Related papers: Decoupling multivariate functions using a nonparam…

Functional data are frequently accompanied by a parametric template that describes the typical shapes of the functions. However, these parametric templates can incur significant bias, which undermines both utility and interpretability. To…

We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents…

This paper considers an $N$-server distributed computing setting with $K$ users requesting functions that are arbitrary multivariable polynomial evaluations of $L$ real (potentially non-linear) basis subfunctions, where each function output…

In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…

The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close…

Activation functions (AFs) are an important part of the design of neural networks (NNs), and their choice plays a predominant role in the performance of a NN. In this work, we are particularly interested in the estimation of flexible…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

Pooling operations, which can be calculated at low cost and serve as a linear or nonlinear transfer function for data reduction, are found in almost every modern neural network. Countless modern approaches have already tackled replacing the…

This work shows that for rational multivariate functions, the Kolmogorov Superposition Theorem (KST) involves several single-variable functions, which can be written down by inspection. In other words, no computation is required for…

A multi-view image sequence provides a much richer capacity for object recognition than from a single image. However, most existing solutions to multi-view recognition typically adopt hand-crafted, model-based geometric methods, which do…

In todays age of data, discovering relationships between different variables is an interesting and a challenging problem. This problem becomes even more critical with regards to complex dynamical systems like weather forecasting and…

Coupled decompositions are a widely used tool for data fusion. As the volume of data increases, so does the dimensionality of matrices and tensors, highlighting the need for more efficient coupled decomposition algorithms. This paper…

Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…

The interdependence and high dimensionality of multivariate signals present significant challenges for denoising, as conventional univariate methods often struggle to capture the complex interactions between variables. A successful approach…

Coupled tensor approximation has recently emerged as a promising approach for the fusion of hyperspectral and multispectral images, reconciling state of the art performance with strong theoretical guarantees. However, tensor-based…

Estimating individual-level treatment effect from observational data is a fundamental problem in causal inference and has attracted increasing attention in the fields of education, healthcare, and public policy.In this work, we concentrate…

Based on tensor neural network, we propose an interpolation method for high dimensional non-tensor-product-type functions. This interpolation scheme is designed by using the tensor neural network based machine learning method. This means…

Interpretability for machine learning models is becoming more and more important as machine learning models become more complex. The functional ANOVA model, which decomposes a high-dimensional function into a sum of lower dimensional…

Tensors or {\em multi-way arrays} are functions of three or more indices $(i,j,k,\cdots)$ -- similar to matrices (two-way arrays), which are functions of two indices $(r,c)$ for (row,column). Tensors have a rich history, stretching over…

Discovering components that are shared in multiple datasets, next to dataset-specific features, has great potential for studying the relationships between different subjects or tasks in functional Magnetic Resonance Imaging (fMRI) data.…