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.
Paper detects communities from graph signals using low-rank excitation modeling.
problem Detect communities in graphs from noisy signals.
method Model signals as graph filter outputs, apply spectral method to covariance matrix.
result Community structure can be retrieved directly from graph signals.
A new model detects and localizes anomalies in multivariate time series data.
problem Anomaly diagnosis in multivariate time series data, especially localization.
method Attention Low-Rank Transformer (ALoRa-T) with low-rank regularization and Attention Low-Rank score.
result The proposed method significantly outperforms state-of-the-art methods in anomaly detection and localization.
Study spherical cap packing with probabilistic methods for detecting low-rank structures.
problem Detecting low-rank structures in high-dimensional Gaussian data.
method Probabilistic spherical cap packing approach for asymptotic bounds and extreme value distributions.
result Developed fast detection method for low-rank structures without spectrum information.
A matrix factorization method detects text outliers using low rank approximations.
problem Challenges in detecting outliers in text data with mostly zero values.
method TONMF based on block coordinate descent (BCD) framework.
result Effective in distinguishing anomalies from natural variations in text data.
Detects changes in signal covariance matrix using extreme eigenvalues.
problem Detects abrupt changes in signal covariance matrix from identity to low-rank.
method Sequential detection based on extreme eigenvalues of sample covariance matrix.
result Effective detection of behavior changes in swarm data.
New algorithm learns low-rank matrices with linear number of samples.
problem Learning low-rank matrices efficiently in latent-variable applications.
method Proposed algorithm that uses linear number of samples in high dimension.
result Learning kimesk, rank-r, matrices requires $Ω( rac{kr}{ε^2})$ samples. Improved defect detection in layered materials using signal separation methods.
problem Challenging defect detection due to strong clutter in layered structures.
method Joint rank and sparsity minimization with an iteratively reweighted nuclear and ℓ1−norm approach, combined with deep learning for parameter optimization. result The proposed approach outperforms conventional methods in terms of accuracy and speed of convergence.
Paper develops a method to robustly cluster tensors with outliers.
problem Clustering tensors contaminated by outliers or sample-specific corruptions.
method Transformed Tensor Low-Rank Representation (OR-TLRR) method.
result Provably recovers row space of clean data and detects outliers.
New method reduces inventory inaccuracies by 10x, saving retailers 4% annually.
problem Inaccurate inventory records cost retailers 4% annually, and manual detection is impractical.
method Proposes a new anomaly detection method for low-rank Poisson matrices using cross-sectional data.
result Our approach reduces anomaly detection costs by up to 10x compared to existing methods.
MOSAIC detects change points in dynamic networks with low-rank and sparse changes.
problem Detecting change points in dynamic networks with specific structural properties.
method Eigen-decomposition-based test with screened signals and residual-based adjustment.
result MOSAIC achieves minimax-optimal detection and testing rates.
New method detects outliers in data with subspaces using sparse representation and random walks.
problem Detecting outliers in data contaminated by subspaces.
method Combines sparse representation with random walks on a graph.
result Correct outlier detection with theoretical guarantees.
Enhanced factored RBMs improve speech detection in noisy conditions.
problem Improving speech detection accuracy in noisy environments.
method Proposes EFTW-RBMs with conditional feature learning and low rank approximation.
result Outperforms existing 1D and 2D speech detection algorithms in various noisy conditions.
Robust VAE detects anomalies in corrupted data.
problem Detect anomalies in data with high corruption.
method Robust Variational Autoencoder (VAE) with four modifications.
result Establishes robustness to outliers and suitability to low-rank modeling.
The paper classifies links with low rank knot Floer and Khovanov homologies.
problem Detecting and classifying links with low rank knot Floer and Khovanov homologies.
method Generalized link Floer homology, used to obtain rank bounds and classify links.
result Knot Floer homology detects T(2,8) and T(2,10). Paper proposes efficient online data thinning for expert analysis.
problem Large-scale streaming data exceeds human analysis capacity.
method Online anomaly detection using dynamic low-rank Gaussian mixture models.
result Proposed method reduces data to unique elements for timely analysis.
Robust PCA detects anomalies and fills gaps in seasonal time series data.
problem Anomaly detection and data imputation in seasonal time series.
method Online robust PCA framework for temporal observations.
result Empirically compared and showed effectiveness in practical situations.
Vision problems ranging from image clustering to motion segmentation to semi-supervised learning can naturally be framed as subspace segmentation problems, in which one aims to recover multiple low-dimensional subspaces from noisy and corrupted input data. Low-Rank Representation (LRR), a convex formulation of the subs…
We present an algorithm, AROFAC2, which detects the (CP-)rank of a degree 3 tensor and calculates its factorization into rank-one components. We provide generative conditions for the algorithm to work and demonstrate on both synthetic and real world data that AROFAC2 is a potentially outperforming alternative to the go…
Meta learns low-rank covariance factors for better uncertainty estimation.
problem Sub-optimal covariance matrices in multi-task settings.
method Meta learns diagonal or diagonal plus low-rank factors using an attentive set encoder.
result Efficiently constructed task-specific covariance matrices improve uncertainty estimation.
Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse components becomes possible. This fundamental identifiability issue arises with tra…
Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank matrix approximation problems. Due to the rank operator being non-convex and discont…
BIND removes background noise from binary matrices, improving detection accuracy and fairness.
problem Real data often violates the i.i.d assumption for binary matrix entries, leading to inaccurate detection.
method BIND optimizes detection by estimating row- and column-wise mixture distributions and eliminating background noise.
result BIND effectively removes background noise and increases detection accuracy and fairness.
Paper proposes CLAIR for efficient LLM fine-tuning across clients.
problem Fine-tuning large language models (LLMs) efficiently and collaboratively.
method Federated LoRA fine-tuning with Collaborative Low-rank Alignment and Identifiable Recovery (CLAIR).
result CLAIR achieves better performance and contamination detection compared to local fine-tuning.
Framework for inferring latent structure from sparse, imperfectly detected bipartite networks.
problem Recovering latent structure from sparse, imperfectly detected bipartite networks in ecology.
method Structured sparse nonnegative low-rank factorization with detection probability estimation and ADMM-based algorithm.
result Improved recovery of latent factors and structure compared to existing methods.
Improves detection of low-rank signals from noisy data matrices.
problem Statistical detection of low-rank signals in noisy data matrices.
method Entrywise pre-transforming data matrix for non-Gaussian noise, sharp phase transition thresholds, central limit theorem for linear spectral statistics, hypothesis test.
result Improves detection of low-rank signals from noisy data matrices, generalizing known results.
LoRAs enable efficient adaptation of large models; this paper explores processing LoRA weights with machine learning.
problem Efficient processing of low-rank weight decompositions in large finetuned models.
method Developed symmetry-aware invariant and equivariant LoL models to process LoRA weights.
result LoL models can predict CLIP scores, finetuning data attributes, and accuracy on downstream tasks.
PCA can detect a low-rank signal in spiked random matrix models, but not always optimally.
problem Understanding when PCA can detect a low-rank signal in the presence of noise.
method Le Cam's notion of contiguity, analysis of spiked Wishart ensemble, and non-spectral tests.
result PCA is sub-optimal for detection in non-Gaussian Wigner ensembles and certain negative spikes in Gaussian Wishart ensemble.
Unified model for signed networks separates balance and anomaly effects.
problem Ignoring sign information in signed networks leads to inaccurate analysis.
method Low rank plus sparse matrix decomposition with regularized formulation.
result The model accurately detects communities and anomalies in signed networks.
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient ascent (a variant of the tensor power method), and hard thresholding of the resid…
New method for robust PCA with exponential family distributions.
problem Recovering low-rank structure from data matrices with outliers.
method Alternating Direction Method of Multipliers for eextRPCA. result Demonstrated effectiveness in steel sheet defect detection and crime activity monitoring.
We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured by solving a non-linear, low-rank representation problem. We show that this low-…
New algorithm improves low-rank matrix estimation accuracy.
problem Estimating low-rank matrices with noisy entries.
method Approximate Message Passing (AMP) combined with spectral initialization.
result Achieves Bayes-optimal accuracy above the spectral threshold.
New method detects low-dimensional manifolds within bounds.
problem Detecting low-dimensional manifolds within bounds.
method Matrix Completion (MC) problem for partially observed distances on a manifold.
result The method provides theoretical guarantees on manifold detection and robustness to non-uniform sampling.
Paper identifies sparse structures and communities in heterogeneous graphical models.
problem Detecting community structures in graphical models.
method Novel decomposition into sparse and low-rank parts, three-stage estimation procedure.
result Consistent model selection for adaptive ℓ1 penalized estimator. A federated model learns shared archetypes from heterogeneous clients in continual learning.
problem Federated learning struggles with client heterogeneity and streaming distribution shifts.
method Clients encode their data as low-rank Hebbian operators, which are sent to a central server for aggregation and factorization into global archetypes.
result Improved global archetype reconstruction and associative retrieval in heterogeneous clients, drift, and novelty settings.
Proposes a novel method for detecting novelty in multi-modal data.
problem Challenges in detecting novelty in high-dimensional, multi-modal data.
method Orthogonalized latent space for disentangling features and defining novelty score.
result Proposed method outperforms state-of-the-art algorithms in novelty detection.
PCA can detect a low-rank signal but is suboptimal for non-Gaussian matrices and synchronization problems.
problem Understanding the optimal and suboptimal performance of PCA in spiked random matrix models.
method Analysis of spiked random matrix models, including Gaussian and non-Gaussian Wigner ensembles, and synchronization problems.
result PCA achieves optimal detection for Gaussian Wigner ensembles under benign priors but is suboptimal for non-Gaussian matrices and synchronization problems.
New method selects kernel bandwidth for SVDD and OCSVM.
problem Selecting optimal Gaussian kernel bandwidth for SVDD and OCSVM.
method Exploits low-rank representation of kernel matrix to suggest bandwidth.
result Method performs well for both low-dimensional and high-dimensional data.
Proposes a method to forecast dependencies between thousands of time series.
problem Computational and numerical difficulties in estimating high-dimensional covariance matrices.
method Combines RNN and Gaussian copula process with low-rank covariance structure.
result Significant accuracy improvements over state-of-the-art baselines.
This paper considers probabilistic estimation of a low-rank matrix from non-linear element-wise measurements of its elements. We derive the corresponding approximate message passing (AMP) algorithm and its state evolution. Relying on non-rigorous but standard assumptions motivated by statistical physics, we characteriz…
Paper develops an online EM algorithm for graph signal inference from streaming data.
problem Joint inference and clustering of graph signals with non-white excitation.
method Mixture model with low-rank plus sparse prior, online EM algorithm.
result Proposed online EM algorithm converges to MAP solution.
This paper presents a Bayesian method for estimating the rank of a low-rank tensor model of joint PMF.
problem Estimating the rank of a low-rank tensor model of joint PMF from observed data.
method Bayesian framework for estimating low-rank components and rank simultaneously, using variational inference.
result Automatic rank detection and improved estimation accuracy compared to cross-validation methods.
Paper introduces an unsupervised tensor-based anomaly detection method for spatiotemporal data.
problem Challenges in detecting anomalies in spatiotemporal data, especially in urban traffic monitoring and medical imaging.
method Formulates anomaly detection as a regularized robust low-rank + sparse tensor decomposition, incorporating spatiotemporal smoothness and local dependencies.
result Demonstrates improved anomaly detection performance on both synthetic and real data.
New method improves image and signal processing with nonconvex rank surrogates and dual momentum.
problem Optimizing nonconvex rank minimization problems in image processing.
method Proposes a novel nonconvex rank surrogate, uses ADMM with dual momentum trick.
result Effective in image and signal processing applications, outperforming state-of-the-art methods.
ZDP detects drift in large language models without labels, proving key theorems and metrics.
problem Detecting drift in large language models without task labels or output evaluations.
method Zero-Direction Probing (ZDP) framework based on null directions of transformer activations, proving theoretical guarantees.
result Proves the Variance--Leak Theorem, Fisher Null-Conservation, Rank--Leak bound, and logarithmic-regret guarantee.
RMCSE improves voltage estimation in low-observability distribution systems.
problem Insufficient measurements in distribution system state estimation.
method Combines matrix completion and power system model, minimizes rank and residual with different weights.
result Robust voltage estimation in low-observability systems without bad data detection.
Model captures sleep patterns in infant data.
problem Infant sleep data analysis with missing values.
method Nonparametric model using low-rank matrix factorization with time-smoothing regularization.
result Extracts meaningful sleep patterns and trends.