Proposes a new signal model for high-dimensional, small-sample-size data.
problem Signal detection in high-dimensional, small-sample-size datasets.
method Intrinsic signal model based on dynamical system assumption.
result Taguchi method effectively detects signals in the proposed model.
Paper proposes efficient methods for clustering and signal recovery in high-dimensional data with block structures.
problem High-dimensional clustering and signal recovery under block signal structures.
method CFA-PCA and MA-PCA methods for sparse and dense block signals.
result Proposed methods achieve computational minimax optimality for clustering and signal recovery.
Develops new tests for high-dimensional models with mixed signal strengths.
problem Challenges in testing models with many signals and high-dimensional data.
method Moment matching formulation for developing new tests.
result Demonstrates optimality of GRIP test for various model types.
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.
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.
Proposes a new dictionary learning method for high-dimensional graph signals.
problem Challenges of traditional sparse representation methods in high-dimensional graph signals.
method Integrates graph topology implicitly through sparse combinations of graph-wavelet functions and explicitly through graph constraints.
result Demonstrates effectiveness in high-dimensional graph signal processing.
The paper improves classification accuracy by leveraging a shared signal across domains in high-dimensional classification.
problem Improving classification accuracy in high-dimensional data with shared signals across domains.
method Transfer learning for linear discriminant analysis, decomposing mean differences into common and domain-specific components.
result Deterministic limits for transfer performance, leading to optimal weights and corrections for bias.
This paper offers a characterization of fundamental limits on the classification and reconstruction of high-dimensional signals from low-dimensional features, in the presence of side information. We consider a scenario where a decoder has access both to linear features of the signal of interest and to linear features o…
Paper tackles blind detection of molecular signals in non-coherent media.
problem Long-tail channel response causes ISI, deteriorating detection performance.
method Develops a high-dimensional non-coherent scheme combining different non-coherent metrics.
result Higher dimensionality in metric space achieves lower bit error rate (BER).
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
Enhances forecasting of complex systems using FKMD.
problem Forecasting high-dimensional dynamical systems with unknown features.
method Featurized Koopman Mode Decomposition (FKMD) using delay embedding and learned Mahalanobis distance.
result Improves prediction accuracy for various complex systems.
SLOE speeds up logistic regression in high dimensions with accurate signal strength estimation.
problem Poor performance of logistic regression in high-dimensional settings.
method SLOE reparameterizes the signal strength for faster and more accurate estimation.
result SLOE provides a fast and accurate method for dimensionality correction in logistic regression.
New AMP algorithm detects change points in high-dimensional GLMs.
problem Detecting change points in high-dimensional GLMs.
method Approximate Message Passing (AMP) algorithm for estimating signals and change points.
result Characterization of AMP algorithm's performance in high-dimensional limit.
Sketching improves change-point detection in high-dimensional data.
problem Sequential detection of changes in high-dimensional signals.
method Linear sketches of signal vectors combined with GLR statistics.
result Sketching can maintain performance even with time-varying projections.
Better signal detection in undersampled data using joint and cross covariances.
problem Detecting shared signals in high-dimensional data with limited samples.
method Analysis of three covariance matrices: individual, cross, and joint.
result Joint and cross covariance matrices detect signals earlier than individual covariances.
Method detects new physics signals without prior knowledge.
problem Selecting signal regions for novel particles.
method Model-agnostic approach using low-pass filtering and density estimation.
result Efficiently identifies data-driven signal regions in high-dimensional feature space.
Unified analysis of ridge regression and discriminant analysis in high-dimensional settings.
problem Analyzing predictive risk in high-dimensional settings with arbitrary covariance.
method Unified analysis using high-dimensional asymptotics and random matrix theory.
result Explicit expression for limiting predictive risk depends on spectrum, signal strength, and aspect ratio.
Studying a softmax-attention model, we show that the learned query converges to the latent signal subspace spanned by the informative direction.
problem Understanding the theoretical principles of attention mechanisms in large-scale token collections.
method Deriving a population objective and analyzing the limiting ordinary differential equation of the learning dynamics.
result The learned query asymptotically recovers the latent signal up to the intrinsic sign ambiguity.
Javanmard and Montanari propose a debiased estimator for high-dimensional regression.
problem Bias in high-dimensional regression models.
method Debiased LASSO estimator.
result Debiased LASSO yields asymptotically normal estimators and valid hypothesis tests.
The Thresholding Method calibrates black box models to control loss function.
problem Balancing high power and loss function control in high-dimensional classification.
method Parameterizing strong signal points through thresholding.
result Empirical performance shows loss function control and reduced overfitting.
Study of Langevin dynamics for tensor PCA recovery in high dimensions.
problem Recovering hidden signal vectors (spikes) from noisy Gaussian tensor observations.
method Langevin dynamics approach for nonconvex optimization.
result Sample complexity matches the single-spike case but degrades for all spikes.
New algorithm resists contamination in high-dimensional regression with optimal performance.
problem Adversarial and measurement errors in high-dimensional data.
method Adversarial Contamination-resistant Iterative Hard Thresholding (AC-IHT) algorithm.
result Achieves minimax near-optimal estimation and signal-adaptive support recovery.
DET unifies geometric and functional alignment for high-dimensional scientific data.
problem Challenges in nonrigid registration for high-dimensional, irregular data.
method Domain Elastic Transform (DET) treats data as functions on irregular domains, using a Bayesian framework for elastic motion registration.
result DET achieves 92% topological preservation on MERFISH data and successfully registers whole-embryo Stereo-seq atlases.
The paper analyzes spectral initialization for nonconvex estimation, revealing phase transitions and computational complexities.
problem Estimating signals in nonconvex settings with spectral initialization.
method Arbitrary generalized linear sensing models, high-dimensional limit analysis.
result Spectral method performance has phase transitions and computational complexity depends on sample-to-signal dimension ratio.
Proposes Population Difference Criterion for visually observed subpopulation differences.
problem Statistical significance of visually observed subpopulation differences in high-dimensional and high-signal contexts.
method Balanced permutation approach and bootstrap confidence interval for quantifying uncertainty.
result Balanced permutation approach is more powerful in high-signal contexts.
Paper studies signal detection in noisy environments with limited communication.
problem Signal detection in Gaussian noise with 1-bit communication constraints.
method Derives lower bounds and exhibits optimal testing strategies.
result Optimal distributed testing strategies attain the derived lower bound.
Paper designs optimal collaboration strategies for signal detection in large networks.
problem Signal detection in large distributed networks with limited communication.
method Designs optimal collaboration strategies using sparse PCA equivalence.
result Optimal collaboration strategies improve detection performance.
MCAP clusters high-dimensional data via adaptive projections, handling large p efficiently.
problem Statistical and computational challenges in high-dimensional mixture models.
method Model-based Clustering via Adaptive Projections (MCAP) using linear projections.
result MCAP reliably detects covariance signals in very high-dimensional problems.
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…
Attention mechanism learns to focus on sparse tokens efficiently.
problem Detecting weak, rare, and sparsely located features in long sequences.
method Theoretical analysis and training of a single-layer attention classifier in a sparse-token classification model.
result A single-layer attention classifier can achieve vanishing test error with logarithmic signal strength growth, unlike linear classifiers requiring linear growth.
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.
We solve a high-dimensional nonlinear model using Gaussian regressors.
problem Recovering a structured signal from high-dimensional data with a nonlinear link function.
method Proposes and analyzes an alternative convex recovery method that treats certain nonlinear link functions as linear in a lifted space.
result Our method successfully recovers the signal when previous methods fail due to a zero proportionality constant.
Detects changes in low-rank signals from high-dimensional data.
problem Detecting changes in low-rank signals from high-dimensional data.
method Sketching-based approach to reduce dimensionality; uses largest eigenvalue of sketch covariance matrices.
result Detects low-rank changes with high probability using sketching of high-dimensional observations.
The paper tackles brain decoding using high-dimensional data.
problem Classifying cognitive states from brain activity data.
method Functional principal component analysis, mutual information networks, and persistent homology.
result Features derived from these methods improve brain decoding accuracy.
Proposes a Monte-Carlo method for sparse signal reconstruction.
problem Reconstructing sparse signals in high-dimensional settings.
method Greedy Monte-Carlo (GMC) search algorithm.
result GMC can achieve perfect reconstruction in undersampling situations.
The paper sets limits on measurements needed for reliable classification of signals.
problem Classifying high-dimensional Gaussian signals from low-dimensional measurements.
method Analyzes upper bounds on measurements for reliable classification in low-noise regime.
result Identifies two operational regimes for reliable classification.
New method detects edges in time-varying networks without minimum signal strength.
problem Detecting edges in time-varying, heavy-tailed, nonparanormal networks.
method Time-varying nonparanormal graphical models, high-dimensional debiasing-free moment estimator, kernel smoothed Kendall's tau correlation matrix.
result Minimax optimal rate of convergence for estimating latent inverse Pearson correlation matrix.
New algorithms detect categorical structures in high-dimensional data.
problem Detecting categorical structures in high-dimensional data.
method Low coordinate degree functions (LCDF) applied to categorical and stochastic block models.
result Unified analysis of LCDF performance for various SBMs and tight lower bounds.
HI-SIGMA improves sensitivity in high-dimensional statistical inference with data-driven background models.
problem Performing high-dimensional statistical inference with complex backgrounds in high-energy physics.
method HI-SIGMA uses generative ML models to learn signal and background distributions, incorporating systematic uncertainties.
result HI-SIGMA provides improved sensitivity compared to classifier-based methods.
LDA-GO improves LDA for high-dimensional data via gradient optimization.
problem LDA struggles in high-dimensional settings due to unreliable covariance matrix estimation.
method LDA-GO learns a low-rank precision matrix via gradient optimization, automatically selecting between Gaussian likelihood and cross-entropy loss.
result LDA-GO outperforms other LDA variants in sparse-signal high-dimensional regimes.
DeepRec uses deep learning to recover signals from one-bit measurements.
problem Signal recovery from one-bit noisy measurements.
method Deep unfolding of inference optimization into deep neural network layers.
result DeepRec improves accuracy and computational efficiency.
New methods implement manifold scattering transform for high-dimensional point cloud data.
problem Classifying data on complex, non-linear manifolds.
method Adapting diffusion maps theory for numerical implementation.
result Effective for signal and manifold classification tasks.
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.
Robust testing of sparse signals in corrupted data.
problem Testing the norm of high-dimensional sparse signals in the presence of arbitrary corruption.
method Two observation models: i.i.d. samples from N(θ,Id) and sparse linear regression model. result The robust testing requires significantly more samples than non-robust testing.
Detects dependencies between high-dimensional data and outcomes.
problem Analyzing educational data with high-dimensional student skills.
method n-TARP clustering to quantify and validate dependencies.
result Valid dependencies between student skills and course grades observed.
New AMP algorithms for rotationally invariant models with reduced complexity.
problem Signal estimation in generalized linear models with arbitrary spectral design matrices.
method Rotationally invariant approximate message passing (AMP) algorithms.
result Performance close to Vector AMP with significantly lower complexity.
Study on Langevin dynamics for recovering planted signals in spiked matrix models.
problem Recovering a planted signal in spiked matrix models.
method Path-wise characterization of overlap using integro-differential equations and explicit formula derivation.
result Sharp phase transition in limiting overlap: positive in one regime, zero in another due to injected noise.
Proposes GAGA algorithm for automatic hyperparameter learning in signal recovery.
problem Difficulty in selecting hyperparameters in traditional signal recovery methods.
method Global Adaptive Generative Adjustment (GAGA) algorithm for automatic hyperparameter learning and signal estimate.
result Consistency of model selection and signal estimate output.