Related papers: Mapping-to-Parameter Nonlinear Functional Regressi…
This study proposes a mathematical programming-based algorithm for the integrated selection of variable subsets and bandwidth estimation in geographically weighted regression, a local regression method that allows the kernel bandwidth and…
We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…
The problem of fixed knot approximation is convex and there are several efficient approaches to solve this problem, yet, when the knots joining the affine parts are also variable, finding conditions for a best Chebyshev approximation…
This paper presents a new methodology, called AFSSEN, to simultaneously select significant predictors and produce smooth estimates in a high-dimensional function-on-scalar linear model with a sub-Gaussian errors. Outcomes are assumed to lie…
We propose a nested reduced-rank regression (NRRR) approach in fitting regression model with multivariate functional responses and predictors, to achieve tailored dimension reduction and facilitate interpretation/visualization of the…
We present a novel approach for the construction of basis functions to be employed in selective or adaptive h-refined finite element applications with arbitrary-level hanging node configurations. Our analysis is not restricted to…
Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…
Numerical preprocessing remains an important component of tabular deep learning, where the representation of continuous features can strongly affect downstream performance. Although its importance is well established for classical…
We propose a novel learning-based approach for robust 3D shape matching. Our method builds upon deep functional maps and can be trained in a fully unsupervised manner. Previous deep functional map methods mainly focus on predicting…
We propose a new, generic and flexible methodology for nonparametric function estimation, in which we first estimate the number and locations of any features that may be present in the function, and then estimate the function parametrically…
Functional regression is very crucial in functional data analysis and a linear relationship between scalar response and functional predictor is often assumed. However, the linear assumption may not hold in practice, which makes the methods…
Functional data analysis tools, such as function-on-function regression models, have received considerable attention in various scientific fields because of their observed high-dimensional and complex data structures. Several statistical…
Regression splines are smooth, flexible, and parsimonious nonparametric function estimators. They are known to be sensitive to knot number and placement, but if assumptions such as monotonicity or convexity may be imposed on the regression…
Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which…
In this paper, we develop a local rank correlation measure which quantifies the performance of dimension reduction methods. The local rank correlation is easily interpretable, and robust against the extreme skewness of nearest neighbor…
Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between…
Random graph models are widely used to understand network properties and graph algorithms. Key to such analyses are the different parameters of each model, which affect various network features, such as its size, clustering, or degree…
We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…
Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this…
We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology…