Related papers: Multivariate Functional Regression via Nested Redu…

In this work, we propose a federated dynamical low-rank training (FeDLRT) scheme to reduce client compute and communication costs - two significant performance bottlenecks in horizontal federated learning. Our method builds upon dynamical…

The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…

In virtualized radio access network (vRAN), the base station (BS) functions are decomposed into virtualized components that can be hosted at the centralized unit or distributed units through functional splits. Such flexibility has many…

For multivariate nonparametric regression, functional analysis-of-variance (ANOVA) modeling aims to capture the relationship between a response and covariates by decomposing the unknown function into various components, representing main…

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…

In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al.…

Deep neural networks have achieved state-of-the-art performance across numerous applications, but their high memory and computational demands present significant challenges, particularly in resource-constrained environments. Model…

Many modern datasets, from areas such as neuroimaging and geostatistics, come in the form of a random sample of tensor-valued data which can be understood as noisy observations of a smooth multidimensional random function. Most of the…

We consider machine learning tasks with low-rank functional tree tensor networks (TTN) as the learning model. While in the case of least-squares regression, low-rank functional TTNs can be efficiently optimized using alternating…

Imposing an effective structural assumption on neural network weight matrices has been the major paradigm for designing Parameter-Efficient Fine-Tuning (PEFT) systems for adapting modern large pre-trained models to various downstream tasks.…

Tomographic imaging is useful for revealing the internal structure of a 3D sample. Classical reconstruction methods treat the object of interest as a vector to estimate its value. Such an approach, however, can be inefficient in analyzing…

Reduced-Rank (RR) regression is a powerful dimensionality reduction technique but it overlooks any possible group configuration among the responses by assuming a low-rank structure on the entire coefficient matrix. Moreover, the temporal…

This paper aims at constructing a good graph for discovering intrinsic data structures in a semi-supervised learning setting. Firstly, we propose to build a non-negative low-rank and sparse (referred to as NNLRS) graph for the given data…

Connectivity structure shapes neural computation, but inferring this structure from population recordings is degenerate: multiple connectivity structures can generate identical dynamics. Recent work uses low-rank recurrent neural networks…

We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [J. Multivariate Anal. 101 (2010) 395-408] have shown that a…

Reduced-rank linear discriminant analysis (RRLDA) is a foundational method of dimension reduction for classification that has been useful in a wide range of applications. The goal is to identify an optimal subspace to project the…

It is well known that kernel ridge regression (KRR) is a popular nonparametric regression estimator. Nonetheless, in the presence of a large data set with size $n\gg 1,$ the KRR estimator has the drawback to require an intensive…

A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work we consider the case, where the target can be represented by a decomposition of spatial…

We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…

Rational and neural network based approximations are efficient tools in modern approximation. These approaches are able to produce accurate approximations to nonsmooth and non-Lipschitz functions, including multivariate domain functions. In…