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…
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48 results for “Recovery Probability”
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…
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.
OLS recovers sparse signals from noisy measurements with high probability.
problem Recovering sparse signals from noisy linear measurements.
method Orthogonal Least-Squares (OLS) algorithm under noisy conditions.
result OLS recovers true support in iterations with high probability under certain conditions.
Unified framework for constructing nonconvex sparse recovery methods.
problem Constructing valid nonconvex regularization functions remains open.
method Unified framework based on probability density function, using Weibull distribution.
result New nonconvex sparse recovery method based on Weibull distribution.
Spectral algorithm recovers clusters in hypergraph with high probability.
problem Exact recovery of clusters in hypergraph stochastic block model.
method Spectral algorithm based on adjacency matrix of hypergraph.
result Exact recovery with high probability for clusters.
Paper improves compressed sensing with prior probability information.
problem Enhancing compressed sensing accuracy with prior information.
method Designing a sensing matrix and sparse recovery algorithm using probability-based prior information.
result Proposed methods outperform existing CS systems in simulations.
Improves sparse recovery with non-linear Fourier features.
problem Sparse recovery challenges with non-linear Fourier features.
method Characterizes sufficient data points for perfect recovery.
result Sufficient data points depend on kernel matrix.
Active seriation recovers item order from noisy pairwise similarity measurements.
problem Recovering an unknown item ordering from noisy pairwise similarity measurements.
method Proposes an active seriation algorithm that provably recovers the latent ordering with high probability.
result Establishes optimal performance guarantees for successful recovery under a uniform separation condition.
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 …
The paper explores how language models can provide reliable state measurements without being interpreted as beliefs.
problem How to use language models to reliably infer states without misinterpreting them as beliefs.
method Developed a semantic map and semiparametric inverse to link language probabilities to state probabilities, avoiding hidden models.
result Conditions for existence, identification, stable recovery, and uniform stability of posterior states from observable language probabilities.
Efficient algorithm for robust recovery in stochastic block models.
problem Robust recovery in stochastic block models.
method Convex optimization framework, addressing optimization landscape challenges.
result Achieves robust recovery without a price of robustness.
Infectious Default Model with Recovery and Continuous Limitphysics.data-an
We introduce an infectious default and recovery model for N obligors. Obligors are assumed to be exchangeable and their states are described by N Bernoulli random variables S_{i} (i=1,...,N). They are expressed by multiplying independent Bernoulli variables X_{i},Y_{ij},Y'_{ij}, and default and recovery infections are …
This paper optimizes how many samples are needed to estimate a population's binary responses.
problem Estimating a distribution from incomplete or corrupted samples.
method The approach involves computing the empirical mean of a certain function, pre-solving a linear program, and using complex-analytic methods.
result Optimal sample complexity for population recovery is determined, showing phase transitions and sensitivity to dimension.
A Unified Framework for Pattern Recovery in Penalized and Thresholded Estimation and its Geometrymath.ST
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.
Partial recovery of node mappings between correlated graphs is possible under specific conditions.
problem Recovering a one-to-one mapping between nodes of two correlated graphs with a fraction of correct matches.
method Analyzing the graph isomorphism problem as a noisy version, considering Erdős-Rényi graphs, and providing conditions for partial recovery.
result Necessary and sufficient conditions for partial recovery of node mappings in correlated graphs are given.
Study exact community recovery in noisy SBM with limited queries.
problem Community recovery in noisy stochastic block models with limited queries.
method Balanced uniform querying, two-stage adaptive strategy, sublinear queries, subsampled graph.
result Adaptive querying can improve exact recovery limits in noisy SBM.
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.
A Generic Sample Splitting Approach for Refined Community Recovery in Stochastic Block Modelsstat.ML
We propose and analyze a generic method for community recovery in stochastic block models and degree corrected block models. This approach can exactly recover the hidden communities with high probability when the expected node degrees are of order or higher. Starting from a roughly correct community partition …
Study sets limits for detecting a subhypergraph in uniform hypergraphs.
problem Recovering a subhypergraph from a uniform hypergraph with different edge probabilities.
method Information-theoretic analysis for weak and exact recovery.
result Sharp conditions for weak or exact recovery of the subhypergraph.
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…
Paper proves tensor ring completion with high probability using convex optimization.
problem Recovering a multi-dimensional array from limited measurements.
method Tensor ring decomposition and convex optimization.
result High probability exact recovery with n^{d/2} r^2 ln^7(n^{d/2}) samples.
New conic relaxations improve sparse signal recovery with fewer observations.
problem Recovering sparse signals from noisy data.
method Comparing two semidefinite relaxations for sparse linear regression.
result Dong's relaxation requires fewer observations for exact recovery.
We connect Causal inference and low-rank recovery via RDT and free probability theory.
problem Determining the applicability of causal inference via low-rank recovery.
method Random Duality Theory, free probability theory, and mathematical rigor.
result Exact closed-form worst case phase transitions for causal inference.
Overparameterized ReLU Neural Networks Learn the Simplest Models: Neural Isometry and Exact Recoverycs.LG
ReLU networks learn simple models even with many parameters, overcoming traditional wisdom.
problem Generalization of overparameterized neural networks.
method Convex optimization and sparse recovery perspective applied to two-layer ReLU networks with standard weight decay.
result ReLU networks learn simple models that explain the data, analogous to sparse recovery in compressed sensing.
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.
Study uses Bayes Hilbert framework to recover probability measure flows from sensors.
problem Recovering probability measure flows from moving sensors in a Hilbert space.
method Bayes Hilbert framework, minimum-energy transport, linearization, variational theory.
result Localized sensors can recover reduced path directions but not full state space.
We study the problem of recovering a hidden community of cardinality from an symmetric data matrix , where for distinct indices , if both belong to the community and otherwise, for two known probability distributions and depending on . If $P={\r…
Study identifies Markov chain model parameters from small assortments.
problem Identifying parameters of Markov chain choice models from large assortments.
method Simple and efficient algorithm to recover parameters from assortments of sizes two and three.
result Parameters of the Markov chain choice model can be identified from assortments of sizes two and three.
New method optimizes MRI sampling patterns for faster scans.
problem Accelerate MRI scans without sacrificing image quality.
method Joint learning of adaptive sampling patterns and model-based recovery.
result Improved MR image quality compared to other methods.
Study spectral properties of sparse random graphs to recover latent vectors.
problem Recovering latent vectors in sparse random geometric graphs.
method Analyzes spectral concentration and uses orthogonal polynomial expansions, decoupling, and matrix concentration.
result Sharpens spectral norm bounds and proves exact recovery for Gaussian mixture models.
Paper tackles community recovery in binary symmetric SBM graphs.
problem Community detection in binary symmetric SBM graphs.
method Proposes a two-stage iterative method using projected power iterations and orthogonal iterations.
result Proposed method can exactly recover communities with high probability in logarithmic sparsity regime.
For a certain class of distributions, we prove that the linear programming relaxation of -medoids clustering---a variant of -means clustering where means are replaced by exemplars from within the dataset---distinguishes points drawn from nonoverlapping balls with high probability once the number of points drawn a…
Fairness constraints improve exact recovery in structured prediction models.
problem Exact recovery of fair binary node labels from noisy observations.
method Analyzed Globerson et al. (2015) model with fairness constraints and improved exact recovery for graphs with poor expansion properties.
result Fairness constraints improve the probability of exact recovery from noisy observations.
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.
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in regression, and group testing. In this paper, we take a unified approach to supp…
Algorithm recovers sparse PCA support from incomplete data.
problem Sparse PCA with incomplete and noisy data.
method Semidefinite program (SDP) relaxation of non-convex -regularized PCA.
result SDP enables exact recovery of true support of sparse leading eigenvector.
Community detection is considered for a stochastic block model graph of n vertices, with K vertices in the planted community, edge probability p for pairs of vertices both in the community, and edge probability q for other pairs of vertices. The main focus of the paper is on weak recovery of the community based on the …
New model for community detection with side information improves recovery accuracy.
problem Community detection in networks with additional node data.
method Data Block Model (DBM) with Chernoff--TV divergence for threshold characterization and efficient algorithm.
result Sharp exact recovery threshold and efficient algorithm for DBM.
The binary symmetric stochastic block model deals with a random graph of vertices partitioned into two equal-sized clusters, such that each pair of vertices is connected independently with probability within clusters and across clusters. In the asymptotic regime of and for fixe…
New method for community detection in sparse directed SBMs with exact recovery guarantees.
problem Exact recovery in sparse directed SBMs, especially with growing communities.
method Two-stage procedure: neighborhood-smoothing followed by -means clustering.
result Exact recovery of all community labels with probability tending to one under mild sparsity and separation conditions.
Optimal low rank tensor recovery requires a minimum number of entries for accurate reconstruction.
problem Exact recovery of high order tensors of low rank from a subset of their entries.
method Riemannian optimization algorithm with initial value from a spectral method, leveraging tensor restricted isometry property and curvature of the manifold.
result Tensor of size of ranks can be reconstructed with high probability from entries.
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.
AOLS improves sparse linear regression with lower costs and better recovery.
problem Inferring sparse vectors from random linear combinations.
method Accelerated Orthogonal Least-Squares (AOLS) algorithm.
result AOLS achieves lower sampling complexity and better recovery probability.
SyncRank recovers global ranking from noisy comparisons with theoretical guarantees.
problem Recovering a global ranking from noisy pairwise comparisons.
method Complex-valued data model and SDP relaxation for exact ranking recovery.
result SyncRank achieves exact ranking recovery with high probability above a critical noise threshold of O(sqrt(n / log n)).
Sharp threshold for exact recovery in non-uniform hypergraph stochastic block model.
problem Community detection in random hypergraphs with non-uniform hyperedge probabilities.
method Sharp threshold established; two efficient algorithms for exact recovery.
result Sharp threshold for exact recovery; information-theoretic lower bound on misclassification.
Paper provides conditions for local recovery of tensor data's Kronecker-structured dictionaries.
problem Local recovery of Kronecker-structured dictionaries for tensor data.
method Derives sufficient conditions for local recovery of coordinate dictionaries.
result Sufficient conditions guarantee recovery of individual coordinate dictionaries up to specified error.
Paper proposes efficient algorithm for recovering sparsity pattern from deterministic missing data.
problem Recovering sparsity pattern from datasets with deterministic missing structure.
method Proposes an efficient algorithm for missing value imputation using topological property of censorship filter.
result Consistently recovers the sparsity pattern with high probability in polynomial time and logarithmic sample complexity.