This paper investigates gradient recovery schemes for data defined on discretized manifolds. The proposed method, parametric polynomial preserving recovery (PPPR), does not require the tangent spaces of the exact manifolds, and they have been assumed for some significant gradient recovery methods in the literature. Ano…
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48 results for “manifold recovery”
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…
New tensor recovery method uses Riemannian optimization on Segre manifold.
problem Recovering low-rank tensors from noisy measurements.
method Riemannian Gradient Descent (RGD) and Riemannian Gauss-Newton (RGN) algorithms over the Segre manifold.
result Proven convergence rates for RGD and RGN under mild noise assumptions.
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.
Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear sub-manifold of a high dimensional ambient space. We introduce SPIN, a first order projected gradient method to recover the signal components. Despite the…
Paper develops a novel kernel-based method for MRI data recovery.
problem Reconstructing dynamic MRI data on manifolds.
method Kernel bi-linear modeling in reproducing kernel Hilbert spaces.
result Validated on synthetic dMRI data, the method outperforms state-of-the-art approaches.
Paper proves IRLS converges to subspace from any start, with practical benefits.
problem Robust subspace estimation in machine learning.
method Iteratively Reweighted Least Squares (IRLS) with dynamic smoothing regularization.
result IRLS converges linearly to the underlying subspace from any initialization under deterministic conditions.
Study on Gaussian-width complexity on statistical manifolds and its applications in learning and recovery.
problem Understanding the geometry of statistical manifolds and its implications for learning and recovery.
method Analysis of Fisher width and inverse-Fisher width, proving their complementary roles and establishing a relation between them.
result Established a sharp relation between Fisher width and inverse-Fisher width, showing they cannot reduce relative to Euclidean scale.
New method avoids spurious critical points for low-rank matrix recovery.
problem Low-rank matrix recovery problems on Riemannian manifold.
method Riemannian gradient descent with random initialization.
result Riemannian gradient descent avoids spurious critical points and converges nearly linearly.
Recovering manifold geometry from geodesic intersections.
problem Recovering the geometry of a Riemannian manifold from geodesic intersection lengths.
method Applying stitching data to solve the delayed collision data problem.
result Geometry of the manifold can be recovered from geodesic intersection lengths.
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.
New algorithm improves signal recovery from noisy measurements with theoretical guarantees.
problem Recovering signals from noisy measurements in inverse problems.
method Wasserstein-based projections (WP) replacing analytic regularization with data-driven denoising.
result WP approximates true projection with high probability, providing theoretical guarantees.
This paper puts forth a novel bi-linear modeling framework for data recovery via manifold-learning and sparse-approximation arguments and considers its application to dynamic magnetic-resonance imaging (dMRI). Each temporal-domain MR image is viewed as a point that lies onto or close to a smooth manifold, and landmark …
Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space. One of the aims of dimension reduction is to find intrinsic coordinates that describe the data manifold. The coordinates returned by the embedding algorithm are abstract, and finding their physical or domain-r…
New method recovers clean data from corrupted samples.
problem Recovering clean data from corrupted samples with uncertainty.
method Probabilistic Tomographic Auto-Encoder method that derives reduced entropy condition approximate inference.
result Superior performance in imputation and de-noising compared to existing methods.
Recovery Swapsq-fin.PR
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 investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. In the Tucker decomposition framework, we show that the Riemannian optimization algorithm with initial value obtained from a spectral method can reconstruct a tensor of size $n\times n \times\c…
Diffusion -means clustering on manifolds: provable exact recovery via semidefinite relaxationsmath.ST
We introduce the {\it diffusion -means} clustering method on Riemannian submanifolds, which maximizes the within-cluster connectedness based on the diffusion distance. The diffusion -means constructs a random walk on the similarity graph with vertices as data points randomly sampled on the manifolds and edges as …
New method beats volumetric barrier for manifold recovery.
problem Reconstructing latent geometry from noisy distances.
method Orthogonal Ring Distance Estimation Routine (ORDER).
result Achieves pointwise distance estimation of order .
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.
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 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 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 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 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 -support norm regularizer.
result Achieves sparse recovery with explicit constants and standard linear rate.
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 …
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 -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.
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.
HSNLD solves robust Hankel recovery efficiently and robustly.
problem Robust Hankel recovery of sparse outliers and missing entries.
method Hankel Structured Newton-Like Descent (HSNLD) algorithm.
result HSNLD achieves linear convergence independent of the condition number.
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.
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.
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.
Guarantees sparse recovery for neural networks with iterative hard thresholding.
problem Recovering sparse network weights in neural networks.
method Structural properties of sparse network weights and iterative hard thresholding algorithm.
result Simple iterative hard thresholding algorithm recovers sparse network weights exactly using linear memory.
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 …
A Generative Adversarial Network (GAN) with generator trained to model the prior of images has been shown to perform better than sparsity-based regularizers in ill-posed inverse problems. Here, we propose a new method of deploying a GAN-based prior to solve linear inverse problems using projected gradient descent (…
A field known as Compressive Sensing (CS) has recently emerged to help address the growing challenges of capturing and processing high-dimensional signals and data sets. CS exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive (or random) linear…
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.
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- regularization. While the current theory provides promis…
New method improves traffic data recovery for streaming data.
problem Improve data quality in traffic data for ITS.
method Online robust tensor recovery algorithm leveraging spatio-temporal correlations and local consistency.
result Significantly improved computational efficiency and high recovery accuracy.
We present a mathematical analysis of a non-convex energy landscape for robust subspace recovery. We prove that an underlying subspace is the only stationary point and local minimizer in a specified neighborhood under a deterministic condition on a dataset. If the deterministic condition is satisfied, we further show t…
We consider the effect of recovery rates on a pool of credit assets. We allow the recovery rate to depend on the defaults in a general way. Using the theory of large deviations, we study the structure of losses in a pool consisting of a continuum of types. We derive the corresponding rate function and show that it has …
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.
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.
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…
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…