Related papers: Functional continuum regression
Functional principal component analysis (FPCA) is an important technique for dimension reduction in functional data analysis (FDA). Classical FPCA method is based on the Karhunen-Lo\`{e}ve expansion, which assumes a linear structure of the…
Functional linear regression is a widely used approach to model functional responses with respect to functional inputs. However, classical functional linear regression models can be severely affected by outliers. We therefore introduce a…
Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…
Partial least squares regression---or PLS---is a multivariate method in which models are estimated using either the SIMPLS or NIPALS algorithm. PLS regression has been extensively used in applied research because of its effectiveness in…
Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal…
We study the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a canonical example of an ill-posed inverse problem. We show that the functional partial least squares (PLS) estimator attains…
Convex regression (CR) is the problem of fitting a convex function to a finite number of noisy observations of an underlying convex function. CR is important in many domains and one of its workhorses is the non-parametric least square…
Functional principal component analysis (FPCA) is a key tool in the study of functional data, driving both exploratory analyses and feature construction for use in formal modeling and testing procedures. However, existing methods for FPCA…
In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This…
In this paper, a functional partial quantile regression approach, a quantile regression analog of the functional partial least squares regression, is proposed to estimate the function-on-function linear quantile regression model. A partial…
Regressing a scalar response on a random function is nowadays a common situation. In the nonparametric setting, this paper paves the way for making the local linear regression based on a projection approach a prominent method for solving…
Functional quadratic regression models postulate a polynomial relationship between a scalar response rather than a linear one. As in functional linear regression, vertical and specially high-leverage outliers may affect the classical…
Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…
We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high-dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, $X(t)$, and a scalar…
In this paper, we consider approximations of principal component projection (PCP) without explicitly computing principal components. This problem has been studied in several recent works. The main feature of existing approaches is viewing…
Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with a single or finite number of random functions (much smaller…
Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…
High-dimensional compositional data are commonplace in the modern omics sciences amongst others. Analysis of compositional data requires a proper choice of orthonormal coordinate representation as their relative nature is not compatible…
Here we propose an algorithm, named generalized orthogonal components regression (GOCRE), to explore the relationship between a categorical outcome and a set of massive variables. A set of orthogonal components are sequentially constructed…
Measurement error is an important problem that has not been very well studied in the context of Functional Data Analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors…