KFT improves tensor forecasting by incorporating side information.
problem Tensor factorization weaknesses in latent factors.
method Kernel Fried Tensor (KFT) with variational inference.
result Superior performance over LightGBM and FFM.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
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48 results for “tensorized variational inference”
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…
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.
A new tensor decomposition method for fMRI data captures both spatial and temporal variability.
problem Challenges in modeling shared and subject-specific structure in multisubject spatiotemporal data, especially in neuroimaging.
method Introduces a spatiotemporal variational tensor decomposition (ST-VTD) framework combining tensor factorization with structured priors for flexible representation of spatial and temporal dynamics.
result Significantly improves latent factor recovery in fMRI data compared to classical and probabilistic decomposition benchmarks.
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.
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.
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…
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.
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.
MSFA clusters high-dimensional spatial data using spline-based covariance structures.
problem Clustering high-dimensional spatial data with flexible covariance structures.
method Mixture of spatial factor analyzers with spline-based covariance and matrix variate factor analyzers for dimensionality reduction.
result Proposed models accurately infer and differentiate distinct spatial patterns in tensor-variate data.
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 took action toward country at time "---known as dyadic events---in order to form an…
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.
Layered graphical models improve discriminative learning efficiency.
problem Improving discriminative learning efficiency in graphical models.
method Designing layered graphical models (LGMs) in analogy to neural networks, using tensorized truncated variational inference and backpropagation.
result LGMs achieve competitive results in image classification, comparable to neural networks.
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…
Interpretable Bayesian Tensor Network Kernel Machines with Automatic Rank and Feature Selectionstat.ML
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.
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 proposes VAE-BPTF for better tensor factorization of sparse, imbalanced count data.
problem Inference of Bayesian Poisson-Gamma models for sparse and imbalanced count data is challenging.
method Variational auto-encoder framework with multi-layer perceptron networks for complex update information sharing and reweighting.
result VAE-BPTF outperforms current models in reconstruction errors and latent factor coherence across real-world datasets.
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.
We propose a method (TT-GP) for approximate inference in Gaussian Process (GP) models. We build on previous scalable GP research including stochastic variational inference based on inducing inputs, kernel interpolation, and structure exploiting algebra. The key idea of our method is to use Tensor Train decomposition fo…
Entropy analysis via kernel methods for probabilistic inference.
problem Entropy analysis of probability distributions.
method Kernel methods and reproducing kernel Hilbert spaces for entropy estimation.
result New upper-bounds on log partition functions for probabilistic inference.
tvGP-VAE models tensor-valued latent variables with Gaussian processes for better data structure representation.
problem Agnostic latent variables in VAEs ignore data structure correlations.
method Proposes tensor-variate Gaussian process prior for variational autoencoder.
result Explicitly modeling correlation structures improves model performance in reconstruction.
Elliptically-Contoured Tensor-variate Distributions with Application to Improved Image Learningstat.ME
Improved image learning using elliptically contoured tensor-variate distributions.
problem Inadequate statistical analysis for tensor-valued data, especially with heavier or lighter tails.
method Developed a family of elliptically contoured tensor-variate distributions and derived their properties and procedures for estimation.
result Tensor-variate classification rules and tensor-on-tensor regression better predict and characterize data than TVN-based methods.
A multi-way factor analysis model is introduced for tensor-variate data of any order. Each data item is represented as a (sparse) sum of Kruskal decompositions, a Kruskal-factor analysis (KFA). KFA is nonparametric and can infer both the tensor-rank of each dictionary atom and the number of dictionary atoms. The model …
A probabilistic, data-driven closure model for RANS simulations with aleatoric, model uncertaintyphysics.flu-dyn
Proposes a new model for RANS simulations with uncertainty.
problem Uncertainty in Reynolds-averaged Navier-Stokes simulations.
method Data-driven closure model with aleatoric uncertainty, Bayesian formulation, sparse indirect data.
result Accurate probabilistic predictions, even in regions of model error.
Extends multivariate regression for tensor-variate data, identifying brain regions and facial characteristics.
problem Challenges in fitting regression models with multivariate responses and covariates.
method Low-rank tensor formats on regression coefficients and tensor-variate normal distribution for errors.
result Maximum likelihood estimators for tensor-on-tensor regression via block-relaxation algorithms.
Bayesian tensor train kernel machine uses Laplace approximation for scalable GP regression.
problem Scalability limitations of Gaussian process regression.
method Bayesian tensor train kernel machine with Laplace approximation and variational inference.
result VI replaces cross-validation and offers up to 65x faster training.
Extends geometrical description of tensor manifolds in tree-based formats.
problem Geometrical description of tensor manifolds in tree-based formats.
method Provided a new geometrical description of manifolds of tensors in tree-based format.
result Geometrical description compatible with Tucker format.
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…
Defines and proves properties of weighted renormalized volume coefficients.
problem None explicitly stated; focuses on mathematical definitions and proofs.
method Defines weighted renormalized volume coefficients and proves their variational nature and polynomial representation.
result Weighted renormalized volume coefficients are variational and can be expressed as polynomials of specific tensors.
Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable, leading to extensive study of approximation methods. Iterative variational methods…
Tensor factorization is a powerful tool to analyse multi-way data. Compared with traditional multi-linear methods, nonlinear tensor factorization models are capable of capturing more complex relationships in the data. However, they are computationally expensive and may suffer severe learning bias in case of extreme dat…
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.
Functional tensors unify probabilistic programming with automatic differentiation.
problem Designing probabilistic programming systems that can handle diverse inference strategies.
method Introducing functional tensors that capture benefits of tensors and continuous probability distributions.
result Functional tensors enable parallel exact inference for various modeling motifs.
This paper presents a multi-dimensional computational method to predict the spatial variation data inside and across multiple dies of a wafer. This technique is based on tensor computation. A tensor is a high-dimensional generalization of a matrix or a vector. By exploiting the hidden low-rank property of a high-dimens…
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.
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.
Bayesian Poisson-Randomized Gamma Tensor Factorization with Application to International Trade Flowsstat.ME
Bayesian hierarchical tensor factorization model for international trade flows
problem Sparse semi-continuous tensor data modeling
method Bayesian hierarchical tensor factorization with Poisson and Gamma models
result Identifies multiway dependence in trade flows
A new method for embedding sparse high-order interactions.
problem Learning embeddings from sparse high-order interaction events.
method Hybridizing sparse hypergraph and matrix Gaussian processes.
result Strong asymptotic bounds on sparsity ratio.
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.
New method for tensor completion using nonconvex dual total variation.
problem Tensor completion from partial measurements with exponential-family noise.
method Proposed dual-TV (DTV) regularizers for tensor completion under exponential-family noise.
result Theoretical upper bounds on recovery error for tensor completion.
Online Tensor Inferencestat.ML
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.
Proposes a new tensor decomposition method for functional temporal data with adaptive complexity.
problem Challenges in temporal tensor decomposition for general tensor data with continuous indexes.
method Encodes continuous spatial indexes as learnable Fourier features and uses neural ODEs for temporal trajectories. Introduces a sparsity-inducing prior for complexity adaptation.
result Significantly outperforms existing methods in prediction performance and robustness against noise.
New findings on shrinking Ricci solitons with vanishing Bach-like tensors.
problem Characterizing gradient shrinking Ricci solitons with vanishing Bach-like tensors.
method Defining and analyzing Bach-like tensors, proving rigidity results, and deriving variational formulas.
result Vanishing Bach-like tensors force solitons to be either Einstein or isometric to the Gaussian soliton.
Proposes a nonparametric tensor factorization for sparse data.
problem Handling sparse tensor data with structural and interpretability benefits.
method Hierarchical Gamma processes and Poisson random measures for tensor-valued process, Dirichlet processes for sampling entry indices, Gaussian processes for values.
result Demonstrates superior performance on benchmark datasets.
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.
In this paper we continue the investigation of Loday's Leibniz cohomology as a new invariant for differentiable manifolds. In particular the Leibniz coboundary of a k-tensor (in the sense of differential geometry) is computed in a local coordinate chart and then interpreted in terms of the calculus of variations. For e…
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 method improves tensor completion by selectively preserving important elements.
problem Recovering corrupted high-dimensional tensor data with missing entries and noise.
method Tensor weighted correlated total variation (TWCTV) regularizer with ADMM algorithm.
result Superior performance in image completion, denoising, and background subtraction tasks.