Unified framework for statistical inference of low-rank tensors.
problem Statistical inference for tensors in high-dimensional data.
method Unified framework using debiasing and tangent space projection.
result Achieves asymptotic normality and minimax-optimal confidence intervals.
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.
It is a significant challenge to design probabilistic programming systems that can accommodate a wide variety of inference strategies within a unified framework. Noting that the versatility of modern automatic differentiation frameworks is based in large part on the unifying concept of tensors, we describe a software a…
Paper bounds tensor decomposition's RLCT, aiding Bayesian inference.
problem Unclear mathematical property of tensor decomposition.
method Algebraic geometrical method for upper bound derivation.
result Upper bound of real log canonical threshold (RLCT) derived.
Paper introduces online tensor inference for real-time data analysis.
problem Real-time processing of high-dimensional tensor data.
method Stochastic Gradient Descent (SGD) for efficient online inference.
result Establishes non-asymptotic convergence and optimal estimation error rate.
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…
Efficient method for tensor linear form inference with noisy incomplete data.
problem Statistical inference of tensor linear forms with incomplete and noisy observations.
method Initial estimate + debiasing + one-step power iteration.
result Optimal uncertainty quantification and statistical-to-computational gaps examined.
Probabilistic approaches for tensor factorization aim to extract meaningful structure from incomplete data by postulating low rank constraints. Recently, variational Bayesian (VB) inference techniques have successfully been applied to large scale models. This paper presents full Bayesian inference via VB on both single…
Bayesian TNKMs automatically infer model complexity and feature relevance.
problem Manual tuning of TN rank and feature dimensions is error-prone and computationally expensive.
method Bayesian approach with hierarchical priors on TN factors for automatic rank and feature selection.
result Superior performance in prediction accuracy, uncertainty quantification, interpretability, and scalability.
Improved tensor rank learning for CPD models using a generalized hyperbolic prior.
problem Inaccurate tensor rank determination leads to overfitting or underfitting in CPD models.
method Introduced a generalized hyperbolic prior for automatic tensor rank learning in probabilistic CPD models.
result Significantly improved performance in learning both low and high tensor ranks, even for low SNR cases.
We present a Bayesian tensor factorization model for inferring latent group structures from dynamic pairwise interaction patterns. For decades, political scientists have collected and analyzed records of the form "country i took action a toward country j at time t"---known as dyadic events---in order to form an…
Causal deep learning tackles causal inference using tensor factor analysis.
problem Addressing causal questions in data using neural networks.
method Tensor factor analysis and neural network architectures (causal capsules, tensor transformer, multilinear projection algorithm).
result Derives deep neural networks for causal inference with tensor factor analysis.
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.
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.
Unified tensor network formalism for combining neural and symbolic AI.
problem Combining neural and symbolic AI approaches remains a challenge.
method Introduces a tensor network formalism capturing sparsity principles.
result Unified treatment identifies tensor network contractions as a fundamental inference class.
A novel Laplace-approximated Bayesian Tensor Network Kernel Machine (LA-TNKM) provides principled uncertainty estimates.
problem How to provide principled uncertainty estimates for tensor network kernel machines.
method Employing a linearized Laplace approximation for Bayesian inference.
result Consistently matches or surpasses Gaussian Processes and BNNs across diverse UCI regression benchmarks.
This paper presents a Bayesian method for estimating the rank of a low-rank tensor model of joint PMF.
problem Estimating the rank of a low-rank tensor model of joint PMF from observed data.
method Bayesian framework for estimating low-rank components and rank simultaneously, using variational inference.
result Automatic rank detection and improved estimation accuracy compared to cross-validation methods.
A new probabilistic BTD method for tensor data.
problem Modeling higher-order tensors with robust inference.
method Probabilistic Block-Term Decomposition using variational Bayesian inference and von-Mises Fisher distribution.
result The proposed pBTD can quantify multi-linear structures robustly.
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.
We present a scalable Bayesian model for low-rank factorization of massive tensors with binary observations. The proposed model has the following key properties: (1) in contrast to the models based on the logistic or probit likelihood, using a zero-truncated Poisson likelihood for binary data allows our model to scale …
Directed networks are pervasive both in nature and engineered systems, often underlying the complex behavior observed in biological systems, microblogs and social interactions over the web, as well as global financial markets. Since their structures are often unobservable, in order to facilitate network analytics, one …
Sparse sampling method for tensor factorization and completion of high rank tensors.
problem Completion of high rank tensors with missing data in recommendation systems.
method Sparse measurements and message-passing algorithms in a high-dimensional limit.
result Theoretical insights and performance analysis of tensor factorization in dense limit.
Bayesian Tensor Network combines prior and data likelihood for efficient prediction and parameter estimation.
problem Overfitting and poor performance in Tensor Network models.
method Introduce prior distribution, use Laplace approximation for posterior predictive distribution, and propose stable initialization for parameter estimation.
result Reduces overfitting and improves performance of Tensor Network models.
Streaming tensor factorization is a powerful tool for processing high-volume and multi-way temporal data in Internet networks, recommender systems and image/video data analysis. Existing streaming tensor factorization algorithms rely on least-squares data fitting and they do not possess a mechanism for tensor rank dete…
Study reveals efficient recovery of multi-modal signals via Bayesian methods and sequential learning.
problem Recovering multiple high-dimensional signals from correlated modalities.
method Bayesian Approximate Message Passing and Sequential Curriculum Learning.
result Sequential learning strategy optimally recovers weak signals in multi-modal settings.
SG-PALM learns interpretable tensor models for high-dimensional data.
problem Learning interpretable tensor models for high-dimensional data.
method SG-PALM combines Sylvester generative model and fast proximal alternating linearized minimization.
result SG-PALM converges linearly to global optimum and scales to high dimensions.
A scalable method for efficient inference in Gaussian process regression networks.
problem Intractable inference in Gaussian process regression networks (GPRN).
method Tensorization of output space, tensor/matrix-normal variational posteriors, joint optimization, and exploiting Kronecker product structure.
result Captures posterior dependencies and improves inference quality for large number of outputs.
Unified approach to tensor PCA and related problems using tensor cumulants.
problem Statistical inference on invariant distributions, particularly tensor PCA.
method Definition and analysis of tensor cumulants to unify and extend previous results.
result Unified explanation of hardness and subexponential-time algorithms for tensor PCA.
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…
A new RNN architecture reduces model size and improves performance.
problem Overparameterization and resource limitations in RNNs.
method Jointly encodes weight matrices using tensor-train factorization.
result Reduces model size by several orders of magnitude without sacrificing performance.
We consider the estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kron…
New method ensures consistent inference across different tensor parallel sizes for large language models.
problem Non-deterministic inference in large language models due to inconsistent reduction orders across GPUs.
method Tree-Based Invariant Kernels (TBIK) that align intra- and inter-GPU reduction orders through a unified hierarchical binary tree structure.
result Bit-wise identical results across different tensor parallel sizes for RL training.
We outline an inherent weakness of tensor factorization models when latent factors are expressed as a function of side information and propose a novel method to mitigate this weakness. We coin our method \textit{Kernel Fried Tensor}(KFT) and present it as a large scale forecasting tool for high dimensional data. Our re…
It is well known that multiplication operations in convolutional layers of common CNNs consume a lot of time during inference stage. In this article we present a flexible method to decrease both computational complexity of convolutional layers in inference as well as amount of space to store them. The method is based o…
A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to plate diagrams for directed graphical models. To exploit efficient t…
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.
CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem e…
Sum-product networks (SPNs) represent an emerging class of neural networks with clear probabilistic semantics and superior inference speed over graphical models. This work reveals a strikingly intimate connection between SPNs and tensor networks, thus leading to a highly efficient representation that we call tensor SPN…
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.
Paper introduces TSSDMN for modeling dynamic multilayer networks.
problem Capturing temporal and cross-layer dynamics in multilayer networks.
method Tensor State Space Model (TSSDMN) using symmetric Tucker decomposition.
result TSSDMN uniquely captures temporal dynamics within and across layers.
BKTR models spatiotemporal data with scalable tensor regression.
problem High computational cost in applying STVC to large-scale spatiotemporal data.
method Summarize STVC coefficients in a tensor, reformulate as low-rank tensor regression, incorporate GP priors for local dependencies.
result BKTR efficiently models large spatiotemporal datasets with reduced parameters and local dependencies.
Paper projects GP basis functions using tensor networks to reduce complexity.
problem Efficiently approximating Gaussian process regression with a large number of basis functions.
method Develops a method using tensor networks to approximate GP regression with an exponential number of basis functions without exponential computational complexity.
result Shows efficient GP regression on an 18-dimensional benchmark data set.
T-Basis represents neural network tensors with fewer parameters.
problem Efficiently representing neural network tensors with fewer parameters.
method T-Basis uses Tensor Rings to represent tensors in a neural network, parameterizing them with a small number of coefficients.
result T-Basis achieves high compression rates with minimal performance loss.
This paper develops a method to train compact neural networks with reduced memory and computational costs.
problem Training large neural networks consumes excessive resources and energy.
method End-to-end training framework using Bayesian tensor decomposition with automatic rank determination.
result The method achieves significant parameter reduction and maintains or improves accuracy.
A new method estimates rare events using tensor trains.
problem Estimating rare event probabilities in high-dimensional problems.
method Approximating optimal importance distribution via tensor-train decompositions and compositions.
result Better variance reduction and efficient computation of rare event probabilities.
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. We formulate and solve a tensor model using a latent-variable approach.
problem Parameter inference for Poisson canonical polyadic tensor models.
method Latent-variable formulation, Expectation-Maximization algorithms, Fisher information matrices.
result Derivation of Fisher information for PCP models, insights into model well-posedness.
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.