Proposes a new method for efficient manifold denoising robust to high dimensional noise.
problem Efficiently denoise manifolds in high dimensional spaces with complicated noise.
method Landmark diffusion and optimal shrinkage under high dimensional noise and compact manifold setup.
result Systematic comparison with other algorithms on simulated and real datasets shows superior performance.
Study on sensor fusion algorithms under high dimensional noise.
problem Behavior of sensor fusion algorithms under high dimensional noise.
method Analysis of NCCA and AD algorithms using Gaussian kernel.
result Robustness of NCCA and AD to high dimensional noise depends on SNR and bandwidth selection.
The paper analyzes how noise affects distances in high-dimensional data and when they remain useful.
problem Noise corrupts distances in high-dimensional data, making them unreliable for identifying true nearest and farthest neighbors.
method The paper uses asymptotic probabilistic expressions to characterize noise effects and decomposes data into ground truth and noise components.
result Under certain conditions, empirical neighborhood relations remain truthful even when distance concentration occurs.
The paper develops a method to model high-dimensional data with many variables and weak signals.
problem Modeling high-dimensional dependent data with many explanatory variables and low signal-to-noise ratio.
method Penalized regression for high-dimensional data, factor modeling of residuals, high-dimensional white noise testing, projected Principal Component Analysis.
result Established asymptotic properties of the proposed method for high-dimensional data.
SPPCSO addresses multicollinearity in high-dimensional data, improving model stability and predictive accuracy.
problem Multicollinearity in high-dimensional data leads to unstable estimation and reduced predictive accuracy.
method SPPCSO integrates principal component regression and L1 regularization to adaptively adjust shrinkage factors.
result SPPCSO achieves stable and reliable estimation in high-noise settings, distinguishing signal variables from noise.
New method clusters high-dimensional data with anisotropic noise.
problem Clustering high-dimensional anisotropic mixtures with varying noise structures.
method Covariance Projected Spectral Clustering (COPO) method that projects data onto a low-dimensional space and reassigns clusters based on estimated covariances.
result COPO achieves minimax-optimal misclustering rates in Gaussian settings.
PCA++ improves robustness to background noise in contrastive learning.
problem Recovering shared signal subspaces from positive pairs in high-dimensional data with structured background noise.
method PCA++ uses hard uniformity-constrained contrastive learning to enforce identity covariance on projected features.
result PCA++ outperforms standard PCA and alignment-only PCA+ in simulations and real-world datasets.
Kernel SVGD improves high-dimensional inference with noise adaptation.
problem Challenges in high-dimensional inference with SVGD.
method Noise Conditional Kernel SVGD (NCK-SVGD) with entropic regularization.
result NCK-SVGD produces samples comparable to GANs and SGLD on computer vision benchmarks.
Many models for sparse regression typically assume that the covariates are known completely, and without noise. Particularly in high-dimensional applications, this is often not the case. This paper develops efficient OMP-like algorithms to deal with precisely this setting. Our algorithms are as efficient as OMP, and im…
Proposes a method to compare noisy high-dimensional datasets with low-dimensional manifolds.
problem Comparing distributions on manifolds in noisy high-dimensional datasets.
method Linking low-rank structure to manifold geometry, developing a scale-invariant distance measure.
result Superior robustness and statistical power compared to existing methods.
We address noisy Euclidean distances in high dimensions, estimating noise levels and correcting distances.
problem Distorted pairwise Euclidean distances due to heteroskedastic noise.
method Developed a hyperparameter-free approach to jointly estimate noise magnitudes and correct distances.
result Our method provides accurate noise magnitude estimates and corrected distances in high-dimensional settings.
Noise Sensitivity Exponent controls statistical-computational gaps in learning.
problem Understanding when learning is statistically possible yet computationally hard in high-dimensional statistics.
method Investigating statistical-computational gaps in single- and multi-index models using Noise Sensitivity Exponent.
result Noise Sensitivity Exponent governs statistical-computational gaps in high-dimensional learning.
Local averaging accurately distills manifold structure from noisy data.
problem Tackles the challenge of uncovering manifold structure from noisy data.
method Two-round mini-batch local averaging method applied to noisy samples.
result Achieves accuracy bound of $d(\hat{\mathbf q}, \mathcal M) \leq σ\sqrt{d\left(1+\frac{κ\mathrm{diam}(\mathcal {M})}{\log(D)}
ight)}$.
Robustly infers manifold density and geometry under high-dimensional noise.
problem Inaccurate kernel density estimation under high-dimensional noise.
method Doubly stochastic normalization of Gaussian kernel.
result Robust tools for density estimation, noise magnitude estimation, and distance approximation.
Proposes GRAB-MDM for robust multiview data fusion.
problem Limited theoretical guarantees for multiview fusion methods in noisy high-dimensional data.
method Generalized Robust Adaptive-Bandwidth Multiview Diffusion Maps (GRAB-MDM) with adaptive bandwidth selection.
result Adaptive bandwidths lead to robust recovery of shared intrinsic structure in noisy multiview data.
Algorithm removes specific training data from models efficiently in high-dimensional settings.
problem Efficiently removing specific training data from high-dimensional models without full retraining.
method Starts from original model parameters, performs Newton steps, adds isotropic Laplacian noise.
result Two Newton steps are sufficient for effective unlearning in high-dimensional problems.
Study privacy and accuracy in high-dimensional LASSO with perturbation mechanisms.
problem Privacy-preserving sparse linear regression in high dimensions.
method Analyzes output and objective perturbation mechanisms using AMP.
result Sparsity affects privacy-accuracy trade-off; stronger regularization improves privacy.
Derives scaling limits and fluctuations for SGD in high dimensions.
problem Understanding SGD behavior in high-dimensional settings with varying noise levels.
method Interacting particle system approach, treating SGD iterates as such, with covariance structure considered.
result Precise three-step phase transition observed in SGD behavior: ballistic, diffusive, then random.
New method learns SDEs with structured noise from data.
problem Learning SDEs with structured noise from data.
method Nonparametric framework for drift and diffusion terms.
result Accurately infers low-dimensional interaction kernels.
Paper finds sample complexity for learning high-dimensional simplices from noisy data.
problem Learning high-dimensional simplices from noisy samples.
method Combines sample compression, high-dimensional geometry, and Fourier analysis.
result Proves sample complexity bound for achieving a simplex within a certain distance from the true simplex.
The paper analyzes the robustness of a minimum ℓ2 interpolator in high-dimensional linear regression.
problem Analyzing the robustness of a minimum ℓ2 interpolator in high-dimensional linear regression. method The paper analyzes the interpolator with minimal ℓ2-norm in a general high-dimensional linear regression framework, proving bounds on prediction loss. result The paper shows that the prediction loss of the interpolator is bounded by (∥β∗∥22rcn(Σ)∨∥ξ∥2)/n with high probability, revealing a transition in rates. DIVI clusters noisy high-dimensional data with stable feature gating.
problem Challenging clustering in high-dimensional noisy data.
method Data-informed variational clustering framework combining global feature gating and adaptive structure growth.
result DIVI performs competitively under severe feature noise and remains computationally feasible.
We develop a classification algorithm for estimating posterior distributions from positive-unlabeled data, that is robust to noise in the positive labels and effective for high-dimensional data. In recent years, several algorithms have been proposed to learn from positive-unlabeled data; however, many of these contribu…
SignSGD analysis quantifies its effects in high dimensions.
problem Understanding signSGD's effects in high-dimensional settings.
method High-dimensional analysis of signSGD, deriving SDE and ODE for risk.
result Quantification of signSGD's effects: effective learning rate, noise compression, diagonal preconditioning, gradient noise reshaping.
This paper sharpens privacy guarantees for high-dimensional PCA under differential privacy.
problem Understanding the exact privacy loss in high-dimensional PCA with differential privacy.
method Analyzes the exponential mechanism in a model-free setting for high-dimensional PCA.
result Sharp utility and privacy characterizations in high dimensions show the difficulty of detecting a target individual's presence.
New approach preserves privacy in high-dimensional data using representation learning.
problem Preserving privacy in high-dimensional data collection.
method Adapting representation learning techniques to add noise to low-dimensional data representations.
result Significantly outperforms current LDP mechanisms in downstream model learning.
Scalable approach for high-dimensional dynamical systems with noise filtering and parameter estimation.
problem Noise filtering and parameter estimation for high-dimensional dynamical systems.
method Flexible latent factor model with orthogonal factor loading matrix and closed-form parameter estimation.
result Substantial acceleration and higher accuracy compared to alternatives.
Paper estimates noise covariance in correlated multi-task linear models.
problem Estimating noise covariance in multi-task high-dimensional linear models with correlated noise.
method Uses multi-task elastic-net and lasso estimators to estimate noise covariance, correcting bias in squared residual matrix.
result Develops a novel estimator of noise covariance that converges at rate n−1/2, matching oracle estimator under suitable conditions. Random smoothing struggles to certify high-dimensional image robustness.
problem Certifying adversarial robustness for high-dimensional images with p>2. method Analysis of random smoothing for ℓp robustness, focusing on ℓ∞. result Noise distribution required for ℓp robustness must have high variance, leading to trivial classifiers. RS-NSGD improves SGD convergence for heavy-tailed noise.
problem Nonconvex optimization with heavy-tailed noise.
method Integrates direction normalization into subspace updates.
result Achieves better oracle complexity than full-dimensional normalized SGD.
The paper tackles noisy labels in high-dimensional data, showing low-dimensional intuitions fail and proposing an optimized method.
problem Noisy labels in high-dimensional data classification.
method Linear classifier with a label noisiness aware loss function, using random matrix theory and Gaussian mixture data model.
result The performance of the linear classifier in high-dimension converges to a limit involving scalar statistics of the data, and the optimal classifier in low-dimension fails.
K-means fails in high dimensions with noise and few samples.
problem Clustering in high-dimensional data with noise and limited samples.
method Simple Gaussian Mixture Model (GMM) analysis.
result Almost every partition becomes a fixed point of k-means in high dimensions.
Noise-aware DP inference improves accuracy for complex models.
problem Inaccurate results and biases in DP inference for complex models.
method Noise-aware stochastic gradient variational inference.
result Accurate coverages and predictive probabilities for complex models.
We propose robust sparse reduced rank regression for analyzing large and complex high-dimensional data with heavy-tailed random noise. The proposed method is based on a convex relaxation of a rank- and sparsity-constrained non-convex optimization problem, which is then solved using the alternating direction method of m…
Autotune optimizes Lasso tuning parameters efficiently and accurately.
problem Efficiently selecting Lasso tuning parameters in high-dimensional models.
method Alternates optimizing regression coefficients and noise standard deviation.
result Autotune outperforms existing methods in low signal-to-noise regimes.
I-BBS identifies latent sub-manifolds from distance matrices, robust to noise.
problem Identifying latent sub-manifolds from distance matrices in high-dimensional spaces.
method Coordinate-free inference using random distance matrix theory and generative noise models.
result Recovering latent geometry from integer-stable signatures of eigenvalues.
New approach removes data influence in high dimensions with single step.
problem Efficiently removing data influence in high-dimensional settings with strong convexity and smoothness assumptions.
method Introduces ε-Gaussian certifiability and analyzes Newton method performance.
result Single Newton step followed by Gaussian noise achieves privacy and accuracy.
We present a theoretical analysis of the training process for a single-layer GAN fed by high-dimensional input data. The training dynamics of the proposed model at both microscopic and macroscopic scales can be exactly analyzed in the high-dimensional limit. In particular, we prove that the macroscopic quantities measu…
New method estimates high-dimensional GoM models efficiently.
problem Estimating GoM models for high-dimensional polytomous data.
method Flattening three-way quasi-tensor into a matrix, performing singular value decomposition.
result Established finite-sample error bounds for estimated parameters.
EigenBayes: A fast, adaptive Bayesian shrinkage approach for high-dimensional matrix factorization
problem Choosing the latent dimension k in factor models method Adaptive spectral shrinkage and empirical Bayes calibration
result Adapts to signal-to-noise ratio and shrinks superfluous components
Study of asymmetric rank-one tensor models with non-Gaussian noise.
problem Analyzing maximum-likelihood estimators for asymmetric rank-one tensor models.
method Spectrally separated branch analysis, resolvent methods, cumulant expansions, Efron-Stein-type variance bounds.
result Asymptotic singular value and mode-wise alignments are robust to non-Gaussian noise.
A model learns causal representations from high-dimensional data.
problem Challenges in learning causal representations from high-dimensional data.
method Formulated a latent variable decoder model, Decoder BCD, for Bayesian causal discovery.
result Shows that using known intervention targets as labels helps in unsupervised Bayesian inference over structure and parameters.
Improves generative models by using heavy-tailed noise in score matching.
problem High-dimensional limitations of Gaussian noise in generative models.
method Extended DSM to generalised normal distribution, relaxed key assumptions, developed iterative noise scaling algorithm.
result Heavy-tailed DSM leads to improved generative performance.
NCVis speeds up data visualization for large datasets.
problem Performance issues in t-SNE for large datasets.
method Noise contrastive estimation for scalable visualization.
result NCVis outperforms state-of-the-art techniques in speed and quality.
Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called robust kernel principal component analysis (RKPCA) to decompose a partially cor…
The paper sets sample complexity bounds for learning high-dimensional simplices in noisy data.
problem Learning high-dimensional simplices from noisy data.
method Sample compression techniques and Fourier-based method for noisy observations.
result Established sample complexity bounds for simplex learning in noisy regimes.
High-dimensional spectroscopy data makes ML models achieve near-perfect accuracy, even when chemical distinctions are absent.
problem Why machine learning models achieve near-perfect accuracy in spectroscopic classification tasks without chemically meaningful features.
method Theoretical analysis grounded in the Feldman-Hajek theorem and concentration of measure, combined with specific experiments on synthetic and real fluorescence spectra.
result Infinitesimal distributional differences in high-dimensional spaces can lead to perfect separability, making models achieve near-perfect accuracy in spectroscopy.
Method generates joint posterior samples of source and foreground mass distributions for gravitational lensing.
problem Challenging inference problem for high-resolution, high signal-to-noise ratio gravitational lensing.
method Combines diffusion-based generative modeling and recurrent inference machines.
result Can model realistic gravitational lensing simulations down to the noise level.