Related papers: Tensor-based multivariate function approximation: …
Modern foundation models such as large language models (LLMs) and large multi-modal models (LMMs) require a massive amount of computational and memory resources. We propose a new framework to convert such LLMs/LMMs into a reduced-dimension…
Carefully designed activation functions can improve the performance of neural networks in many machine learning tasks. However, it is difficult for humans to construct optimal activation functions, and current activation function search…
In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…
To analyze the abundance of multidimensional data, tensor-based frameworks have been developed. Traditionally, the matrix singular value decomposition (SVD) is used to extract the most dominant features from a matrix containing the…
Multivariate function approximation is a fundamental problem in machine learning. Classic multivariate function approximations rely on hand-crafted basis functions (e.g., polynomial basis and Fourier basis), which limits their approximation…
We provide a comparative study between neural word representations and traditional vector spaces based on co-occurrence counts, in a number of compositional tasks. We use three different semantic spaces and implement seven tensor-based…
A multivariate quantile regression model with a factor structure is proposed to study data with many responses of interest. The factor structure is allowed to vary with the quantile levels, which makes our framework more flexible than the…
We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…
Recent advances in probabilistic modelling have led to a large number of simulation-based inference algorithms which do not require numerical evaluation of likelihoods. However, a public benchmark with appropriate performance metrics for…
Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex…
To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…
The paper considers function-valued tensors, viewed as multidimensional arrays with entries in an abstract Hilbert space. Despite the absence of the algebraic structure of a field, the geometric inner-product structure suffices to introduce…
Recent developments of advanced driver-assistance systems necessitate an increasing number of tests to validate new technologies. These tests cannot be carried out on track in a reasonable amount of time and automotive groups rely on…
Statistical inference for tensors has emerged as a critical challenge in analyzing high-dimensional data in modern data science. This paper introduces a unified framework for inferring general and low-Tucker-rank linear functionals of…
Marginal Structural Models (MSMs) are popular for causal inference of sequential treatments in longitudinal observational studies, which however are sensitive to model misspecification. To achieve flexible modeling, we envision the…
Multivariate functional data can be intrinsically multivariate like movement trajectories in 2D or complementary like precipitation, temperature, and wind speeds over time at a given weather station. We propose a multivariate functional…
Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…
We consider supervised learning (regression/classification) problems with tensor-valued input. We derive multi-linear sufficient reductions for the regression or classification problem by modeling the conditional distribution of the…
Adaptive designs are increasingly used in clinical trials and online experiments to improve participant outcomes by dynamically updating treatment allocation as data accumulate. In practice, experimenters often consider multiple candidate…
The main aim of this paper is to develop a new algorithm for computing nonnegative low rank tensor approximation for nonnegative tensors that arise in many multi-dimensional imaging applications. Nonnegativity is one of the important…