Advances word embedding methods using Markov processes.
problem Improving semantic understanding of word representations.
method Ground embeddings in cognitive literature, unify and generalize metric recovery methods.
result New algorithms for metric recovery and embedding on graphs and manifolds.
Paper explores exact recovery of communities in weighted graphs using Gaussian and exponential distributions.
problem Exact recovery of communities in weighted graphs with Gaussian and exponential distributions.
method Introduces a new semi-metric to describe conditions for exact recovery and analyzes conditions for both complete and incomplete graphs.
result Necessary and sufficient conditions for exact recovery are asymptotically tight and applicable to both complete and incomplete graphs.
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.
Study on Gaussian-width complexity on statistical manifolds and its applications in learning and recovery.
problem Understanding the geometry of statistical manifolds and its implications for learning and recovery.
method Analysis of Fisher width and inverse-Fisher width, proving their complementary roles and establishing a relation between them.
result Established a sharp relation between Fisher width and inverse-Fisher width, showing they cannot reduce relative to Euclidean scale.
The paper tracks patient recovery using graphs of joint movement data.
problem Tracking individual patient recovery trajectories in physical therapy.
method Bayesian learning of Random Geometric Graphs from joint movement data.
result Optimal exercise routines can be recommended based on patient recovery data.
The paper recovers node-variables from noisy pairwise measurements using information theory.
problem Recovering node-variables from noisy pairwise measurements.
method Developed a unified framework using information-theoretic tools to characterize recovery criteria for various graph structures and channel transition measures.
result Characterized the minimum channel divergence measures and the minimum sample complexity for exact recovery.
New method recovers clusters in non-convex finite metric spaces with oracle queries.
problem Exact recovery of clusters in non-convex finite metric spaces.
method Introducing (β,γ)-convexity and a deterministic algorithm using oracle queries. result Clusters can be recovered using O(k2logn+k2(6/βγ)dens(X)) same-cluster queries. Study recovers Lorentzian metrics from boundary data, proving local rigidity.
problem Recovering a Lorentzian metric from scattering data on a boundary.
method Analyzes jet and real analyticity of metrics near lightlike points.
result Metric can be recovered up to gauge transformations near lightlike strictly convex points.
We analyze directed, unweighted graphs obtained from xi∈Rd by connecting vertex i to j iff ∣xi−xj∣<ε(xi). Examples of such graphs include k-nearest neighbor graphs, where ε(xi) varies from point to point, and, arguably, many real world graphs such as co-purchasing graphs. We ask whethe…
Unified framework for uniform signal recovery in nonlinear GCS with 1-bit/quantized measurements.
problem Uniform recovery guarantees for nonlinear generative compressed sensing.
method Unified framework using generalized Lasso and Lipschitz approximation.
result Uniform recovery of all signals in the ball up to an error of ε using approximately O(k/ε^2) samples.
Metric can be recovered from full ordinal information on a geodesic space.
problem Recovering a metric from full ordinal information in a geodesic space.
method Constructing a metric based on full ordinal information and establishing a Gromov-Hausdorff distance bound.
result The metric can be uniquely determined from full ordinal information up to a constant factor.
A new method for signal recovery in high dimensions using projections and diffusion models.
problem Recovering a latent signal from noisy observations with unknown support.
method Metric projection estimator based on score matching in a diffusion model.
result The posterior distribution concentrates near the metric projection of the observed signal.
We derive an arbitrage free relationship between recovery swap rates, digital default swap spreads and conventional CDS spreads, and argue that the fair forward recovery rate used in recovery swaps must contain a convexity premium over the expected recovery value.
A-Ward p{eta} improves hierarchical clustering with faster convergence and better recovery.
problem Hierarchical clustering's slow convergence and limited cluster variety.
method Anomalous pattern initialisation and extension of Ward and Ward p algorithms.
result A-Ward p{eta} provides better cluster recovery than Ward and Ward p.
New method beats volumetric barrier for manifold recovery.
problem Reconstructing latent geometry from noisy distances.
method Orthogonal Ring Distance Estimation Routine (ORDER).
result Achieves pointwise distance estimation of order n−2/(d+5). Transfer learning improves loan recovery rate forecasting under data scarcity.
problem Data scarcity in loan portfolios limits RR modeling accuracy.
method Introduces FT-MDN-Transformer, a mixture-density tabular Transformer architecture for TL.
result FT-MDN-Transformer outperforms baseline models in RR forecasting, especially under covariate and conditional shifts.
Method uses Seq2Seq learning to automatically generate recovery commands for ICT systems.
problem Manual decision-making for recovery commands is time-consuming and error-prone.
method Seq2Seq neural network model trained on past logs and commands.
result The model can estimate accurate recovery commands from new failures.
A new model explains U- and Swoosh-shaped stock price recovery during the COVID-19.
problem Modeling stock price recovery during the COVID-19 with V- and L-shaped recovery.
method Introducing a sentiment variable θ to quantify investor sentiment and simulate U- and Swoosh-shaped recovery. result The model explains U- and Swoosh-shaped recovery of sectoral indices with positive sentiment.
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.
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.
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 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…
Hyperbolic embeddings reduce dimensions for hierarchical data with high precision.
problem Embedding hierarchical data structures like synonym or type hierarchies efficiently.
method Combinatorial construction and hyperbolic multidimensional scaling (h-MDS) for metric spaces.
result Hyperbolic embeddings achieve high precision with few dimensions, e.g., 0.989 MAP with only 2 dimensions on WordNet.
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…
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.
This paper addresses the problem of inferring sparse causal networks modeled by multivariate auto-regressive (MAR) processes. Conditions are derived under which the Group Lasso (gLasso) procedure consistently estimates sparse network structure. The key condition involves a "false connection score." In particular, we sh…
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 on recovering Lorentzian metrics from scattering data.
problem Recovering Lorentzian metrics from scattering data on a boundary.
method Analyzing the role of boundary distance functions and linearizing the light ray transform.
result Scattering rigidity can be reduced to boundary rigidity of magnetic systems.
Deep models struggle with non-stationary Gaussian fields, but DDPM and score-SDE perform best.
problem Evaluating deep generative models on non-stationary Gaussian random fields.
method Comprehensive evaluation of four DGMs (FM, DDPM, score-SDE, VAE) on a known non-stationary Gaussian random field.
result DDPM and score-SDE recover the covariance structure reasonably well, while FM and VAE have difficulties.
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…
Study finds the cutoff for exact recovery in Gaussian mixture models.
problem Determining the separation of cluster centers for exact recovery in Gaussian mixture models.
method Used information theory and SDP relaxation of K-means clustering. result Sharp threshold for exact recovery of cluster labels without assuming cluster center symmetry.
Paper introduces robust subspace recovery methods for noisy data.
problem Finding a low-dimensional subspace in corrupted data.
method Explains advantages and disadvantages of subspace recovery algorithms.
result Outlines unsolved problems in robust subspace recovery.
Study optimal portfolio selection with Recovery Average Value at Risk, showing better control over liabilities.
problem Optimizing portfolios with a new risk measure under known or uncertain distributions.
method Existence results for mean-risk optimal portfolios under different distributional assumptions.
result Portfolio selection under Recovery Average Value at Risk provides better control over liabilities.
Bayesian model predicts sexual function recovery after prostatectomy.
problem Predicting sexual function recovery after prostatectomy surgery.
method Bayesian model using pre-treatment information.
result Personalized predictions of sexual function recovery.
Paper proves conditions for nonconvex matrix recovery to avoid spurious local minima.
problem Ensuring no spurious local minima in nonconvex matrix recovery.
method Sharp restricted isometry bounds proof technique.
result RIP constant of δ < 1/2 is necessary and sufficient for exact recovery.
Study finds economic cycle affects bank loan recovery rates.
problem Understanding how economic conditions impact bank loan recovery rates.
method Used a two-state Markov switching mechanism to model credit cycle states and analyze recovery rates.
result Recovery rates and their determinants differ between good and bad economic times.
The paper improves conditions for unique recovery in homomorphic sensing of subspaces.
problem Unique recovery of points in a linear subspace from their images under linear maps.
method Tighter and simpler conditions for unique recovery in single and subspace arrangement cases, extending to noise stability.
result Conditions for unique recovery in homomorphic sensing are improved and unified.
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.
Study evaluates DGMs' ability to recover non-stationary Gaussian fields.
problem Assessing DGMs' learning of non-stationary Gaussian random fields.
method Comprehensive evaluation of four DGMs (FM, DDPM, score-SDE, VAE) on a known non-stationary Gaussian random field.
result DDPM and score-SDE recover covariance structure reasonably well, while FM and VAE struggle.
Guarantees recovery of compressible signals from adversarial noise.
problem Recovering compressible signals from noise and adversarial attacks.
method Extends adversarial defense framework to ℓ0, ℓ2, and ℓ∞ norms. result Recovery guarantees for various signal recovery methods under different noise types.
New method improves dictionary recovery from over-realized models.
problem Theoretical guarantees for model recovery in dictionary learning are limited.
method Search over larger over-realized models to facilitate dictionary recovery.
result Model recovery can be upper-bounded by empirical risk and generalization gap.
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.
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.
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.
New sampling strategies for graph signal recovery show faster convergence rates.
problem Signal recovery on irregular graphs.
method Two sampling strategies: random and experimentally designed. Proposed recovery strategies based on these.
result Experimentally designed sampling converges faster than random sampling for irregular graphs.
Recover simple irreversible Finsler geometry from travel time data
problem Stable recovery of a simple irreversible Finsler geometry
method Use a Gromov-Hausdorff distance adapted to irreversible metric spaces
result Unique and Lipschitz-stable recovery
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.
This study models credit default swap premiums with a stochastic recovery rate.
problem Analyzing credit default swap premiums with varying recovery rates.
method Develops a model using stochastic recovery rates.
result Models credit default swap premiums effectively with a stochastic recovery rate.