Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA), NonnegativeMatrix and Tensor Factorization (NMF/NTF), Smooth Component Analysis (Smo…
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48 results for “multiway analysis”
Efficient tensor decomposition for count data models achieves near-optimal multiway analysis.
problem Efficient tensor decomposition for count data models.
method Rank-constrained maximum-likelihood estimator for tensor decomposition.
result Achieves multiway analysis with variance matching Cramér-Rao Lower Bound up to constants and logarithmic factors.
The paper develops methods for causal function estimation and inference with multiway clustered data.
problem Estimation and inference for causal functions under multiway clustering.
method Two-step procedure using machine learning for nuisance parameters and projection onto basis functions.
result Rejects the null hypothesis of uniformly zero effects and reveals heterogeneous treatment effects.
The paper explores how multiway data from PDEs can be accurately tracked using EnKF with specific covariance and precision estimators.
problem Tracking sparse and multiway structures in dynamical processes governed by PDEs.
method Examined several multiway covariance and precision matrix estimators in the context of physics-driven forecasting and EnKF.
result Multiway data from Poisson and convection-diffusion PDEs can be accurately tracked using EnKF with appropriate estimators.
New method for multiway clustering of 3rd order tensors.
problem Clustering of 3rd order tensors.
method MCAM method based on affinity matrix and clustering.
result Competitive results on synthetic and real datasets.
Developed a multiway classification method for sparse data.
problem Classification of multiway arrays with sparsity.
method Extended Distance Weighted Discrimination (DWD) to multiway context, accounting for sparsity.
result Improves classification accuracy in multiway structured data.
Missing data is an important challenge when dealing with high dimensional data arranged in the form of an array. In this paper, we propose methods for estimation of the parameters of array variate normal probability model from partially observed multiway data. The methods developed here are useful for missing data impu…
Paper develops efficient DML estimators for multiway clustered data without cross-fitting.
problem Efficient inference in models with multiway clustered dependence.
method Neyman-orthogonal moment conditions combined with localisation-based empirical process approach.
result Valid inference achieved without cross-fitting, showing debiased GMM estimators are asymptotically linear and normal.
We consider the problem of identifying multiway block structure from a large noisy tensor. Such problems arise frequently in applications such as genomics, recommendation system, topic modeling, and sensor network localization. We propose a tensor block model, develop a unified least-square estimation, and obtain the t…
We extend contrastive learning theory for multiway classification and prove convergence guarantees.
problem Efficient self-supervised training for multiway classification tasks.
method Contrastive representation learning with multiple negative samples and convergence guarantees for gradient descent.
result Convergence guarantees for contrastive learning with gradient descent of an overparametrized encoder.
We introduce a Bayesian nonparametric regression model for data with multiway (tensor) structure, motivated by an application to periodontal disease (PD) data. Our outcome is the number of diseased sites measured over four different tooth types for each subject, with subject-specific covariates available as predictors.…
New algorithm for multiway spectral clustering on Grassmann manifolds.
problem Efficiently computing multiple eigenvectors of a nonlinear graph Laplacian.
method Direct multiway spectral clustering in -norm, reformulated as minimization on Grassmann manifold.
result Monotonic decrease of balanced graph cuts leads to optimal solutions.
Proposes a method to handle sparse multiway count data with false zeros using zero-truncated Poisson regression.
problem Handling sparse multiway count data corrupted by false zeros.
method Zero-truncated Poisson regression with tensor completion.
result Accurate estimation of multiway count data from approximately non-zero counts.
dCMF models evolving patterns in multiway data with temporal dynamics.
problem Capturing evolving patterns in multiway datasets with temporal dependencies.
method Time-aware coupled factorization model constrained by LDS structure.
result dCMF outperforms alternatives in capturing complex dynamics.
We describe a probabilistic PARAFAC/CANDECOMP (CP) factorization for multiway (i.e., tensor) data that incorporates auxiliary covariates, SupCP. SupCP generalizes the supervised singular value decomposition (SupSVD) for vector-valued observations, to allow for observations that have the form of a matrix or higher-order…
Tensor analysis tackles complex multidimensional data across fields.
problem Efficiently extracting information from high-dimensional data.
method Interdisciplinary approach combining statistics, optimization, and numerical linear algebra.
result Significant progress in tensor analysis over the last decade.
The paper ranks items based on top choices in multiway comparisons.
problem Ranking items based on top choices in multiway comparisons.
method Uniform sampling scheme, statistical rates of convergence, asymptotic normality, maximum likelihood estimator, Gaussian multiplier bootstrap.
result Proposed inference framework for ranking items through maximum pairwise difference statistic.
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a certain "contrast function" over the unit sphere. These algorithms, partly inspired by…
SyGlasso models tensor data dependencies using Sylvester equations.
problem Capturing multiway dependencies in tensor-valued data.
method Based on Sylvester equation, uses nodewise regression for estimation.
result Demonstrates simultaneous estimation of brain connectivity and temporal dependencies.
Paper proposes a new tensor model for mixed memberships and provides error bounds.
problem Estimating mixed memberships in higher-order multiway data.
method Tensor mixed-membership blockmodel, higher-order orthogonal iteration algorithm (HOOI), simplex corner-finding algorithm.
result Consistency of estimation procedure with error bounds under specific conditions.
Dual-Channel Tensor Neural Network (DC-TNN) decomposes tensor data into low-rank and sparse components for better estimation and inference.
problem Tensor-valued data with multilinear dependencies are challenging to process due to loss of multiway geometry under vectorization.
method DC-TNN decomposes tensors into a low-rank core and a sparse refinement, processing them through coupled neural channels.
result Established non-asymptotic risk bounds and developed structure-aware conformal ROC and AUC confidence bands.
Study shows linear predictors fail with missing data, but simpler approximations and neural networks can work.
problem Building predictors with missing data when the target is a linear function of observed data.
method Analyzed the Gaussian case and proposed a linear function of multiway interactions. Studied a simple approximation and proved generalization bounds. Showed multilayer perceptrons with ReLU activation can be consistent.
result Simple approximations and neural networks can be effective in handling missing data, especially with sufficient data.
Develops a new tensor model for clustering with degree correction.
problem Clustering with unknown degree heterogeneity in multiway data.
method Degree-corrected tensor block model with estimation guarantees.
result Demonstrates an intrinsic statistical-to-computational gap for tensors of order three or greater.
Tensor decomposition is a well-known tool for multiway data analysis. This work proposes using stochastic gradients for efficient generalized canonical polyadic (GCP) tensor decomposition of large-scale tensors. GCP tensor decomposition is a recently proposed version of tensor decomposition that allows for a variety of…
Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks…
A new tensor completion method handles missing data with missing not at random entries.
problem Handling missing data in tensors where the probability of observation depends on other entries.
method Estimate propensities using convex relaxation, then use higher-order SVD with inverse propensities weights.
result Finite-sample error bounds on the completed tensor are provided.
Tensor Regressionstat.ML
Tensor Regression tackles high-dimensional data analysis.
problem Challenges in traditional data representation methods for high-dimensional data.
method Systematic study and analysis of tensor-based regression models.
result Provides solutions for specific regression tasks with multiway data.
The growing use of neuroimaging technologies generates a massive amount of biomedical data that exhibit high dimensionality. Tensor-based analysis of brain imaging data has been proved quite effective in exploiting their multiway nature. The advantages of tensorial methods over matrix-based approaches have also been de…
This work tackles sparse coding in DLRA for interpretable multiway data.
problem Sparse coding in DLRA for interpretable multiway data.
method Proposes a new sparse-coding subproblem (MSC) and several algorithms to solve it.
result DLRA extends low-rank approximations, reducing variance and enhancing interpretability.
Paper proposes efficient methods for high-order clustering in tensor block models.
problem High-order clustering of multiway datasets in neuroimaging, genomics, etc.
method Tensor block model and computationally efficient algorithms (HLloyd, HSC)
result Achieves high-order exact clustering with statistical optimality and computational efficiency.
Relational machine learning studies methods for the statistical analysis of relational, or graph-structured, data. In this paper, we provide a review of how such statistical models can be "trained" on large knowledge graphs, and then used to predict new facts about the world (which is equivalent to predicting new edges…
Nonsingular estimation of high dimensional covariance matrices is an important step in many statistical procedures like classification, clustering, variable selection an future extraction. After a review of the essential background material, this paper introduces a technique we call slicing for obtaining a nonsingular …
The paper improves spectral ranking methods for diverse comparison graphs.
problem Estimating preference scores from multiway comparisons with heterogeneous sizes.
method Develops a two-step spectral method for estimating preference scores and their uncertainties.
result The two-step spectral method achieves the same asymptotic efficiency as the Maximum Likelihood Estimator (MLE).
Canonical correlation analysis (CCA) has been one of the most popular methods for frequency recognition in steady-state visual evoked potential (SSVEP)-based brain-computer interfaces (BCIs). Despite its efficiency, a potential problem is that using pre-constructed sine-cosine waves as the required reference signals in…
New method for tensor completion from specific mode observations.
problem Recovering multiway data tensors from partial observations.
method Tensor train decomposition for fiber-wise observations.
result Deterministic recovery guarantees for specific observation patterns.
Estimates isotonic functions under unknown permutations, achieving optimal statistical and computational efficiency.
problem Estimating isotonic functions with unknown permutations in multiway comparison data.
method Mirsky partition estimator for minimax optimal and adaptive estimation.
result Achieves optimal worst-case statistical performance and computational efficiency.
Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging problem is related to determination of model complexity (i.e., multilinear rank), e…
Data analysis and machine learning have become an integrative part of the modern scientific methodology, offering automated procedures for the prediction of a phenomenon based on past observations, unraveling underlying patterns in data and providing insights about the problem. Yet, caution should avoid using machine l…
MultiwayPAM clusters LLM-as-a-Judge scores to reveal evaluator bias.
problem Revealing bias in LLM evaluations of text quality.
method Tensor clustering with MultiwayPAM method.
result Medoids reveal cluster membership of questions, answerers, and evaluators.
In this work we propose a simple and easily parallelizable algorithm for multiway graph partitioning. The algorithm alternates between three basic components: diffusing seed vertices over the graph, thresholding the diffused seeds, and then randomly reseeding the thresholded clusters. We demonstrate experimentally that…
Statistical and Computational Efficiency for Smooth Tensor Estimation with Unknown Permutationsmath.ST
We tackle tensor denoising with unknown permutations, achieving optimal recovery with polynomial estimators.
problem Structured tensor denoising with unknown permutations in recommendation systems, neuroimaging, etc.
method Developed a constrained least-squares estimator in a block-wise polynomial family.
result Achieved the minimax error bound with polynomial estimators of degree up to .
Bayesian Tensor Ring factorization improved for scalability and handling of discrete data.
problem Scalability issues and handling of discrete data in Bayesian Tensor Ring factorization.
method Proposes a novel Bayesian Tensor Ring model with a nonparametric Multiplicative Gamma Process prior and Pólya-Gamma augmentation for discrete data. Developed efficient Gibbs sampler and online EM algorithm for scalability.
result Significantly improved scalability and handling of discrete data compared to previous methods.
We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a multilinear Bernoulli model, develop a rank-constrained likelihood-based estima…
A privacy-preserving framework detects faults in circular economy processes.
problem Lack of shared data across company borders due to privacy concerns.
method Federated Principal Component Analysis (PCA) and Secure Multiparty Computation.
result The proposed FedMSPC framework outperforms standard PCA in fault detection.
Tensor-on-tensor regressionstat.ME
We propose a framework for the linear prediction of a multi-way array (i.e., a tensor) from another multi-way array of arbitrary dimension, using the contracted tensor product. This framework generalizes several existing approaches, including methods to predict a scalar outcome from a tensor, a matrix from a matrix, or…
This paper establishes the consistency of a family of graph-cut-based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on minimizing objective functionals defined on proximity graphs of the given sample. Our f…
Mixes higher-order simplicial complexes for data augmentation.
problem Lack of labeled data for complex systems with multiway interactions.
method Proposes mixup mechanisms for simplicial complexes, including linear and nonlinear mixup, and a convex clustering mixup.
result Synthetic simplicial complexes interpolate between existing data based on homomorphism densities.
BRTR improves robust tensor completion with automatic rank detection.
problem Robust tensor completion from incomplete data with outliers.
method Bayesian robust tensor ring decomposition (BRTR) with variational Bayesian (VB) algorithm.
result Automatic detection of TR rank and improved performance over state-of-the-art methods.