arXiv research

The paper improves conditions for unique recovery in homomorphic sensing of subspaces.

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 ($p \in (0,1]$) 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 $b = A x$. It is known that under certain conditions on $A$, $x$ can be re…

Given an overcomplete dictionary $A$ and a signal $b = Ac^*$ for some sparse vector $c^*$ whose nonzero entries correspond to linearly independent columns of $A$, classical sparse signal recovery theory considers the problem of whether $c^*$ can be recovered as the unique sparsest solution to $b = A c$. It is now well-…

This paper improves credit risk analysis by incorporating state-dependent recovery rates into a factor model.

This work provides a guaranteed tensor recovery method by combining low-rankness and smoothness priors.

New guarantees for uniquely identifying transport maps and vector fields from finite measure-valued data.

New method recovers matrices with nonlinear structures using optimization on Grassmann manifold.

New analysis enables inversion of deep generative models with unique solutions.

Adaptive IP approach optimizes intervention design for causal graph recovery.

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.

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.

Simplifies solving noisy SDPs for low rank matrix recovery problems.

Recover simple irreversible Finsler geometry from travel time data

The paper analyzes sparse PCA for incomplete data and proves support recovery conditions.

This research tackles sample complexity in causal graph recovery with temporal heterogeneity.

Spectral flow connects manifold geometry to rigidity criteria.

Paper recovers latent causal structure and linear transformation from indirect observations.

This study develops a dynamic inverse optimization framework to recover hidden, time-varying preferences from observed allocation trajectories.

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.

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

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.

New algorithm recovers 3D molecule structures from noisy data.

Develops a new solver for path-dependent PDEs using signature kernels.

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.

Method uses Seq2Seq learning to automatically generate recovery commands for ICT systems.

CPR models complex decision processes by breaking them into context-specific policies, improving interpretability and accuracy.

A new model explains U- and Swoosh-shaped stock price recovery during the COVID-19.

New method identifies physical constants from video data alone.

This paper improves support recovery in universal one-bit compressed sensing.

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 $\ell_1$ 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.

Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing works on tensor recovery have focused on data losses and random noises. Only a few …

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.

HSNLD solves robust Hankel recovery efficiently and robustly.

New method improves dictionary recovery from over-realized models.