We develop latent variable models for Bayesian learning based low-rank matrix completion and reconstruction from linear measurements. For under-determined systems, the developed methods are shown to reconstruct low-rank matrices when neither the rank nor the noise power is known a-priori. We derive relations between th…
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48 results for “low-rank relations”
The paper proposes using low rank assumption to improve causal structure learning in DAGs.
problem Challenges in learning causal structures in high-dimensional, non-sparse DAGs.
method Exploits low rank assumption of DAG adjacency matrix to adapt causal structure learning methods.
result Maximum rank is highly related to hubs, suggesting low rank for scale-free networks.
Proposes a low-rank bilinear pooling model for link prediction in knowledge graphs.
problem Link prediction in incomplete knowledge graphs.
method Factorized bilinear pooling model with Tucker decomposition constraints.
result Efficient and parameter-efficient model with low-rank approximation.
Algorithm leverages low-rank relations between surrogate tasks for structured prediction.
problem Structured prediction with large or infinite-dimensional surrogate spaces.
method Trace norm regularization to leverage relationships between surrogate outputs without explicit coding/decoding functions.
result Our algorithm can improve generalization performance over previous methods.
Equivalent formulations for low-rank matrix optimization are proven.
problem Low-rank matrix optimization with rank constraints.
method Established geometric landscape connections between manifold and factorization formulations.
result Equivalence between manifold and factorization formulations at FOSPs, SOSPs, and strict saddles.
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…
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.
We study the problem of prediction for evolving graph data. We formulate the problem as the minimization of a convex objective encouraging sparsity and low-rank of the solution, that reflect natural graph properties. The convex formulation allows to obtain oracle inequalities and efficient solvers. We provide empirical…
Proposes a low-rank deep CNN for multi-task learning.
problem Multi-task learning with deep neural networks.
method Low-rank deep network with nuclear norm and sparsity penalties.
result Improves performance on multiple tasks compared to standard models.
Paper tackles fair low-rank approximation and column subset selection.
problem Minimize loss over sub-populations in machine learning.
method Developed algorithms for fair low-rank approximation and fair column subset selection.
result Achieved polynomial time algorithms for fair low-rank approximation.
FLAMBE tackles RL in low rank MDPs by learning features.
problem Dealing with the curse of dimensionality in RL.
method Develops FLAMBE, a method that engages in exploration and representation learning for RL in low rank transition models.
result FLAMBE efficiently learns features for RL in low rank transition models.
Efficient Low-Rank Matrix Estimation, Experimental Design, and Arm-Set-Dependent Low-Rank Banditsstat.ML
Novel method for efficient low-rank matrix estimation and bandit algorithms.
problem Low-rank matrix estimation and bandit problems.
method LowPopArt method for low-rank matrix estimation and novel experimental design criterion.
result Improved recovery guarantees and regret bounds for low-rank bandit algorithms.
We present a novel algebraic combinatorial view on low-rank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the treatment of single entries in a closed theoretical and practical framework. More s…
We connect Causal inference and low-rank recovery via RDT and free probability theory.
problem Determining the applicability of causal inference via low-rank recovery.
method Random Duality Theory, free probability theory, and mathematical rigor.
result Exact closed-form worst case phase transitions for causal inference.
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.
Study uncovers new phase transitions in asymmetric causal inference scenarios.
problem Understanding typical phase transitions in asymmetric causal inference.
method Combining Causal inference (C-inf) and Low-rank recovery (LRR) with Random duality - Free probability theory (RDT-FPT).
result Discovering a doubling low-rankness phenomenon in asymmetric scenarios.
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.
This work learns low-rank hyperbolic embeddings for tasks with hierarchical structures.
problem Learning hyperbolic embeddings of tasks with hierarchical structures.
method Formulated as manifold optimization problems and proposed computationally efficient algorithms.
result Efficacy of the proposed approach demonstrated through empirical results.
Deep-SLR reduces SLR complexity with CNN, enabling efficient parallel MRI.
problem High computational complexity in SLR matrix completion.
method Convolutional Neural Network (CNN) trained to estimate annihilation relations from imperfect k-space measurements.
result Significant reduction in runtime by three orders of magnitude compared to SLR schemes.
New model encodes multivariate signals more efficiently with sparsity and low-rank constraints.
problem Efficiently encoding multivariate signals with sparsity and low-rank constraints.
method Multivariate convolutional sparse coding with tensor algebra, CP decomposition, and alternating optimization.
result Proves model closely related to Kruskal tensor regression problem with theoretical guarantees.
Provable Emergence of Deep Neural Collapse and Low-Rank Bias in -Regularized Nonlinear Networkscs.LG
The paper connects neural collapse and low-rank bias in networks with L2 regularization.
problem Understanding the emergence of low-rank bias and neural collapse in L2-regularized networks.
method Unified theoretical framework linking TCV and rank of weight matrices, proving global optimality of DNC1, and establishing a benign landscape property.
result Zero TCV across intermediate layers minimizes representation cost under natural architectural constraints, and DNC1 is globally optimal.
We propose a method to infer stochastic low-rank RNNs from neural data.
problem Fitting low-rank RNNs to noisy, stochastic neural data.
method Variational sequential Monte Carlo methods for stochastic low-rank RNNs.
result Lower dimensional latent dynamics compared to state-of-the-art methods.
New nonconvex regularizers improve low-rank matrix recovery efficiency and accuracy.
problem Efficiently recover low-rank matrices from incomplete data.
method Factor group-sparse regularization, related to Schatten-p norms.
result Improved generalization error bounds for Schatten-p norms as p decreases.
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.
Most existing approaches address multi-view subspace clustering problem by constructing the affinity matrix on each view separately and afterwards propose how to extend spectral clustering algorithm to handle multi-view data. This paper presents an approach to multi-view subspace clustering that learns a joint subspace…
Deep ReLU networks escape from the origin via saddle points with a low-rank bias.
problem Understanding the dynamics of gradient descent in deep ReLU networks.
method Analysis of escape directions and singular values of weight matrices.
result The first singular value of the -th layer weight matrix is at least larger than any other singular value.
Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is simultaneously low-rank and sparse. However, such problems are highly challenging t…
New method estimates and completes tensors from ordinal data, improving accuracy and efficiency.
problem Estimating and completing tensors from incomplete, ordinal observations.
method Multi-linear cumulative link model with rank-constrained M-estimator.
result The proposed estimator achieves faster convergence and is minimax optimal.
CP degeneracy affects tensor regression solutions, especially in high dimensions.
problem CP degeneracy in tensor regression.
method Analysis of CP degeneracy and development of a penalized strategy.
result A general penalized strategy to overcome CP degeneracy in tensor regression.
In the past decade, sparse and low-rank recovery have drawn much attention in many areas such as signal/image processing, statistics, bioinformatics and machine learning. To achieve sparsity and/or low-rankness inducing, the norm and nuclear norm are of the most popular regularization penalties due to their co…
The Nystrom method is an efficient technique used to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by working exclusively with a subset of its columns. In this work we relate this as…
Predict missing movie ratings or graph embeddings with low rank matrices.
problem Predicting missing entries in a ratings matrix or graph embeddings with known linear relations.
method Low rank matrix completion approach applied to graph embeddings.
result Effective methods for predicting missing entries in matrices and graph embeddings.
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation matrix completion in various fields such as the financial market and the low-ra…
BoRA finetunes multi-task LLMs by sharing information through hierarchical priors.
problem Limited data for some tasks in multi-task LLMs.
method Bayesian hierarchical low-rank adaption.
result BoRA outperforms individual and unified model approaches.
Stochastic gradient descent (SGD) on a low-rank factorization is commonly employed to speed up matrix problems including matrix completion, subspace tracking, and SDP relaxation. In this paper, we exhibit a step size scheme for SGD on a low-rank least-squares problem, and we prove that, under broad sampling conditions,…
Low Rank Forecastingstat.ML
Low-rank forecasting improves consistency in time series predictions.
problem Forecasting multiple values of a time series using past values.
method Breaks forecasting into estimating a latent state and future values, using convex optimization.
result Forecast consistency is achieved, meaning estimates of the same value at different times are consistent.
Faster GW alignment for incomparable point clouds via low-rank couplings.
problem Aligning points across incomparable point clouds.
method Low-rank couplings and costs to solve Gromov-Wasserstein framework in linear time.
result Linear-time computation of Gromov-Wasserstein distances.
Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization method for stable recovery of low-rank matrices in the noisy case. The procedure is…
Completing a data matrix X has become an ubiquitous problem in modern data science, with applications in recommender systems, computer vision, and networks inference, to name a few. One typical assumption is that X is low-rank. A more general model assumes that each column of X corresponds to one of several low-rank ma…
Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time approximations, such as spectral and inducing-point methods, have been suggested and a…
Gradient descent solves asymmetric low-rank matrix factorization efficiently.
problem Optimizing asymmetric low-rank matrix factorization with non-convex and non-smoothness issues.
method Randomly initialized gradient descent with new symmetrization and perturbation techniques.
result Gradient descent converges to a global minimum of the asymmetric low-rank factorization problem.
We propose a sparse and low-rank tensor regression model to relate a univariate outcome to a feature tensor, in which each unit-rank tensor from the CP decomposition of the coefficient tensor is assumed to be sparse. This structure is both parsimonious and highly interpretable, as it implies that the outcome is related…
Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to be one of the most accurate and efficient, and formed a major component of the wi…
Proposes MvLPE for better multi-view representation learning.
problem Learning representations from multi-view data with varying correlations.
method Integrates multi-view data into a centroid view while maintaining low-rank reconstruction relations.
result MvLPE outperforms existing methods on benchmark datasets.
Spectral algorithm reduces samples needed for multitask regression.
problem Jointly recover shared and task-specific components in low-rank multitask regression.
method Common mechanism regression (CMR) model with a non-iterative spectral algorithm.
result Provable non-convex bi-linear structure is overcome with spectral algorithm.
As opposed to manual feature engineering which is tedious and difficult to scale, network representation learning has attracted a surge of research interests as it automates the process of feature learning on graphs. The learned low-dimensional node vector representation is generalizable and eases the knowledge discove…
There has recently been considerable interest in completing a low-rank matrix or tensor given only a small fraction (or few linear combinations) of its entries. Related approaches have found considerable success in the area of recommender systems, under machine learning. From a statistical estimation point of view, the…
Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisonsstat.ME
Low-rank framework for task-specific LLM ranking from sparse comparisons.
problem Challenges in reliable task-specific ranking of LLMs under sparse, imbalanced comparisons.
method Low-rank modeling of task-by-model ability matrix, max-norm accurate estimator, task-wise top-K recovery guarantees, uncertainty quantification framework.
result Improves sample efficiency and produces tighter, better-calibrated ranking certificates.