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Related papers: Functional linear regression that's interpretable

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Rule models are often preferred in prediction tasks with tabular inputs as they can be easily interpreted using natural language and provide predictive performance on par with more complex models. However, most rule models' predictions are…

Machine Learning · Computer Science 2023-11-27 Lena Stempfle , Fredrik D. Johansson

In a regression setting with a response vector and given regressor vectors, a typical question is to what extent the response is related to these regressors, specifically, how well it can be approximated by a linear combination of the…

Statistics Theory · Mathematics 2025-02-03 Lutz Duembgen , Laurie Davies

Due to its strong interpretability, linear regression is widely used in social science, from which significance test provides the significance level of models or coefficients in the traditional statistical inference. However, linear…

Machine Learning · Computer Science 2020-06-08 Jiaye Teng , Yang Yuan

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.…

Machine Learning · Statistics 2013-01-16 Hachem Kadri , Philippe Preux , Emmanuel Duflos , Stéphane Canu

The paper considers functional linear regression, where scalar responses $Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a…

Statistics Theory · Mathematics 2009-02-26 Christophe Crambes , Alois Kneip , Pascal Sarda

To address functional-output regression, we introduce projection learning (PL), a novel dictionary-based approach that learns to predict a function that is expanded on a dictionary while minimizing an empirical risk based on a functional…

Machine Learning · Statistics 2022-02-09 Dimitri Bouche , Marianne Clausel , François Roueff , Florence d'Alché-Buc

The paper proposes to analyze epidemiological data using regression models which enable subject-matter (epidemiological) interpretation of such data whether with uncorrelated or correlated predictors. To this end, response functions should…

Applications · Statistics 2020-02-20 Anatoly N. Varaksin , Vladimir G. Panov

To tackle interpretability in deep learning, we present a novel framework to jointly learn a predictive model and its associated interpretation model. The interpreter provides both local and global interpretability about the predictive…

Machine Learning · Computer Science 2022-02-24 Jayneel Parekh , Pavlo Mozharovskyi , Florence d'Alché-Buc

When observations are curves over some natural time interval, the field of functional data analysis comes into play. Functional linear processes account for temporal dependence in the data. The prediction problem for functional linear…

Methodology · Statistics 2023-12-12 Johannes Klepsch , Claudia Klüppelberg

For optimization models to be used in practice, it is crucial that users trust the results. A key factor in this aspect is the interpretability of the solution process. A previous framework for inherently interpretable optimization models…

Optimization and Control · Mathematics 2026-02-13 Marc Goerigk , Michael Hartisch , Sebastian Merten , Kartikey Sharma

Deep learning has achieved remarkable success across many domains, but it has also created a growing demand for interpretability in model predictions. Although many explainable machine learning methods have been proposed, post-hoc…

Machine Learning · Computer Science 2026-01-28 Shijian Xu , Marcello Massimo Negri , Volker Roth

Functional linear discriminant analysis offers a simple yet efficient method for classification, with the possibility of achieving a perfect classification. Several methods are proposed in the literature that mostly address the…

Methodology · Statistics 2020-12-14 Juhyun Park , Jeongyoun Ahn , Yongho Jeon

We propose an extensive framework for additive regression models for correlated functional responses, allowing for multiple partially nested or crossed functional random effects with flexible correlation structures for, e.g., spatial,…

Methodology · Statistics 2013-11-26 Fabian Scheipl , Ana-Maria Staicu , Sonja Greven

A general formulation of the linear model with functional (random) explanatory variable $X = X(t), t \in T$ , and scalar response Y is proposed. It includes the standard functional linear model, based on the inner product in the space…

Statistics Theory · Mathematics 2020-12-02 José R. Berrendero , Alejandro Cholaquidis , Antonio Cuevas

Model diagnostics and forecast evaluation are two sides of the same coin. A common principle is that fitted or predicted distributions ought to be calibrated or reliable, ideally in the sense of auto-calibration, where the outcome is a…

Methodology · Statistics 2024-09-27 Tilmann Gneiting , Johannes Resin

We tackle estimation and prediction at non-visted sites in a spatial semi-functional linear regression model with derivatives that combines a functional linear model with a nonparametric regression one. The parametric part is estimated by a…

Statistics Theory · Mathematics 2022-11-22 Stéphane Bouka , Kowir Pambo Bello , Guy Martial Nkiet

A partial least squares regression is proposed for estimating the function-on-function regression model where a functional response and multiple functional predictors consist of random curves with quadratic and interaction effects. The…

Methodology · Statistics 2020-12-11 Ufuk Beyaztas , Han Lin Shang

We introduce a novel interpretable tree based algorithm for prediction in a regression setting. Our motivation is to estimate the unknown regression function from a functional decomposition perspective in which the functional components…

Machine Learning · Statistics 2023-08-04 Munir Hiabu , Enno Mammen , Joseph T. Meyer

Estimating linear regression using least squares and reporting robust standard errors is very common in financial economics, and indeed, much of the social sciences and elsewhere. For thick tailed predictors under heteroskedasticity this…

Methodology · Statistics 2020-08-17 Neil Shephard

We consider the model of nonregular nonparametric regression where smoothness constraints are imposed on the regression function $f$ and the regression errors are assumed to decay with some sharpness level at their endpoints. The aim of…

Statistics Theory · Mathematics 2014-10-02 Moritz Jirak , Alexander Meister , Markus Reiß