A new tree method for tensor data improves regression accuracy.
problem Efficiently modeling tensor data for regression problems.
method Scalar-output regression tree models for scalar-on-tensor problems, and tensor-on-tensor problems using additive tree ensemble approaches.
result The tensor-input tree (TT) method outperforms tensor-input GP models in efficiency and accuracy.
New method tackles non-smooth tensor data for better recovery.
problem Non-smooth changes in tensor data degrade traditional t-SVD methods.
method Learnable tensor nuclear norm, Alternating Proximal Multiplier Method (APMM), multi-objective tensor recovery framework.
result The proposed method effectively recovers tensor data with non-smooth changes.
A new tensor completion method using tensor networks with Tucker wrapper.
problem Low-rank tensor completion in various applications.
method Solving LRTC as a system of nonlinear equations using a two-level alternative least squares method.
result The method converges to the exact solution at a linear rate with high probability.
JULIA combines multi-linear and nonlinear models for tensor completion.
problem Complex patterns in real-world tensors require a unified model.
method JULIA unifies multi-linear and nonlinear models with flexible component assignment and efficient alternating optimization.
result JULIA outperforms existing methods in large-scale tensor completion.
We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the reconstructed tensor is unique and always minimizes the KL divergence from an inpu…
Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity of matrix factorization methods. In this paper, we propose a new method for CP te…
Proposes FATTNN for tensor-on-tensor regression with improved prediction and reduced computation.
problem Tensor-on-tensor regression with complex tensor structures and nonlinear relationships.
method Integrates tensor factor models into deep neural networks to handle nonlinearity and reduce data dimensionality.
result Significant improvements in prediction accuracy and computational efficiency over traditional methods.
Two methods preserve tensor structure for reduced dimensionality in tensor regression.
problem Reducing dimensionality of tensor predictors for improved interpretation and accuracy.
method Developed two tensor dimension reduction methods using Tucker and CP decompositions.
result Substantial improvement in accuracy over existing methods in simulations and applications.
Tensor CANDECOMP/PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We build on the idea of count sketches, but introduce many novel ideas which are un…
Paper proposes a new method for exact recovery in robust tensor principal component analysis.
problem Exact recovery of low-rank and sparse components in tensors.
method Proposes a new method based on tensor-tensor product and t-SVD to solve a convex optimization problem.
result Exact recovery achieved in a deterministic fashion without randomness assumptions.
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient ascent (a variant of the tensor power method), and hard thresholding of the resid…
Proposes a new method for high-dimensional density estimation.
problem Estimating high-dimensional probability density functions efficiently.
method Tensorizing flow method combining tensor-train and flow-based generative modeling.
result Efficiently constructs an approximate density in tensor-train form and trains a flow model to match empirical distribution.
A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although they are not presented this way, can be viewed as spectral methods on matrices bui…
New methods solve tensor-on-tensor regression with unknown rank, revealing benefits of over-parameterization.
problem Connecting tensor responses to tensor covariates with unknown intrinsic rank.
method Riemannian gradient descent and Riemannian Gauss-Newton methods for tensor-on-tensor regression.
result Riemannian optimization methods converge linearly and quadratically to a statistically optimal estimate in rank over-parameterized settings.
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.
Robust TOT regression method handles outliers in tensor data.
problem Outliers in tensor data affect standard TOT regression.
method ROTOT method using a single loss function for outliers and robust MPCA for predictor.
result ROTOT method reduces influence of both casewise and cellwise outliers.
New method estimates tensors from noisy data with missing entries.
problem Tensor estimation from noisy observations with missing entries.
method Sign series representation for tensor completion, addressing low- and high-rank signals.
result Excess risk bounds, estimation error rates, and sample complexities established.
Tensor decomposition recovers Gaussian mixtures from moments.
problem Recovering Gaussian mixture models from datasets.
method Symmetric tensor decomposition of moment tensors built from empirical moments.
result Identifiable tensors with interpolation degree less than half their order.
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.
Recently, the \textit{Tensor Nuclear Norm~(TNN)} regularization based on t-SVD has been widely used in various low tubal-rank tensor recovery tasks. However, these models usually require smooth change of data along the third dimension to ensure their low rank structures. In this paper, we propose a new definition of da…
Bayesian tensor train method recovers streaming data with high accuracy.
problem Recovering high-order, incomplete, and noisy streaming data.
method Bayesian tensor train decomposition using streaming variational Bayes method.
result The proposed SPTT algorithm excels in recovering streaming data compared to state-of-the-art methods.
New tensor recovery method improves efficiency under strict complementarity.
problem Efficiently recovering low-rank tensors using tensor nuclear norm.
method Developed strict complementarity condition for tensor nuclear norm ball and applied to gradient methods.
result Standard gradient methods achieve linear convergence and nearly linear runtime under strict complementarity.
Adaptive algorithm learns tensor network structures from data.
problem Identifying optimal tensor network structure from data.
method Greedy approach starting from rank one tensor, small rank increments.
result Adaptive algorithm identifies efficient tensor network structures.
Tensor-based method simplifies causal skeleton discovery.
problem Discover causal relationships between variables.
method Express associations as tensors to reduce dimensionality.
result Causal skeleton can be determined using pair-wise tensors.
A tensor model for meta-learning adapts to task-specific features.
problem Learning shared representations for diverse tasks without task-specific observable information.
method Modeling meta-parameters as an order-3 tensor, estimating through tensor regression and method of moments.
result Tensor-based approach improves meta-learning performance with fewer samples.
New method for tensor classification with missing data.
problem Handling incomplete tensor data in high-dimensional classification.
method High-dimensional tensor linear discriminant analysis with TGMM and Tensor LDA-MD.
result Established convergence rates and minimax optimal bounds for misclassification rate.
Enhances tensor regression for interpretability and performance.
problem Interpreting and modeling multidimensional tensor data with structural heterogeneity.
method Generalized Nonnegative Structured Kruskal Tensor Regression (NS-KTR) with hybrid regularization and nonnegativity constraints.
result NS-KTR outperforms conventional methods in synthetic and real hyperspectral datasets.
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.
GETF efficiently decomposes large-scale Boolean tensors.
problem Efficiently factorizing large-scale Boolean tensors.
method Geometric Expansion for all-order Tensor Factorization (GETF).
result GETF significantly improves reconstruction accuracy and efficiency.
In this paper, we resolve many of the key algorithmic questions regarding robustness, memory efficiency, and differential privacy of tensor decomposition. We propose simple variants of the tensor power method which enjoy these strong properties. We present the first guarantees for online tensor power method which has a…
A new method for decomposing non-negative tensors using energy-based modeling.
problem Challenges in traditional tensor decomposition methods, especially global optimization and rank selection.
method Energy-based modeling of tensors, considering interactions between modes for global optimization.
result Demonstrates effectiveness in tensor completion and approximation, revealing a relationship between many-body and low-rank approximations.
Efficiently price high-dimensional Bermudan options using tensor compression.
problem High-dimensional option pricing with computational complexity.
method Hierarchical tensor compression for Monte Carlo and dual martingale methods.
result Tensor compression alleviates the curse of dimensionality for Bermudan option pricing.
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.
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.
Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex or a nonconvex cost function, which is a generalization of the matching pursuit…
Spatio-temporal data compression method reduces memory usage.
problem Efficiently storing and analyzing large spatio-temporal datasets.
method Adaptive sampling of tensor slices to compress and preserve structure.
result SkeTenSmooth outperforms other sampling methods in retaining patterns.
Proposes a method to recover sparse tensors with covariate info.
problem Sparse tensor with high missing entries and many zeros.
method Covariate-assisted Sparse Tensor Completion (COSTCO) using latent components.
result 23% accuracy improvement over baseline in advertisement dataset.
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.
New method tackles tensor regression with robust Kaczmarz approach.
problem Reconstructing tensor signals from corrupted measurements.
method Quantile-based randomized Kaczmarz method for tensor linear systems.
result Improved convergence and robustness to adversarial corruptions.
OpEvo automates tensor operator optimization for better efficiency.
problem Manual optimization of tensor operators is inefficient and limited.
method OpEvo uses evolutionary computation with topology-aware mutation.
result OpEvo finds optimal configurations with less effort and variance.
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.
We theoretically and experimentally investigate tensor-based regression and classification. Our focus is regularization with various tensor norms, including the overlapped trace norm, the latent trace norm, and the scaled latent trace norm. We first give dual optimization methods using the alternating direction method …
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.
Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of node features and interactions thereof, together with the tensor data. Such data…
Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex interactions among objects are multi-linear, and are thus insufficient to repres…
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.
In this paper, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD. The main motivation is that a lower tubal rank tensor can be obtained by usin…
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.