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.
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. 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…
We present a Bayesian non-negative tensor factorization model for count-valued tensor data, and develop scalable inference algorithms (both batch and online) for dealing with massive tensors. Our generative model can handle overdispersed counts as well as infer the rank of the decomposition. Moreover, leveraging a repa…
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.
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 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.…
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…
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.
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 (m−2)(m+1)/2. 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.
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 …
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.
Flow Matching for count data improves sample quality and efficiency.
problem Mapping between count distributions across batches or time points in high-dimensional count data.
method count-FM, a flow-matching framework based on a continuous-time birth-death process with local unit jumps.
result count-FM achieves better sample quality than representative baselines while using fewer parameters.
The abstract reviews models for analyzing count data.
problem Challenges in analyzing count data with standard methods.
method Review of generalized linear models and multinomial models.
result Fundamental connections between multinomial and count models.
Proposes a robust EM algorithm for analyzing incomplete panel count data.
problem Missing reports in panel count data.
method Functional EM algorithm for non-parametric counting process mean function estimation.
result Robust to misspecification of Poisson process assumption and missing completely at random.
The paper proposes count echo state networks for forecasting graduate student enrollments.
problem Forecasting graduate student enrollments from historical data.
method Developed hierarchical count echo state networks and compared them to Poisson autoregressions and negative binomial models.
result Hierarchical negative binomial based echo state network is the superior model.
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.
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.
p-SNE embeds Poisson count data into low dimensions preserving structure.
problem Embedding high-dimensional sparse Poisson data into a low-dimensional space.
method p-SNE (Poisson Stochastic Neighbor Embedding) using KL divergence and Hellinger distance.
result p-SNE recovers meaningful structure in real-world count datasets.
Novel Bayesian method for high-dimensional count data prediction.
problem Count data in high-dimensional settings requires feature selection.
method Pseudo-Bayesian framework with scaled Student prior and exponential weights.
result Strong performance compared to Lasso in various settings.
Quantum theory improves counting overlapping clusters.
problem Counting overlapping clusters in machine learning.
method Applied quantum theory using path integral technique.
result Quantum theory provides a robust statistical method for counting clusters.
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…
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…
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.
Better neural arithmetic logic units improve cell counting model generalization.
problem Neural networks struggle with high cell counts outside training data range.
method Introduced Neural Arithmetic Logic Units (NALU) for arithmetic operations in existing architectures.
result Improved cell counting accuracy for higher numeric ranges with better generalization.
The paper improves count data regression models for overdispersed data.
problem Improving regression models for overdispersed count data.
method Double ℓ1-regularized negative binomial regressions. result Oracle inequalities and consistency for Lasso estimators of partial regression coefficients.
Generative model identifies temporal count data components with regime-dependent contributions.
problem Modeling temporal count data with regime-dependent dynamics.
method Generative framework combining regime-adaptive dynamics with Poisson log-normal emissions.
result Established identifiability of the model and revealed co-variation patterns and regime shifts.
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.
Multivariate count data are defined as the number of items of different categories issued from sampling within a population, which individuals are grouped into categories. The analysis of multivariate count data is a recurrent and crucial issue in numerous modelling problems, particularly in the fields of biology and e…
This work refines Cover's theory for binary classification on low-dimensional data.
problem The challenge of analyzing how low-dimensional data structures affect classification models.
method Refines Cover's function-counting theory to account for low-dimensional data structure.
result Derives dichotomy counts and analyzes the impact of data structure on classification models.
ENTED efficiently decomposes binary and count tensors using nonparametric Gaussian processes.
problem Handling high-dimensional and sparse binary and count data with traditional tensor decompositions.
method ENTED uses nonparametric Gaussian processes and sparse orthogonal variational inference to handle binary and count tensors.
result ENTED outperforms traditional methods in binary and count tensor completion tasks.
Bayesian model tackles spatial count data issues with flexible non-parametric techniques.
problem Challenges in traditional parametric models for spatial count data with unbalanced distributions and complex dependencies.
method Bayesian semi-parametric spatial dispersed count model combining non-parametric techniques and adapted count models.
result Demonstrates superior performance in managing dispersion and capturing intricate spatial patterns.
Graphical estimation of count time series dependencies.
problem Estimating dependencies between multivariate count time series.
method Parameter-driven generalized linear model with l1-type regularization and MCEM algorithm.
result Characterization of disease spread interdependence and sources/sinks in Greater Mumbai.