Related papers: On function-on-function regression: Partial least …

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…

Regression analysis is an important instrument to determine the effect of the explanatory variables on response variables. When outliers and bias errors are present, the standard weighted least squares estimator may perform poorly. For this…

In machine learning it is common to interpret each data point as a vector in Euclidean space. However the data may actually be functional i.e.\ each data point is a function of some variable such as time and the function is discretely…

In some real world applications, such as spectrometry, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of…

Large health surveys increasingly collect high-dimensional functional data from wearable devices, and function on scalar regression (FoSR) is often used to quantify the relationship between these functional outcomes and scalar covariates…

Linear regression and classification methods with repeated functional data are considered. For each statistical unit in the sample, a real-valued parameter is observed over time under different conditions related by some neighborhood…

This paper considers the partially functional linear model (PFLM) where all predictive features consist of a functional covariate and a high dimensional scalar vector. Over an infinite dimensional reproducing kernel Hilbert space, the…

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…

Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…

We propose a new prediction method for multivariate linear regression problems where the number of features is less than the sample size but the number of outcomes is extremely large. Many popular procedures, such as penalized regression…

The functional linear model is a popular tool to investigate the relationship between a scalar/functional response variable and a scalar/functional covariate. We generalize this model to a functional linear mixed-effects model when repeated…

In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…

Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…

We introduce a new class of non-linear function-on-function regression models for functional data using neural networks. We propose a framework using a hidden layer consisting of continuous neurons, called a continuous hidden layer, for…

This paper develops a novel spatial quantile function-on-scalar regression model, which studies the conditional spatial distribution of a high-dimensional functional response given scalar predictors. With the strength of both quantile…

Traditionally regression analysis answers questions about the relationships among variables based on the assumption that the observation values of variables are precise numbers. It has long been dominated by least squares techniques, mostly…

The paper deals with generalized functional regression. The aim is to estimate the influence of covariates on observations, drawn from an exponential distribution. The link considered has a semiparametric expression: if we are interested in…

In this article, we extend predictor envelope models to settings with multivariate outcomes and multiple, functional predictors. We propose a two-step estimation strategy, which first projects the function onto a finite-dimensional…

We propose a Bayesian approach to estimating parameters in multiclass functional models. Unordered multinomial probit, ordered multinomial probit and multinomial logistic models are considered. We use finite random series priors based on a…

Irregular functional data in which densely sampled curves are observed over different ranges pose a challenge for modeling and inference, and sensitivity to outlier curves is a concern in applications. Motivated by applications in…