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.
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…
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.
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.
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.
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.
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…
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.
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…
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.
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.
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…
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.
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…
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 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.…
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 IR2log22(I) 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 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.
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 p-norm, reformulated as minimization on Grassmann manifold. result Monotonic decrease of balanced graph cuts leads to optimal solutions.
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.
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.
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.
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.
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.
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 …
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.
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.
Bayesian method reconstructs hidden higher-order interactions from network data.
problem Lack of explicit higher-order interactions in pairwise network data.
method Bayesian approach based on parsimony, infers higher-order structures when statistically supported.
result Demonstrated applicability to various datasets, synthetic and empirical.
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.
Proposes a method to enhance multi-view learning by maximizing higher order correlations.
problem Losing intrinsic interconnections among multiple views in pairwise correlation maximization.
method Formulates multi-view data as a low rank approximation problem using higher order correlation tensor and solves it with the generating polynomial method.
result Consistently outperforms prior methods on real multi-view data.
Improved GAN performance using higher-order Wasserstein moments.
problem Stabilizing and enhancing GANs for better mode coverage and stability.
method Deriving and training a GAN with a modified Wasserstein distance using higher-order moments.
result Training a GAN with higher-order Wasserstein moments improves performance, even with increased computational cost.
In this paper, we introduce the notion of motif closure and describe higher-order ranking and link prediction methods based on the notion of closing higher-order network motifs. The methods are fast and efficient for real-time ranking and link prediction-based applications such as web search, online advertising, and re…
Enhances stock movement prediction using Higher Order Transformers for multimodal time-series data.
problem Predicting stock movements in financial markets with complex dynamics.
method Introduced Higher Order Transformers, extending self-attention and transformer architecture to capture complex market dynamics. Employed low-rank tensor decomposition and kernel attention to manage computational complexity. Integrated technical and fundamental analysis from historical prices and tweets.
result Demonstrated effectiveness of the method on the Stocknet dataset, improving stock movement prediction.
Method provides formal guarantees for decomposing model uncertainty.
problem Decomposing model uncertainty into aleatoric and epistemic components.
method Higher-order calibration using k-snapshots.
result Formal guarantees for aleatoric uncertainty matching real-world distribution.
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…
This paper describes a general framework for learning Higher-Order Network Embeddings (HONE) from graph data based on network motifs. The HONE framework is highly expressive and flexible with many interchangeable components. The experimental results demonstrate the effectiveness of learning higher-order network represe…
Users form information trails as they browse the web, checkin with a geolocation, rate items, or consume media. A common problem is to predict what a user might do next for the purposes of guidance, recommendation, or prefetching. First-order and higher-order Markov chains have been widely used methods to study such se…
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…
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.
GENIE accelerates DDM synthesis with higher-order solvers.
problem Efficiently solving the differential equation for high-quality generation.
method Higher-order Taylor methods, utilizing Jacobian-vector products.
result GENIE significantly accelerates synthesis compared to previous solvers.
A new method captures higher-order interactions in data clusters.
problem Accurately characterizing complex higher-order variable interactions.
method Local Correlation Explanation (CorEx) method: clustering and total correlation.
result Captures higher-order interactions at a local scale.
Novel higher-order group synchronization for noisy local measurements on hypergraphs.
problem Synchronizing higher-order local measurements on hyperedges to global estimates on nodes.
method Message passing algorithm for global synchronization of higher-order measurements.
result Higher-order method outperforms standard pairwise synchronization methods in certain applications.
TGCCA analyzes higher-order tensors using orthogonal rank-R CP decomposition.
problem Handling higher-order structures in multi-block data analysis.
method Tensor Generalized Canonical Correlation Analysis (TGCCA) with orthogonal rank-R CP decomposition.
result TGCCA outperforms state-of-the-art methods on simulated and real data.
Simplicial neural networks extend graph neural networks to handle higher-order interactions.
problem Handling higher-order interactions in complex data structures.
method Define a convolution operation for simplicial complexes and use it to construct convolutional neural networks.
result SNNs effectively impute missing data in coauthorship complexes.
Paper proposes a new method to identify causal graphs with latent variables using higher-order cumulants.
problem Estimating causal directed acyclic graphs with latent confounders.
method Uses higher-order cumulants to identify causal structures among observed and latent variables.
result Validates the proposed algorithm through simulations and real-world data.
New principle for optimal control with higher order differential constraints.
problem Optimal control problems with higher order differential constraints.
method Derivation of the Principle of Minimal Labour and generalization of Pontryagin Maximum Principle.
result Generalized Pontryagin Maximum Principle for higher order constraints.
Training deep neural networks with spatio-temporal (i.e., 3D) or multidimensional convolutions of higher-order is computationally challenging due to millions of unknown parameters across dozens of layers. To alleviate this, one approach is to apply low-rank tensor decompositions to convolution kernels in order to compr…