Related papers: Tensor Formulation of the General Linear Model wit…

We proposed the tensor-input tree (TT) method for scalar-on-tensor and tensor-on-tensor regression problems. We first address scalar-on-tensor problem by proposing scalar-output regression tree models whose input variable are tensors (i.e.,…

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…

Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…

Factorization models express a statistical object of interest in terms of a collection of simpler objects. For example, a matrix or tensor can be expressed as a sum of rank-one components. However, in practice, it can be challenging to…

This article presents a generic approach to convolution that significantly differs from conventional methodologies in the current Machine Learning literature. The approach, in its mathematical aspects, proved to be clear and concise,…

In model development, model calibration and validation play complementary roles toward learning reliable models. In this article, we expand the Bayesian Validation Metric framework to a general calibration and validation framework by…

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…

Modern decision-making scenarios often involve data that is both high-dimensional and rich in higher-order contextual information, where existing bandits algorithms fail to generate effective policies. In response, we propose in this paper…

We consider the question: what is the abstraction that should be implemented by the computational engine of a machine learning system? Current machine learning systems typically push whole tensors through a series of compute kernels such as…

Tensor computations, with matrix multiplication being the primary operation, serve as the fundamental basis for data analysis, physics, machine learning, and deep learning. As the scale and complexity of data continue to grow rapidly, the…

We combine Recurrent Neural Networks with Tensor Product Representations to learn combinatorial representations of sequential data. This improves symbolic interpretation and systematic generalisation. Our architecture is trained end-to-end…

Matrix models are a highly successful framework for the analytic study of random two dimensional surfaces with applications to quantum gravity in two dimensions, string theory, conformal field theory, statistical physics in random geometry,…

Researchers are increasingly incorporating numeric high-order data, i.e., numeric tensors, within their practice. Just like the matrix/vector (MV) paradigm, the development of multi-purpose, but high-performance, sparse data structures and…

We generalize and simplify an earlier approach. In three dimensions we present the most general averaging formula in lowest order which respects the requirements of covariance. It involves a bitensor, made up of a basis of six tensors, and…

We define a general product of two $n$-dimensional tensors $\mathbb {A}$ and $\mathbb {B}$ with orders $m\ge 2$ and $k\ge 1$, respectively. This product is a generalization of the usual matrix product, and satisfies the associative law.…

Large tensor (multi-dimensional array) data are now routinely collected in a wide range of applications, due to modern data collection capabilities. Often such observations are taken over time, forming tensor time series. In this paper we…

We propose a new encoder-decoder approach to learn distributed sentence representations that are applicable to multiple purposes. The model is learned by using a convolutional neural network as an encoder to map an input sentence into a…

The notion of a tensor captures three great ideas: equivariance, multilinearity, separability. But trying to be three things at once makes the notion difficult to understand. We will explain tensors in an accessible and elementary way…

Deep neural networks generalize well on unseen data though the number of parameters often far exceeds the number of training examples. Recently proposed complexity measures have provided insights to understanding the generalizability in…

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…