Related papers: Tensor-on-tensor regression
We establish non-asymptotic efficiency guarantees for tensor decomposition-based inference in count data models. Under a Poisson framework, we consider two related goals: (i) parametric inference, the estimation of the full distributional…
A novel framework is introduced to formalize identifiability in well-specified but ill-posed linear regression models. The framework is distribution-free and accommodates highly correlated features that may or may not relate to the…
Modeling with multidimensional arrays, or tensors, often presents a problem due to high dimensionality. In addition, these structures typically exhibit inherent sparsity, requiring the use of regularization methods to properly characterize…
This article introduces a novel approach to the mathematical development of Ordinary Least Squares and Neural Network regression models, diverging from traditional methods in current Machine Learning literature. By leveraging Tensor…
We propose a method for estimating coefficients in multivariate regression when there is a clustering structure to the response variables. The proposed method includes a fusion penalty, to shrink the difference in fitted values from…
Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates…
Most existing studies on linear bandits focus on the one-dimensional characterization of the overall system. While being representative, this formulation may fail to model applications with high-dimensional but favorable structures, such as…
In this paper, we consider diffusion index forecasting with both tensor and non-tensor predictors, where the tensor structure is preserved with a Canonical Polyadic (CP) tensor factor model. When the number of non-tensor predictors is…
We introduce a tensor-based model of shared representation for meta-learning from a diverse set of tasks. Prior works on learning linear representations for meta-learning assume that there is a common shared representation across different…
We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient…
We present a windowed technique to learn parsimonious time-varying autoregressive models from multivariate timeseries. This unsupervised method uncovers interpretable spatiotemporal structure in data via non-smooth and non-convex…
There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…
Tensors decompositions are a class of tools for analysing datasets of high dimensionality and variety in a natural manner, with the Canonical Polyadic Decomposition (CPD) being a main pillar. While the notion of CPD is closely intertwined…
We propose a Bayesian tensor regression model to accommodate the effect of multiple factors on phenotype prediction. We adopt a set of prior distributions that resolve identifiability issues that may arise between the parameters in the…
Generative Adversarial Network (GAN) and its variants exhibit state-of-the-art performance in the class of generative models. To capture higher-dimensional distributions, the common learning procedure requires high computational complexity…
This paper studies the problem of estimating a large coefficient matrix in a multiple response linear regression model when the coefficient matrix could be both of low rank and sparse in the sense that most nonzero entries concentrate on a…
Aiming at abundant scientific and engineering data with not only high dimensionality but also complex structure, we study the regression problem with a multidimensional array (tensor) response and a vector predictor. Applications include,…
We consider the problem of solving mixed random linear equations with $k$ components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels…
This paper develops a novel Bayesian approach for nonlinear regression with symmetric matrix predictors, often used to encode connectivity of different nodes. Unlike methods that vectorize matrices as predictors that result in a large…
Penalization schemes like Lasso or ridge regression are routinely used to regress a response of interest on a high-dimensional set of potential predictors. Despite being decisive, the question of the relative strength of penalization is…