Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal processing and bioinformatics. Recently, much progress has been made in theories, algori…
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48 results for “low-rank analysis”
Hankel low-rank approximation and completion in time series analysis and forecasting: a brief reviewmath.NA
The paper reviews Hankel low-rank methods for time series analysis and forecasting.
problem Developing efficient methods for time series analysis and forecasting.
method Hankel low-rank approximation and completion techniques.
result Discussion of methods and challenges in obtaining optimal solutions.
A unified error analysis for randomized low-rank approximation with application to data assimilationmath.NA
Unified error analysis for low-rank approximation improves data assimilation performance.
problem Analyzing the error in low-rank approximation methods for data assimilation.
method Unified stochastic analysis framework for Frobenius norm error bounds on centered and non-standard Gaussian matrices.
result Unified bounds provide clearer interpretations and enable better practical choices for covariance matrices.
Low-rank signal modeling has been widely leveraged to capture non-local correlation in image processing applications. We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches. The low-rank tensors are fed into the alternative direction multiplier method (ADMM) …
IRCUR accelerates RPCA by using CUR decomposition for efficient low rank estimation.
problem Dimension reduction in robust principal component analysis.
method IRCUR employs CUR decomposition to update the low rank component efficiently.
result IRCUR achieves significant computational efficiency compared to existing algorithms.
ScaledGD improves gradient descent for ill-conditioned low-rank matrix estimation.
problem Efficiently solving ill-conditioned low-rank matrix estimation problems.
method Scaled Gradient Descent (ScaledGD) with adaptive pre-conditioners.
result Linear convergence rate independent of condition number, low per-iteration cost.
Leave-One-Out Analysis for Nonconvex Robust Matrix Completion with General Thresholding Functionscs.IT
Paper analyzes robust matrix completion with efficient nonconvex method and leave-one-out analysis.
problem Robust matrix completion with sparse noise.
method Alternates between projected gradient step for low-rank and thresholding step for sparse noise.
result Achieves linear convergence for general thresholding functions.
Sparse PCA is a widely used technique for high-dimensional data analysis. In this paper, we propose a new method called low-rank principal eigenmatrix analysis. Different from sparse PCA, the dominant eigenvectors are allowed to be dense but are assumed to have a low-rank structure when matricized appropriately. Such a…
We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate to the rank. Here we study low-rank matrix reconstruction using both the trace-norm, as well as the less-studied max-no…
Develops PRPCA for smooth image recovery combining low-rank and smoothness.
problem Image matrix recovery under low-rank and smoothness assumptions.
method Projected Robust PCA (PRPCA) framework combining low-rank and smoothness.
result Explicit statistical guarantees for PRPCA, reducing matrix dimensionality.
Novel Fréchet regression method handles errors-in-variables with low-rank covariates.
problem Regression with noisy and limited covariate data.
method Combines global Fréchet regression and principal component regression for low-rank structure.
result Improved efficiency and accuracy in high-dimensional and noisy data settings.
Novel low-rank neural decoder improves -ECoG neural decoding.
problem Challenging neural decoding from high-dimensional -ECoG data.
method Low-rank structure in neural network decoder.
result Low-rank decoder outperforms standard PCA.
We propose a new framework for the analysis of low-rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the classical low-rank SVD for matrices and multi-linear SVD for tensors. Then, building …
Generalized Low Rank Modelsstat.ML
Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well known techniques in da…
Paper proposes a new method to separate low rank and sparse matrices without bias.
problem Recovering low rank and sparse matrices from measurements.
method Uses nonconvex regularizers and alternating proximal gradient descent.
result Error bounds for the algorithm applied to sparse optimization, matrix completion, and robust PCA.
In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a rank constraint. We consider a matrix completion problem for Hankel matrices an…
Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume that the input partially-observed matrix is low rank. The success of these methods…
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 , rank-, matrices requires $Ω( rac{kr}{ε^2})$ samples.
Paper introduces a new histogram estimator for nonparametric density estimation that improves performance.
problem Smoothness-based nonparametric density estimators are not optimal for all types of data.
method Incorporates a multi-view latent variable model into histogram-style estimators.
result A new histogram estimator converges faster to multi-view models in error.
Dictionary learning and component analysis models are fundamental for learning compact representations that are relevant to a given task (feature extraction, dimensionality reduction, denoising, etc.). The model complexity is encoded by means of specific structure, such as sparsity, low-rankness, or nonnegativity. Unfo…
Various problems in data analysis and statistical genetics call for recovery of a column-sparse, low-rank matrix from noisy observations. We propose ReFACTor, a simple variation of the classical Truncated Singular Value Decomposition (TSVD) algorithm. In contrast to previous sparse principal component analysis (PCA) al…
We provide new approximation guarantees for greedy low rank matrix estimation under standard assumptions of restricted strong convexity and smoothness. Our novel analysis also uncovers previously unknown connections between the low rank estimation and combinatorial optimization, so much so that our bounds are reminisce…
SALT models combine ARHMM and SLDS for efficient, interpretable time-series analysis.
problem Efficient modeling of systems with time-varying dynamics and long-range dependencies.
method Switching autoregressive low-rank tensor models parameterized with a low-rank factorization.
result SALT models provide a balance of interpretability and efficiency, outperforming ARHMMs and SLDSs.
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.
We revisit the use of Stochastic Gradient Descent (SGD) for solving convex optimization problems that serve as highly popular convex relaxations for many important low-rank matrix recovery problems such as \textit{matrix completion}, \textit{phase retrieval}, and more. The computational limitation of applying SGD to so…
Low-rank approximations of data matrices are an important dimensionality reduction tool in machine learning and regression analysis. We consider the case of categorical variables, where it can be formulated as the problem of finding low-rank approximations to Boolean matrices. In this paper we give what is to the best …
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 .
result Demonstrated effectiveness in steel sheet defect detection and crime activity monitoring.
Multimodal research is an emerging field of artificial intelligence, and one of the main research problems in this field is multimodal fusion. The fusion of multimodal data is the process of integrating multiple unimodal representations into one compact multimodal representation. Previous research in this field has exp…
FedLoRU improves FL efficiency by using low-rank updates.
problem Communication inefficiency and performance reduction in Federated Learning.
method Proposes FedLoRU, a low-rank update framework for FL, which reduces communication costs while maintaining performance.
result FedLoRU achieves convergence rates similar to FedAvg and is robust to heterogeneous and large numbers of clients.
New approach to convex hulls for low-rank problems.
problem Characterizing convex hulls for low-rank sets.
method Matrix perspective function and orthogonal projection matrices.
result Strong relaxations for various low-rank problems.
factor analysismath.OC
New method for factor analysis using nuclear and norms.
problem Finding a low-rank plus sparse decomposition from noisy covariance matrix.
method Formulated an optimization problem with nuclear norm, norm, and KL divergence. Used alternating minimization algorithm.
result Algorithm effectively decomposes covariance matrices in synthetic and real datasets.
We introduce a new framework for optimal transport using Schatten-p regularization to recover low-rank structures.
problem Optimal transport problems with low-rank structure recovery.
method Schatten-p norm regularization to promote low-rank structure in transport maps and plans.
result Unified convex programs for low-rank structure recovery with theoretical guarantees and efficient algorithms.
New algorithm for weighted low rank approximation with provable guarantees.
problem Weighted low rank approximation (WLRA) is computationally hard.
method Reweights the low rank solution using the weight matrix itself.
result Provably optimal approximation guarantees for WLRA.
Weight Decay induces low-rank weight matrices in neural networks, improving generalization.
problem Improving generalization in neural networks.
method Training ReLU NN with Weight Decay and Stochastic Gradient Descent.
result The weight matrix of a trained NN is approximately rank-two.
Paper introduces G-LowTESTR for efficient tensor bandits.
problem Efficient decision-making in multi-dimensional data with non-linear reward functions.
method Generalized low-rank tensor contextual bandits model and G-LowTESTR algorithm.
result G-LowTESTR achieves superior regret bound compared to vectorization and matricization methods.
Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure learning. In this paper, we demonstrate interesting connections between the two, espe…
Proposes a low-rank PGD attack for more efficient adversarial training.
problem Efficiency and effectiveness of adversarial training methods.
method Variation of PGD to compute low-rank perturbations.
result Low-rank PGD attacks are more efficient and comparable to traditional attacks.
The report analyzes Legendre decomposition for tensor data.
problem Finding effective lower dimensional representations of tensors.
method Theoretical analysis of dual parameters and dually flat manifold properties, followed by experimental verification and clustering.
result Parameters on submanifold cannot be directly used as low-rank representations.
Robust Low-rank Matrix Completion via an Alternating Manifold Proximal Gradient Continuation Methodcs.LG
New method improves robust low-rank matrix completion for computer vision.
problem Robust low-rank matrix completion for partially observed data.
method Formulated as a nonsmooth Riemannian optimization problem over Grassmann manifold, solved with an alternating manifold proximal gradient continuation method.
result Demonstrated advantages over existing approaches in background extraction from surveillance videos.
We accelerate the power method for strong low-rank approximation using fast sketching.
problem Efficiency bottleneck in power method for large target ranks.
method Developed an algorithmic and theoretical framework for accelerating the power method using fast sketching.
result Simple and provably efficient methods for singular value decomposition, low-rank factorization, and Nyström approximation.
Paper proposes a new algorithm for graph learning with covariance constraints.
problem Graphical models and factor analysis not jointly leveraged in graph learning processes.
method Penalized maximum likelihood estimation of an elliptical distribution with Riemannian optimization.
result Effectiveness of the proposed approach demonstrated on real-world data sets.
We simplify SSL by approximating redundant structural components with low-rank factorization.
problem Improving self-supervised learning performance with limited labeled data.
method Low-rank approximation of structural redundancy, introducing ε_s to measure approximation quality.
result The proposed method enhances SSL performance, as shown by theoretical and experimental validations.
Low-Rank Thinningstat.ML
New method reduces summary points for datasets while maintaining quality.
problem Thinning datasets to reduce summary points while maintaining quality.
method Low-rank analysis of sub-Gaussian thinning.
result Guarantees high-quality compression for any distribution and kernel.
Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via convex relaxations. Nuclear norm regularization is the prevailing convexifying technique for dealing …
Paper analyzes convergence of PAM method for low-rank factorization models.
problem Convergence analysis of PAM method with subspace correction for low-rank factorization models.
method Majorized proximal alternating minimization (PAM) method with subspace correction.
result Established full convergence of PAM method under KL property and column -norm condition.
Exact Linear Convergence Rate Analysis for Low-Rank Symmetric Matrix Completion via Gradient Descentmath.OC
Gradient descent achieves exact linear convergence rate for symmetric matrix completion.
problem Low-rank symmetric matrix completion using gradient descent.
method Local analysis of gradient descent for symmetric matrices without additional assumptions.
result Closed-form expression of exact linear convergence rate matches practice.
LEARNER improves low-rank matrix estimation using source population data.
problem Improving low-rank matrix estimation in target populations with diverse data sources.
method LEARNER uses similarity in latent spaces between source and target populations to enhance estimation.
result LEARNER often outperforms benchmark methods, especially with higher signal-to-noise ratios in the source population.
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous theoretical analysis. We show that the proposed algorithms enjoy linear convergence a…