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.
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…
We address some theoretical guarantees for Schatten-p quasi-norm minimization (p∈(0,1]) in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measurement operator, we provide a sufficient condition for exact recovery of low-rank matrices. This condition…
Given an overcomplete dictionary A and a signal b that is a linear combination of a few linearly independent columns of A, classical sparse recovery theory deals with the problem of recovering the unique sparse representation x such that b=Ax. It is known that under certain conditions on A, x can be re…
The paper tackles subspace-preserving recovery of sparse signals from overcomplete dictionaries.
problem Recovering sparse signals from overcomplete dictionaries when the signal lies in a subspace of the dictionary.
method Geometric conditions and covering radius/angular distance to ensure subspace-preserving recovery.
result Theoretical analysis shows that subspace-preserving recovery is possible without requiring incoherence or restricted isometry of the dictionary.
This paper improves credit risk analysis by incorporating state-dependent recovery rates into a factor model.
problem Accurate default forecasting in credit risk analysis.
method Extends a one-factor Gaussian copula model to include state-dependent recovery rates and a common factor.
result The proposed model outperforms other models in default prediction, especially during hectic periods.
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.
New guarantees for uniquely identifying transport maps and vector fields from finite measure-valued data.
problem Unique recovery of transport maps and vector fields from finite measure-valued data.
method Use of Whitney and Takens embedding theorems to establish conditions for unique identification.
result New metric for comparing diffeomorphisms and analogous results in infinitesimal settings.
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.
New analysis enables inversion of deep generative models with unique solutions.
problem Inverting deep generative models like GANs and VAEs.
method Sparse representation theory and layer-wise inversion pursuit algorithms.
result Invertible solutions for generative models with unique latent vectors.
Adaptive IP approach optimizes intervention design for causal graph recovery.
problem Designing efficient interventions to recover causal relationships from data.
method Iterative integer programming approach for optimizing information gain.
result Adaptive IP approach achieves full causal graph recovery with fewer interventions.
This paper develops a spectral theory of Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space (Borel right process (BRP)) and the stochastic discount factor (SDF) is a positive semimartingale multiplicative functional of X. A key …
In this paper we formulate a corporate bond (CB) pricing model for deriving the term structure of default probabilities (TSDP) and the recovery rate (RR) for each pair of industry factor and credit rating grade, and these derived TSDP and RR are regarded as what investors imply in forming CB prices in the market at eac…
Concave regularization methods provide natural procedures for sparse recovery. However, they are difficult to analyze in the high dimensional setting. Only recently a few sparse recovery results have been established for some specific local solutions obtained via specialized numerical procedures. Still, the fundamental…
New method improves human mesh recovery for obese people.
problem Improving mesh recovery for obese people.
method Generative optimization of mesh parameters from 2D keypoints.
result Significant improvement in mesh recovery performance on obese person images.
We study the problem of recovery both the attenuation a and the source f in the attenuated X-ray transform in the plane. We study the linearization as well. It turns out that there are natural Hamiltonian flow that determines which singularities we can recover. If the perturbations δa, δf are supported in a com…
The study analyzes aftershocks of stock market crashes using statistical methods.
problem Understanding the aftershocks of stock market crashes during crises.
method Structural break analysis and statistical methods applied to 1987 crash, 2008 financial crisis, and 2020 COVID-19 pandemic.
result The recovery of stock price during the COVID-19 pandemic may be faster than the financial crisis of 2008.
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.
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
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 ℓ1-regularized PCA problem. result Support of the sparse leading eigenvector can be recovered with high probability.
This research tackles sample complexity in causal graph recovery with temporal heterogeneity.
problem Recovering a unique causal graph from observational data with temporal heterogeneity.
method Integrates time-series dynamics and multi-environment heterogeneity to constrain the problem, enabling a rigorous analysis of statistical limits.
result Unified necessary identifiability conditions and explicit information-theoretic bounds quantify the sample complexity under different noise distributions.
Spectral flow connects manifold geometry to rigidity criteria.
problem Tackling rigidity of simply-connected closed manifolds.
method Spectral deformation flow and invariant-based approach.
result Spherical profile is the unique manifold-compatible asymptotic realization.
Paper recovers latent causal structure and linear transformation from indirect observations.
problem Recovering latent causal structure and linear transformation from indirect observations.
method Established sufficient conditions for DAG recovery, leveraged score function properties, and used soft/hard interventions.
result Perfect recovery of latent DAG structure and linear transformation up to scaling using soft interventions, hard interventions with additional hypothesis testing.
This study develops a dynamic inverse optimization framework to recover hidden, time-varying preferences from observed allocation trajectories.
problem The gap between classical optimization theory and real-world practice, especially in the presence of drift and shocks.
method Dynamic inverse optimization framework using a drift-aware estimator grounded in convex analysis and online learning theory.
result Sharp static and dynamic regret bounds for the framework, demonstrating its responsiveness to gradual drift and sudden shocks.
We model the term structure of the forward default intensity and the default density by using Lévy random fields, which allow us to consider the credit derivatives with an after-default recovery payment. As applications, we study the pricing of a defaultable bond and represent the pricing kernel as the unique solution …
New approach improves classification guarantees by focusing on direction rather than regression risk.
problem Improving classification guarantees in binary classification problems.
method Establishing a geometric distinction between classification and regression, leveraging scale invariance.
result Improved guarantees for classification risk compared to regression risk.
This paper describes a flexible and tractable bottom-up dynamic correlation modelling framework with a consistent stochastic recovery specification. The stochastic recovery specification only models the first two moments of the spot recovery rate as its higher moments have almost no contribution to the loss distributio…
Signed pairwise interactions conflate uniqueness, redundancy, and synergy
problem Signed pairwise interactions conflate uniqueness, redundancy, and synergy
method Stochastic Hi-Fi
result Stochastic Hi-Fi recovers structure missed by scalar baselines
Generative adversarial networks (GANs) transform latent vectors into visually plausible images. It is generally thought that the original GAN formulation gives no out-of-the-box method to reverse the mapping, projecting images back into latent space. We introduce a simple, gradient-based technique called stochastic cli…
There is a recent surge of interest in identifying the sharp recovery thresholds for cluster recovery under the stochastic block model. In this paper, we address the more refined question of how many vertices that will be misclassified on average. We consider the binary form of the stochastic block model, where n ver…
Paper analyzes VI for location-scale families, proving robustness guarantees for mean and correlation recovery.
problem Misspecification in VI for intractable target densities.
method Variational inference on location-scale families with symmetries.
result VI recovers mean and correlation matrix under specific symmetries.
New algorithm recovers 3D molecule structures from noisy data.
problem Recovering 3D molecule structures from noisy, randomly rotated copies.
method Smoothed analysis of orbit recovery over SO(3) using frequency marching. result Quasi-polynomial time algorithm for orbit recovery over SO(3). Develops a new solver for path-dependent PDEs using signature kernels.
problem Solving path-dependent PDEs (PPDEs) efficiently and accurately.
method Uses signature kernels to solve PPDEs by approximating the solution with minimal norm in a reproducing kernel Hilbert space.
result Proves the consistency of the numerical scheme, ensuring convergence to PPDE solutions as the number of collocation points increases.
We generalize Merton's asset valuation approach to systems of multiple financial firms where cross-ownership of equities and liabilities is present. The liabilities, which may include debts and derivatives, can be of differing seniority. We derive equations for the prices of equities and recovery claims under no-arbitr…
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.
CPR models complex decision processes by breaking them into context-specific policies, improving interpretability and accuracy.
problem Interpreting dynamic human decision-making processes in medical contexts.
method Develops Contextualized Policy Recovery (CPR) framework for multi-task learning, modeling each context-specific policy as a linear map.
result Achieves state-of-the-art performance in predicting medical decisions, closing the gap between interpretable and black-box methods.
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.
New method identifies physical constants from video data alone.
problem Identifying physical constants from video data.
method Proves level-set slope-coverage condition ensures local affine mapping to true physical state, enabling exact parameter recovery.
result Underdamped systems identifiable from a single video clip, other regimes require three diverse trajectories.
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 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…
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.
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 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.
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 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.