represents points in a polytope by convex combinations of sparse v…
Paper develops a novel kernel-based method for MRI data recovery.
problem Reconstructing dynamic MRI data on manifolds.
method Kernel bi-linear modeling in reproducing kernel Hilbert spaces.
result Validated on synthetic dMRI data, the method outperforms state-of-the-art approaches.
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.
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.