Related papers: Bayesian Adaptive Tucker Decompositions for Tensor…

Tensor train (TT) decomposition, a powerful tool for analyzing multidimensional data, exhibits superior performance in many machine learning tasks. However, existing methods for TT decomposition either suffer from noise overfitting, or…

Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during training and inference phases. Given its easy implementation and flexibility, one promising…

Vector autoregressions (VARs) are popular model for analyzing multivariate economic time series. However, VARs can be over-parameterized if the numbers of variables and lags are moderately large. Tensor VAR, a recent solution to…

In many application areas, data are collected on a categorical response and high-dimensional categorical predictors, with the goals being to build a parsimonious model for classification while doing inferences on the important predictors.…

This article proposes a Bayesian approach to regression with a scalar response against vector and tensor covariates. Tensor covariates are commonly vectorized prior to analysis, failing to exploit the structure of the tensor, and resulting…

We introduce a novel longitudinal mixed model for analyzing complex multidimensional functional data, addressing challenges such as high-resolution, structural complexities, and computational demands. Our approach integrates dimension…

Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition. This is useful because complexity can be significantly reduced and the treatment of large-scale data sets…

We present a flexible Bayesian semiparametric mixed model for longitudinal data analysis in the presence of potentially high-dimensional categorical covariates. Building on a novel hidden Markov tensor decomposition technique, our proposed…

We propose a new model for multi-token prediction in transformers, aiming to enhance sampling efficiency without compromising accuracy. Motivated by recent work that predicts the probabilities of subsequent tokens using multiple heads, we…

While nonparametric density estimators often perform well on low dimensional data, their performance can suffer when applied to higher dimensional data, owing presumably to the curse of dimensionality. One technique for avoiding this is to…

Infinite Tucker Decomposition (InfTucker) and random function prior models, as nonparametric Bayesian models on infinite exchangeable arrays, are more powerful models than widely-used multilinear factorization methods including Tucker and…

Bottom-Up Hidden Tree Markov Model is a highly expressive model for tree-structured data. Unfortunately, it cannot be used in practice due to the intractable size of its state-transition matrix. We propose a new approximation which lies on…

A novel regularizer of the PARAFAC decomposition factors capturing the tensor's rank is proposed in this paper, as the key enabler for completion of three-way data arrays with missing entries. Set in a Bayesian framework, the tensor…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

In autoregressive modeling for tensor-valued time series, Tucker decomposition, when applied to the coefficient tensor, provides a clear interpretation of supervised factor modeling but loses its efficiency rapidly with increasing tensor…

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…

Tensor-valued data are becoming increasingly available in economics and this calls for suitable econometric tools. We propose a new dynamic linear model for tensor-valued response variables and covariates that encompasses some well-known…

In the last decades, tensors have emerged as the right tool to represent multidimensional data in a compact yet informative manner. Moreover, it is well-known that by performing low-rank factorizations of such tensors one is often able to…

Effective non-parametric density estimation is a key challenge in high-dimensional multivariate data analysis. In this paper,we propose a novel approach that builds upon tensor factorization tools. Any multivariate density can be…

Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…