Paper improves MVSC using tensor low-rank modeling.
problem Improving multi-view spectral clustering.
method Structured tensor low-rank norm for MVSC optimization.
result Proposed method outperforms state-of-the-art methods.
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48 results for “Low-rank Tensor”
Optimal low rank tensor recovery requires a minimum number of entries for accurate reconstruction.
problem Exact recovery of high order tensors of low rank from a subset of their entries.
method Riemannian optimization algorithm with initial value from a spectral method, leveraging tensor restricted isometry property and curvature of the manifold.
result Tensor of size of ranks can be reconstructed with high probability from entries.
New method uses low-rank tensor factor analysis for better image restoration.
problem Restoring images from limited data.
method Low-rank tensor factor analysis combined with ADMM.
result The method outperforms traditional approaches, especially at low sampling rates.
A low-rank tensor model simplifies multi-dimensional Markov chains.
problem Simplifying the dynamics of multi-dimensional Markov chains.
method Low-rank tensor decomposition for multi-dimensional state spaces.
result Our tensor model requires fewer parameters and samples than conventional methods.
Paper develops inference methods for low-rank tensors without debiasing.
problem Statistical inference for low-rank tensor models.
method Two-iteration alternating minimization for asymptotic distribution.
result Asymptotic distributions and confidence regions for singular subspaces.
ScaledGD algorithm estimates low-rank tensors efficiently from corrupted data.
problem Estimating meaningful information from corrupted tensor data.
method Scaled gradient descent (ScaledGD) algorithm with tailored spectral initializations.
result ScaledGD achieves linear convergence at a constant rate independent of condition number.
Robust tensor ring completion improves tensor recovery accuracy and efficiency.
problem Tensor completion sensitivity to sparse components.
method Robust Tensor Ring Completion (RTRC) with weighted nuclear norms and l1 regularization.
result Exact recovery guarantees and superior performance in various tasks.
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 …
Develops methods to estimate high rank tensors from noisy data.
problem Estimating high rank tensors from noisy observations.
method Generative latent variable tensor model, polynomial-time spectral algorithm.
result Achieves computationally optimal rate for signal tensor estimation.
Tensor regression networks improve neural network compression and regularization.
problem Improving neural network compression and regularization with low-rank tensor approximations.
method Investigating various low-rank tensor approximations in tensor regression networks.
result Tensor regression networks with Global Average Pooling layer outperformed in deep CNNs, while shallow CNNs with tensor regression and dropout achieved lower test error.
Bayesian model improves image completion accuracy by automatically learning low rank structure.
problem Improving image completion accuracy with limited data and avoiding overfitting.
method Developed a Bayesian low rank tensor ring model with multiplicative interaction and Student-T distribution for sparse core factors.
result The proposed method outperforms state-of-the-art image completion techniques, especially in recovery accuracy.
Paper proposes a method for estimating sparse and low-rank tensors from sketchings.
problem Estimating sparse and low-rank tensors from limited data.
method Two-stage non-convex implementation using sparse tensor decomposition and thresholded gradient descent.
result Exact and stable recovery of tensors in noisy and noiseless cases with high probability.
Unified model for tensor completion using low-rank and sparse Tucker decomposition.
problem Estimating missing data from incomplete tensor measurements.
method Unified low-rank and sparse enhanced Tucker decomposition model with ADMM.
result Our model achieves higher recovery accuracy on various real-world data sets.
Scaling and Scalability: Provable Nonconvex Low-Rank Tensor Estimation from Incomplete Measurementscs.LG
New algorithm recovers tensor factors from incomplete measurements efficiently.
problem Recovering tensor factors from incomplete measurements.
method Scaled gradient descent (ScaledGD) algorithm with spectral initializations.
result ScaledGD provably converges linearly for tensor completion and regression.
New method improves tensor completion for weakly-dependent spatiotemporal data.
problem Improving tensor completion for weakly-dependent data on graphs.
method Introducing -norm and Graph Laplacian penalties for low-rank tensor decomposition and completion.
result Improved performance in metro passenger flow prediction.
Proposes tensor Q-rank for better tensor rank recovery in complex data.
problem Improving tensor rank recovery for complex data with low sampling rate.
method Introduces tensor Q-rank and two selection methods for , proposing VMTQN and MOTQN models.
result Demonstrates superior performance in tensor completion problems compared to TNN-based methods.
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.
Paper develops RGN method for estimating low-rank tensors from noisy measurements.
problem Estimating low-rank tensors from noisy linear measurements.
method Riemannian Gauss-Newton (RGN) method for efficient low-rank tensor estimation.
result First local quadratic convergence guarantee of RGN for low-rank tensor estimation in noisy settings.
Derives smooth homogeneous structures for low-rank tensors.
problem Understanding the geometry of low-rank tensors.
method Analyzes sets of fixed CP, multilinear, and TT rank tensors to derive smooth homogeneous manifolds.
result Derives Riemannian metrics with complete geodesics.
Develops TOFU for tensor bandits with low-rank structure.
problem Linear bandit models fail to capture high-dimensional, low-rank tensor structures.
method Develops TOFU, a tensor bandit algorithm that estimates low-dimensional subspaces and uses norm constraints.
result Improves regret bound by a multiplicative factor that grows exponentially in system order.
A new framework improves tensor completion accuracy by considering numerical priors.
problem Tensor completion accuracy loss due to ignoring numerical priors.
method Generalized CP Decomposition Tensor Completion (GCDTC) framework incorporating numerical priors.
result GCDTC framework outperforms state-of-the-arts in non-negative tensor completion.
Introduces tensor bandits for multi-dimensional online decision making.
problem Optimal decision making in multi-dimensional online scenarios.
method Stochastic low-rank tensor bandits, tensor elimination, tensor epoch-greedy, tensor ensemble sampling.
result Tensor elimination and tensor epoch-greedy algorithms outperform existing methods.
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.
A new tensor p-shrinkage nuclear norm improves low-rank tensor completion.
problem Estimating tensors from partial observations with low rank.
method Proposed tensor p-shrinkage nuclear norm (p-TNN) and an efficient algorithm.
result Upper bound of recovery error provided for the LRTC model.
Statistically Optimal and Computationally Efficient Low Rank Tensor Completion from Noisy Entriesstat.ML
New method for estimating low rank tensors from noisy data efficiently.
problem Estimating low rank tensors from noisy entries.
method Polynomial-time computable estimating procedure based on power iteration and spectral initialization.
result Achieves minimax optimal rates of convergence for noisy tensor completion.
Proposes GTTN for discovering all low-rank structures in deep multi-task learning.
problem Discovering all low-rank structures among tasks in deep multi-task models.
method Introduces GTTN, a convex combination of matrix trace norms of all tensor flattenings, to automatically determine the importance of components.
result Demonstrates the effectiveness of GTTN on real-world datasets.
The paper shows how gradient flow on over-parametrized tensor decomposition behaves like deflation.
problem Understanding the training dynamics of gradient flow on tensor decomposition.
method Empirical observation and mathematical proof of gradient flow dynamics for orthogonally decomposable tensors.
result Gradient flow dynamics for orthogonally decomposable tensors follows a tensor deflation process, recovering all tensor components.
Unified approach tackles high-dimensional tensor bandits with convex optimization and weakly decomposable regularizers.
problem Challenges in high-dimensional generalized tensor bandits where existing algorithms fail.
method Proposes a generalized linear tensor bandits algorithm with a unified analytical framework using convex optimization and weakly decomposable regularizers.
result Unified analytical framework provides better bounds and broader applicability compared to existing methods.
ISLET efficiently estimates low-rank tensors with optimal performance and speed.
problem Efficient estimation of low-rank tensors with optimal performance and speed.
method Importance sketching for low-rank tensor estimation.
result ISLET achieves sharp minimax optimality in mean-squared error under low-rank Tucker assumptions.
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.
Paper connects tensor regression and Gaussian processes for multi-way data analysis.
problem Learning high-order correlations from multi-way data.
method Demonstrates connections between low-rank tensor regression and Gaussian processes, proving oracle inequality and learning curve.
result Low-rank tensor regression is equivalent to constrained Bayesian inference in Gaussian processes, with learning dependent on eigenvalues and variable correlations.
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 AMP algorithms reveal phase transitions in tensor recovery.
problem Understanding algorithmic behavior of low-rank tensor decompositions.
method Derive Bayesian AMP algorithms and use dynamic mean field theory.
result Reveals phase transitions between easy, hard, and impossible inference regimes.
Paper proposes an optimal framework for tensor estimation across various applications.
problem Generalized tensor estimation problems in computational imaging, genomics, and network analysis.
method Unified projected gradient descent approach to find low-rank tensor fits under generalized parametric models.
result Achieves minimax optimal rate of convergence in estimation error for various tensor estimation problems.
Study on core consistency preservation in compressed tensors.
problem Ensuring low-rank structure is maintained during tensor compression.
method Theoretical analysis and experimental validation of compression schemes.
result Identified sufficient conditions for preserving core consistency.
Proposes BHT-ARIMA for forecasting multiple short time series.
problem Forecasting multiple short time series with mutual correlations.
method Block Hankel tensors, Tucker decomposition, generalized tensor ARIMA.
result Improves forecasting accuracy and reduces computational cost.
Proposes a new tensor grid method for image completion.
problem Image completion from missing data.
method Low-rank tensor grid with two-stage density matrix renormalization group initialization and alternating least squares factorization.
result The proposed tensor grid method outperforms existing methods in image recovery accuracy.
Unified algorithm for tensor decomposition supports multiple loss functions and models.
problem Efficient tensor decomposition for various models and loss functions.
method Hierarchical combination of ADMM and MM for optimization.
result Wide-range applications can be solved by the proposed algorithm.
Proposes a model to relate a tensor feature to a univariate outcome using sparse and low-rank components.
problem Relating a univariate outcome to a feature tensor with sparse and low-rank components.
method Divide-and-conquer strategy, stagewise estimation procedure for unit-rank tensor regression.
result The stagewise solution paths converge to those of regularized regression as step size goes to zero.
Efficient multimodal fusion reduces complexity and improves performance.
problem Multimodal data fusion with tensor transformations.
method Low-rank Multimodal Fusion using tensors.
result Significant reduction in computational complexity with competitive performance.
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.
Estimates joint probability distribution from 1-way marginals using low-rank tensors and random projections.
problem Nonparametric estimation of joint probability mass function (PMF) from limited data.
method Low-rank tensor decomposition and random projections to link data to PMF estimation.
result Estimates joint density from 1-way marginals using transformed space and novel algorithm.
Efficient solver for nonconvex tensor regularization reduces computational cost.
problem Computational inefficiency in extending nonconvex regularization to tensor learning.
method Proximal average algorithm with adaptive momentum, maintaining sparse plus low-rank structure.
result Shows good statistical performance and accuracy on tensor completion problems.
TensorGuide improves LoRA efficiency and expressivity through joint tensor-train optimization.
problem Limited expressivity and generalization of standard LoRA.
method TensorGuide uses a unified tensor-train structure with controlled Gaussian noise to generate correlated low-rank matrices.
result TensorGuide achieves superior accuracy and scalability with fewer parameters compared to standard LoRA and TT-LoRA.
This work provides a guaranteed tensor recovery method by combining low-rankness and smoothness priors.
problem Guaranteed tensor recovery with theoretical guarantees for low-rank and smoothness priors.
method Developed a new regularization term that combines low-rankness and smoothness priors, proving exact recovery guarantees.
result Rigorously proved exact recovery guarantees for tensor completion and tensor robust principal component analysis.
SLTR model preserves tensor structure and reduces prediction time costs.
problem Efficiently predicting tensor data relationships with structural preservation.
method SLTR model enforces sparsity and low-rankness via proximal gradient method.
result SLTR achieves better solutions with significantly reduced time costs.
New algorithm improves tensor completion performance.
problem Tensor completion for partially observed data.
method Adaptive ADMM optimization framework for low-rank tensor completion.
result New method outperforms conventional techniques in NMSE.
New method reduces tensor completion sample complexity to nearly optimal levels.
problem Low rank tensor completion with noisy measurements.
method Using atomic-norm and max-quasi-norm for tensor completion.
result Optimal sample complexity of achieved for tensor completion.