New definition of joint stationarity improves process recovery over graphs.
problem Regression tasks with high-dimensional multivariate processes dependent on graph topology.
method Introduces joint stationarity, a new definition that reduces estimation variance and complexity.
result One reliably learns covariance structure from a single realization and solves MMSE problems nearly linearly in time.
Paper analyzes adaptive Lasso for high-dimensional diffusion processes, improving support recovery and bias.
problem Support recovery for high-dimensional diffusion processes under sparsity constraints.
method Adaptive Lasso estimator for d-dimensional ergodic diffusion process, focusing on linear models.
result Adaptive Lasso achieves support recovery and asymptotic normality for drift parameter under certain conditions.
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 …
Survey on nonconvex penalties for sparse and low-rank recovery in various fields.
problem Achieving sparsity and low-rankness in signal processing, statistics, and machine learning.
method Analysis of nonconvex penalties and their applications.
result Nonconvex penalties can significantly improve performance in various applications.
Estimates spatio-temporal Hawkes processes using tensor recovery.
problem Estimating influence functions for spatio-temporal Hawkes processes.
method Formulates influence function as a tensor kernel, assumes low-rank structure, solves as convex optimization problem.
result Provides theoretical guarantees and demonstrates efficiency with simulations.
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.
Recently, Ross showed that it is possible to recover an objective measure from a risk-neutral measure. His model assumes that there is a finite-state Markov process X that drives the economy in discrete time. Many authors extended his model to a continuous-time setting with a Markov diffusion process X with state space…
Continuous vector representations of words and objects appear to carry surprisingly rich semantic content. In this paper, we advance both the conceptual and theoretical understanding of word embeddings in three ways. First, we ground embeddings in semantic spaces studied in cognitive-psychometric literature and introdu…
Paper reviews advances in solving sparsest vector problem in subspaces.
problem Finding the sparsest vector in a low-dimensional subspace.
method Geometric analysis of optimization landscapes and efficient nonconvex optimization algorithms.
result Recent advances in global nonconvex optimization for sparsest vector problem.
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.
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…
Paper proposes a new method for exact recovery in robust tensor principal component analysis.
problem Exact recovery of low-rank and sparse components in tensors.
method Proposes a new method based on tensor-tensor product and t-SVD to solve a convex optimization problem.
result Exact recovery achieved in a deterministic fashion without randomness assumptions.
Paper calculates loan loss after default using Bayesian model.
problem Determining loan loss after borrower default.
method Bayesian scheme considering repayment period, volumes, moments, and parameters.
result Allows setting LGD less than or equal to 1 for accurate estimates.
New model for multivariate discrete event data with flexible interactions.
problem Modeling multivariate discrete event data with categorical interactions.
method Developed a new modeling approach with convex constraints, two estimation procedures (LS and ML).
result Proposed model can capture arbitrary shapes of historical event influence.
Majority voting neural networks improve binary compressed sensing for sparse signal recovery.
problem Sparse signal recovery in binary compressed sensing.
method Majority voting neural networks with a cross entropy-like term and L1 regularization.
result The majority voting neural network achieves excellent recovery performance, approaching optimal performance as the number of component nets grows.
Paper refines null space conditions for nuclear norm minimization in low-rank matrix recovery.
problem Establishing conditions for successful nuclear norm minimization recovery of low-rank matrices.
method Developed new null space conditions for nuclear norm minimization, proving their necessity and sufficiency.
result Weak null space condition is sufficient but not necessary for nuclear norm minimization recovery, providing a new necessary and sufficient condition.
GPMM recovers latent signals from noisy mixtures using Bayesian inference.
problem Recovering latent signals from noisy mixed measurements.
method Gaussian process mixture of measurements (GPMM) with Bayesian inference.
result GPMM outperforms standard GP in signal recovery.
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.
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 nimesnimes⋯imesn of ranks (r,⋯,r) can be reconstructed with high probability from O((rd+dnr)log(d)) entries. Theoretical justification for image inpainting using diffusion models.
problem Improving sample recovery in image inpainting without retraining.
method Analysis of RePaint algorithm and proposing RePaint+ to correct misalignment. result RePaint+ algorithm provably recovers the true sample with linear convergence. New method tackles non-smooth tensor data for better recovery.
problem Non-smooth changes in tensor data degrade traditional t-SVD methods.
method Learnable tensor nuclear norm, Alternating Proximal Multiplier Method (APMM), multi-objective tensor recovery framework.
result The proposed method effectively recovers tensor data with non-smooth changes.
New framework uses score-based priors to solve ill-conditioned polynomial equations, improving signal recovery from noisy data.
problem Recovering signals from low-order moments in inverse problems, especially ill-conditioned polynomial equations.
method Integrates score-based diffusion priors with moment-based estimators to regularize and solve nonlinear inverse problems.
result Diffusion priors improve recovery from third-order moments and make super-resolution MTD feasible.
Paper improves AIRL by enhancing policy imitation and addressing reward recovery issues.
problem Inadequate policy imitation and limited transferable reward recovery in AIRL.
method Substituted built-in algorithm with SAC for policy updating and proposed PPO-AIRL + SAC hybrid framework.
result SAC improves policy imitation but hinders reward recovery; PPO-AIRL + SAC achieves satisfactory transfer effect.
Paper develops a new algorithm for sparse signal recovery.
problem Sparse signal recovery from noisy observations.
method Iterative Stochastic Optimization using Stochastic Mirror Descent.
result Linear convergence during preliminary phase of the routine.
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.
New model captures state-dependent variability in partially observed systems.
problem Structured stochasticity not captured by constant-variance models.
method State-coupled stochastic volatility framework with particle expectation-maximization.
result Model consistently reduces recovery bias under partial observation.
The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex analysis and optimization over spaces of tensors is now gaining much interest due to its potential applications to signal processing, statistics…
Optimizes loan recovery timing by forecasting cash flows.
problem Minimizing overall credit loss in loan portfolios.
method Forecast future cash flows using probabilistic and Markov chain models.
result Empirical illustration of loss-optimal recovery timing.
Recovering hidden influence networks from cascade data using Jacobian-based machine learning.
problem Recovering influence networks behind dynamic cascades.
method CascadeNet, a Jacobian-based machine learning framework.
result CascadeNet achieves high accuracy in network recovery.
Improves signal recovery speed and performance via meta-learning.
problem Slow and costly signal recovery in compressed sensing.
method Jointly trains a generator and optimisation process for reconstruction via meta-learning.
result Significantly improved both performance and speed of signal recovery.
A new method enhances signal recovery with FDR control.
problem Challenging signal recovery in compressive sensing.
method Knockoff-guided compressive sensing framework with FDR control.
result Guaranteed FDR control leads to more accurate signal reconstruction.
Study recovers spike order in noisy tensor estimation without SNR assumptions.
problem Estimating multiple signal vectors from noisy tensor observations.
method Gradient flow optimization of a nonconvex function.
result Determines sample complexity for efficient permutation recovery.
Bayesian deconditional embeddings solve complex function recovery.
problem Recovering original functions from conditional mean observations.
method Formalizes deconditional kernel mean embeddings as Bayesian inference, connects to task-transformed Gaussian processes.
result Establishes deconditional kernel means as posterior predictive mean, providing Bayesian interpretations and uncertainty.
QPCA improves PCA for cyclostationary data.
problem Improving PCA for cyclostationary data.
method Formulated as an optimization problem, QPCA decomposes into frequency-domain PCA problems.
result Optimized basis for cyclostationary data.
Interpretable RNN uses sparse recovery for better performance.
problem Interpreting the internal workings of RNNs.
method Sequential Sparse Recovery + SISTA algorithm.
result SISTA-RNN achieves better performance and is more interpretable.
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.
Extends IBP for non-diagonal latent covariance structures, improving feature recovery and denoising.
problem Modeling latent features with smoothness characteristics.
method Extend Indian Buffet Process to include non-diagonal latent covariance structures.
result Smoothness prior improves feature recovery and denoising under appropriate conditions.
Solves signal recovery from few linear measurements using convex duality.
problem Recovering signals from limited linear measurements in various applications.
method Develops a convex-concave min-max reformulation for linear inverse problems.
result Simple ascent-descent algorithms for solving linear inverse problems.
In this paper incomplete-information models are developed for the pricing of securities in a stochastic interest rate setting. In particular we consider credit-risky assets that may include random recovery upon default. The market filtration is generated by a collection of information processes associated with economic…
New neural network LDAMP outperforms existing algorithms in image recovery.
problem Challenging problem of fast and accurate compressive image recovery.
method Inspired by D-AMP, developed LDAMP neural network architecture.
result LDAMP outperforms BM3D-AMP and NLR-CS in accuracy and run time.
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.
LCRSR recovers latent row space for multi-view clustering.
problem Efficiently recover latent representation from multiple views.
method LCRSR assumes latent representation from multiple views, recovers row space, and determines subspace membership.
result LCRSR recovers complete subspace structure efficiently.
Paper recovers lattice signal partitions efficiently.
problem Estimating lattice partition from noisy data.
method Uses dyadic CART for computationally-efficient partition recovery.
result Consistently estimates partition with optimal error rate.
EFiGP uses Fourier and eigen-decomposition for efficient ODE parameter estimation.
problem Parameter estimation and trajectory reconstruction for noisy, sparse, nonlinear ODE systems.
method EFiGP integrates Fourier transformation and eigen-decomposition into a physics-informed Gaussian Process framework.
result EFiGP efficiently estimates ODE parameters and recovers trajectories from noisy data.
This paper recovers smooth functions from noisy modulo samples using a three-stage strategy.
problem Recovering Hölder smooth functions from noisy modulo samples.
method Three-stage strategy: denoising with local polynomial estimators, unwrapping, and spline-based quasi-interpolant.
result Uniform error rates for Hölder class functions with high probability.
3d-SMRnet speeds up MPI system matrix recovery to 1 minute with high quality.
problem Slow system matrix recovery in MPI due to recalibration.
method 3d-System Matrix Recovery Network using deep learning.
result 3d-SMRnet recovers 3d system matrix with 64x subsampling in 1 minute.
Jointly learns feature and sample relevancies for robust sparse recovery.
problem Sparse recovery sensitivity to data contaminants like outliers or misspecified noise.
method Jointly learns feature and sample relevancies via marginal likelihood optimization.
result Consistent sparse and robust prediction models across diverse tasks.
The study recovers airflow from thoracic and abdominal movements using advanced signal processing.
problem Challenges in measuring airflow from thoracic and abdominal movements using small, inexpensive devices.
method Synchrosqueezing transform and locally stationary Gaussian process regression.
result Accurate prediction of airflow achieved in both normal sleep and anesthesia transition cases.