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.
Paper studies superconvergence on surface meshes using gradient recovery.
problem Proving superconvergence on deviated surfaces.
method Introduces geometric supercloseness and an algorithmic framework for gradient recovery.
result Validates theoretical results with numerical examples.
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 proposes a multi-task model for CECT macromolecule classification, segmentation, and recovery.
problem Challenges in recognizing and recovering macromolecular structures due to structural diversity and imaging limitations.
method A novel multi-task 3D CNN model that shares learned features across tasks.
result Multi-task model outperforms single-task methods and discovers novel structures.
HSNLD solves robust Hankel recovery efficiently and robustly.
problem Robust Hankel recovery of sparse outliers and missing entries.
method Hankel Structured Newton-Like Descent (HSNLD) algorithm.
result HSNLD achieves linear convergence independent of the condition number.
In recent years research on credit risk modelling has mainly focused on default probabilities. Recovery rates are usually modelled independently, quite often they are even assumed constant. Then, however, the structural connection between recovery rates and default probabilities is lost and the tails of the loss distri…
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.
We study the problem of corrupted sensing, a generalization of compressed sensing in which one aims to recover a signal from a collection of corrupted or unreliable measurements. While an arbitrary signal cannot be recovered in the face of arbitrary corruption, tractable recovery is possible when both signal and corrup…
The paper analyzes the stability of parameter recovery in Linear Structural Equation Models.
problem Understanding the stability of parameter recovery in Linear Structural Equation Models (LSEM).
method Condition number analysis for bow-free LSEM and random input parameter analysis.
result For bow-free LSEM, parameter recovery is stable under certain conditions and with high probability.
The current research on credit risk is primarily focused on modeling default probabilities. Recovery rates are often treated as an afterthought; they are modeled independently, in many cases they are even assumed constant. This is despite of their pronounced effect on the tail of the loss distribution. Here, we take a …
In "extreme" computational imaging that collects extremely undersampled or noisy measurements, obtaining an accurate image within a reasonable computing time is challenging. Incorporating image mapping convolutional neural networks (CNN) into iterative image recovery has great potential to resolve this issue. This pape…
We consider the problem of signal recovery on graphs as graphs model data with complex structure as signals on a graph. Graph signal recovery implies recovery of one or multiple smooth graph signals from noisy, corrupted, or incomplete measurements. We propose a graph signal model and formulate signal recovery as a cor…
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.
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…
Paper proposes efficient methods for clustering and signal recovery in high-dimensional data with block structures.
problem High-dimensional clustering and signal recovery under block signal structures.
method CFA-PCA and MA-PCA methods for sparse and dense block signals.
result Proposed methods achieve computational minimax optimality for clustering and signal recovery.
Improved algorithm for partial recovery of tree-structured graphs with noisy data.
problem Learning Ising tree models with noisy observations.
method Symmetrized Geometric Averaging (SGA) algorithm with improved sample complexity.
result Significantly better sample complexity for partial tree recovery.
The paper tackles partial inference in structured prediction using a convex optimization approach.
problem Maximizing a score function with unary and pairwise potentials in graph label spaces.
method Generative model approach with two-stage convex optimization for label recovery.
result Conditions for recovering a majority of labels with provable guarantees.
Study reveals issues with neural autoregressive models and proposes mode recovery cost.
problem Unreasonable affinity of neural autoregressive models to short and long sequences.
method Investigates modes of ground-truth, empirical, and decoding-induced distributions via mode recovery cost.
result Mode recovery cost varies depending on ground-truth distribution and impacts decoding-induced distribution.
In recent years, a class of dictionaries have been proposed for multidimensional (tensor) data representation that exploit the structure of tensor data by imposing a Kronecker structure on the dictionary underlying the data. In this work, a novel algorithm called "STARK" is provided to learn Kronecker structured dictio…
We consider the effect of recovery rates on a pool of credit assets. We allow the recovery rate to depend on the defaults in a general way. Using the theory of large deviations, we study the structure of losses in a pool consisting of a continuum of types. We derive the corresponding rate function and show that it has …
Paper explores limits of high-order clustering with planted structures.
problem Statistical and computational limits of high-order clustering with planted structures.
method Developed methods for detection and recovery of clusters, identified signal-to-noise ratio boundaries.
result Sharp boundaries of signal-to-noise ratio for statistical and computational feasibility.
New method improves traffic data recovery for streaming data.
problem Improve data quality in traffic data for ITS.
method Online robust tensor recovery algorithm leveraging spatio-temporal correlations and local consistency.
result Significantly improved computational efficiency and high recovery accuracy.
Two methods improve tensor recovery in Ising models, revealing gene interactions.
problem Improving tensor recovery in Ising models for complex data structures.
method Pseudolikelihood and interaction screening approaches for tensor learning.
result Both methods achieve tensor recovery with sample size logarithmic in nodes, exponential in strength and degree.
Survey of structured low-rank algorithms for MR signal recovery.
problem Recovering multidimensional signals from few non-uniform measurements.
method Structured low-rank matrix completion formulation.
result Performance guarantees and fast algorithms for large-scale MR problems.
Guarantees sparse recovery for neural networks with iterative hard thresholding.
problem Recovering sparse network weights in neural networks.
method Structural properties of sparse network weights and iterative hard thresholding algorithm.
result Simple iterative hard thresholding algorithm recovers sparse network weights exactly using linear memory.
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.
StrTransformer recovers sources without labels by optimizing latent matrices and enforcing structural constraints.
problem Unsupervised blind source recovery in signal processing.
method Source-wise structured Transformer framework with latent source matrix optimization, structural regularization, and branch-specific weights.
result StrTransformer learns distinct temporal-scale structures and recovers source-aligned latent trajectories.
We study graph matching with correlated Gaussian features and find thresholds for exact recovery.
problem Graph matching with correlated Gaussian features.
method Information-theoretic thresholds and conditions for exact and almost exact recovery.
result Contextual information introduces a richer structure, with thresholds for exact and almost exact recovery no longer coinciding.
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 examine the recovery of block sparse signals and extend the framework in two important directions; one by exploiting signals' intra-block correlation and the other by generalizing signals' block structure. We propose two families of algorithms based on the framework of block sparse Bayesian learning (BSBL). One fami…
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.
While defaults are rare events, losses can be substantial even for credit portfolios with a large number of contracts. Therefore, not only a good evaluation of the probability of default is crucial, but also the severity of losses needs to be estimated. The recovery rate is often modeled independently with regard to th…
This work provides a guaranteed tensor recovery method by combining low-rankness and smoothness priors.
problem Guaranteed tensor recovery with theoretical guarantees for low-rank and smoothness priors.
method Developed a new regularization term that combines low-rankness and smoothness priors, proving exact recovery guarantees.
result Rigorously proved exact recovery guarantees for tensor completion and tensor robust principal component analysis.
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.
This paper develops a general theoretical framework to analyze structured sparse recovery problems using the notation of dual certificate. Although certain aspects of the dual certificate idea have already been used in some previous work, due to the lack of a general and coherent theory, the analysis has so far only be…
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…
Unified framework for pattern recovery in penalized and thresholded estimation.
problem Pattern recovery in penalized and thresholded estimation methods.
method Defining a novel pattern notion based on subdifferentials, introducing accessibility and noiseless recovery conditions.
result Unified and extended conditions for pattern recovery in a broad class of penalized estimators.
We give a comprehensive review of credit term structure modeling methodologies. The conventional approach to modeling credit term structure is summarized and shown to be equivalent to a particular type of the reduced form credit risk model, the fractional recovery of market value approach. We argue that the corporate p…
The study uses Random Matrix Theory to identify structural changes in stock markets during shocks.
problem Understanding structural changes in stock markets during exogenous shocks.
method Random Matrix Theory and complexity gap analysis.
result The complexity gap collapses during shocks, indicating strong synchronization, and widens before shocks, signaling a rich structure.
Bottom-up algorithms outperform top-down in hierarchical community detection at intermediate levels.
problem Finding the optimal hierarchical community structure in networks.
method A bottom-up algorithm for hierarchical clustering of networks.
result Bottom-up algorithms achieve the information-theoretic threshold for exact recovery at intermediate levels of the hierarchy.
Paper proposes a novel graph recovery attack from node embeddings.
problem Privacy risks of integrating graph embeddings with machine learning pipelines.
method Model-agnostic graph recovery attack exploiting preserved structural information in node embeddings.
result Adversaries can recover graph edges with decent accuracy from node embeddings alone.
A new method for efficient causal structure learning at scale.
problem Causal structure learning is computationally challenging at scale.
method Relaxed sparsest-permutation formulation with support-level relaxation and masked zero-fill incomplete Cholesky factorization.
result The method enables scalable comparison of candidate orderings and matches the accuracy of slower baselines.
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.
Integrating wind power into the grid is challenging because of its random nature. Integration is facilitated with accurate short-term forecasts of wind power. The paper presents a spatio-temporal wind speed forecasting algorithm that incorporates the time series data of a target station and data of surrounding stations…
Detection of dense cycles in graphs reveals a gap between easy detection and hard recovery.
problem Detecting and recovering dense cycles in Erdős-Rényi graphs.
method Characterization of computational thresholds for detection and recovery using low-degree polynomial algorithms.
result A gap exists between the detection and recovery thresholds for certain parameter regimes.
Improved image reconstruction from sparse measurements using generative models.
problem Signal recovery from limited compressed measurements.
method Generative model with constrained latent variables for stable signal reconstruction.
result Improved reconstruction accuracy and preservation of realistic features.
New risk measure improves creditor protection in financial regulation.
problem Current solvency requirements fail to control the size of recovery on creditors' claims.
method Developed Recovery Value at Risk (Recovery VaR) to control recovery on creditors' claims.
result Recovery VaR flexibly controls recovery on creditors' claims and integrates protection needs into management incentives.
A new clustering method improves recovery guarantees by re-embedding data.
problem Improving recovery guarantees in clustering algorithms.
method Chaining four techniques: leapfrog distances, multidimensional scaling, spectral methods, and sum-of-norms clustering.
result Re-embedding data improves recovery guarantees of clustering.