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.
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…
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 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.
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…
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.
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 logn or higher. Starting from a roughly correct community partition …
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…
New algorithm recovers model coefficients and supports from noisy data.
problem Simultaneous estimation and support recovery in linear models with Gaussian noise.
method Projection-based algorithm for STG regularized minimization problem, proving convergence and support recovery guarantees.
result New algorithm outperforms existing methods in support recovery for various data setups.
Efficient algorithms for sparse parameter recovery in mixture models.
problem Support recovery of high-dimensional sparse latent vectors in mixture models.
method Efficient algorithms with logarithmic sample complexity dependence on dimensionality.
result First guarantees on support recovery for various mixture models.
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.
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.
Improves graph recovery in Gaussian graphical modeling.
problem Calibrating regularization parameters for graph recovery.
method Thresholded adaptive validation applied to graphical lasso.
result Thresholding pipeline improves graph recovery.
We determine the information-theoretic cutoff value on separation of cluster centers for exact recovery of cluster labels in a K-component Gaussian mixture model with equal cluster sizes. Moreover, we show that a semidefinite programming (SDP) relaxation of the K-means clustering method achieves such sharp threshol…
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.
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.
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.
We find that factors explaining bank loan recovery rates vary depending on the state of the economic cycle. Our modeling approach incorporates a two-state Markov switching mechanism as a proxy for the latent credit cycle, helping to explain differences in observed recovery rates over time. We are able to demonstrate ho…
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.
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 …
Flat minima lead to better generalization in low-rank matrix recovery models.
problem Understanding why flat minima generalize well in overparameterized models.
method Analysis of overparameterized matrix and bilinear sensing, robust PCA, covariance matrix estimation, and neural networks with quadratic activation functions.
result Flat minima, measured by the trace of the Hessian, exactly recover the ground truth in low-rank matrix recovery models under standard statistical assumptions.
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.
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.
Study shows DNNs can recover functions with fewer samples than model parameters at overparameterization.
problem Determining reliable function recovery in overparameterized deep neural networks.
method Introducing 'local linear recovery' (LLR) and proving upper bounds on sample sizes for recovery.
result Upper bounds on optimistic sample sizes for function recovery in overparameterized DNNs are achieved.
We propose a Bayesian model that predicts recovery curves based on information available before the disruptive event. A recovery curve of interest is the quantified sexual function of prostate cancer patients after prostatectomy surgery. We illustrate the utility of our model as a pre-treatment medical decision aid, pr…
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.
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.
We provide analytical pricing formula of corporate defaultable bond with both expected and unexpected default in the case with stochastic default intensity. In the case with constant short rate and exogenous default recovery using PDE method, we gave some pricing formula of the defaultable bond under the conditions tha…
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.
Study models stock price recovery during COVID-19, distinguishing V and L-shape recoveries.
problem Analyzing stock price recovery during the COVID-19 pandemic.
method Developed a stock price model based on net-fund-flow and financial antifragility.
result Quality stocks with higher financial antifragility show V-shape recovery, while those with lower antifragility show L-shape recovery.
We propose a general modeling and algorithmic framework for discrete structure recovery that can be applied to a wide range of problems. Under this framework, we are able to study the recovery of clustering labels, ranks of players, signs of regression coefficients, cyclic shifts, and even group elements from a unified…
A new method trains and samples from energy-based models using diffusion recovery likelihood.
problem Training and sampling high-dimensional datasets with energy-based models is challenging.
method Trains EBMs with a diffusion recovery likelihood method, maximizing conditional probabilities of data at different noise levels.
result Generates high-fidelity images with low FID and inception scores, and accurately estimates normalized data density.
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.
New method explains computational barriers in high-dimensional statistical models.
problem Understanding detection-recovery gaps in high-dimensional inference.
method Combining algorithmic contiguity and cross-validation reduction to obtain conditional computational lower bounds.
result Mild control of low-degree advantage is sufficient to explain computational barriers for recovery.
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.
Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study the problem of robust low-rank tensor recovery in a convex optimization framework,…
Optimizes ranking of top-k players from partial comparison data.
problem Identifying the top-k players from incomplete pairwise comparisons.
method Maximum Likelihood Estimator (MLE) and Spectral Method.
result MLE achieves optimal partial and exact recovery, while Spectral Method is sub-optimal.
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.
This work uses diffusion models for accurate signal recovery from semi-parametric models.
problem Recovering signals from semi-parametric single index models with discontinuous link functions.
method Proposes an efficient reconstruction method using diffusion models that requires one round of sampling and inversion.
result Demonstrates more accurate reconstructions with fewer evaluations compared to competing methods.
New findings on community recovery in SBM with many communities.
problem Determining community recovery conditions in SBM with more than sqrt(n) communities.
method Constructing motifs and counting them to prove community recovery above the proposed threshold.
result Proving community recovery above the proposed threshold in SBM with K >= sqrt(n) communities.
Exact recovery method for community detection in Gaussian mixtures with dependent noise.
problem Community detection in Gaussian mixtures with dependent and heterogeneous noise.
method Maximum likelihood estimator (MLE) for constrained quadratic optimization problem, using Σ-whitened separation and local inequalities. result Sharp exact-recovery threshold and no-gap mechanism in the unknown-size setting.
We reveal a model rank that predicts successful recovery of target functions at overparameterization.
problem Understanding the mysterious good generalization performance of overparameterized nonlinear models.
method Rank stratification and linear stability theory for general nonlinear models.
result Linearly stable functions are preferred by nonlinear training, and model rank predicts minimal training data size.
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…
New SAE algorithm proves feature recovery for LLMs with theoretical guarantees.
problem Achieving interpretable features in large language models (LLMs).
method Proposed a statistical framework and bias adaptation technique for sparse autoencoders (SAEs).
result Proved correct recovery of all monosemantic features under specific data sampling.
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.
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.
The stochastic block model (SBM) is a random graph model with different group of vertices connecting differently. It is widely employed as a canonical model to study clustering and community detection, and provides a fertile ground to study the information-theoretic and computational tradeoffs that arise in combinatori…
In this paper, we consider the problem of estimating the underlying graph associated with an Ising model given a number of independent and identically distributed samples. We adopt an \emph{approximate recovery} criterion that allows for a number of missed edges or incorrectly-included edges, in contrast with the widel…