PenFFR

The goal of PenFFR is to design a penalized funtion-on-funtion linear regression with multiples functional and scalar covariates. This package allows you to build two types of functional linear models: - The concurrent linear model whose equation is given by : $$\mathrm{y}i(t) = \beta_0(t) + \sum{\ell=1}^p\beta_\ell(t)\mathrm{x}i^\ell(t) + \varepsilon_i(t)$$ - The integral linear model given by : $$\mathrm{y}i(t) = \beta_0(t) + \sum{\ell=1}^p\int_0^t\beta\ell(s,t)\mathrm{x}_i^\ell(s),ds + \varepsilon_i(t)$$

Parameters are estimated using a spline-based expansion with a number of basis functions that you can set.

To handle heterogeneous data, we also provide a Mixture-of-Experts (MoE) version of the linear concurrent model. The conditional density of $\mathrm{Y}(t)$ according to the function-on-function MoE (FFMoE) model is $$\begin{eqnarray} f(\mathrm{Y}(t)|\mathrm{X}(t),\Psi(t)) &=& \sum_{k=1}^\mathrm{K}\pi_k(\mathrm{X}(t),\alpha_k(t)) \Phi(\mathrm{Y}(t);\mathrm{X}(t)\beta_k(t),\sigma^2_k),\label{ME2} \end{eqnarray}$$ with $$\begin{itemize} \item $\pi_k(\mathrm{X}(t),\ \alpha_k(t))$ the mixture proportion of group $k$, also called the $k^{\text{th}}$ gated network function, depending on the covariate $\mathrm{X}(t)$ through group specific functional parameter $\alpha_k(t)$. More details will be provided in the next section; \item $\Psi_k(t) = (\beta_k(t),\alpha_k(t))$ are the functional parameters; \item $\Phi(\mathrm{Y}(t); \mathrm{X}_i(t)\beta_k(t), \sigma^2_k)$ is the Gaussian density probability function of mean $\mathrm{X}(t)\beta_k(t)$ and variance $\sigma^2_k$. \end{itemize}$$

Download

You can download the package

• Version 0.0.1

Or clone from Gitlab :

$ git clone https://gitlab.tech.orange/rlsoftwarenet/penffr.git

Cite

If you use this software, please cite the following work :

• Jean Steve Tamo Tchomgui, Julien Jacques, Guillaume Fraysse, Vincent Barriac, Stéphane Chrétien. A mixture of experts regression model for functional response with functional covariates. Statistics and Computing, 2024, 34 (154), s11222-024-10455-z.

• Jean Steve Tamo Tchomgui, Julien Jacques, Vincent Barriac, Guillaume Fraysse, Stéphane Chrétien. A Penalized Spline Estimator for Functional Linear Regression with Functional Response. 2024. hal-04120709v3.

For any questions, Please contact Jean Steve Tamo Tchomgui at or Guillaume Fraysse at .

License

Copyright (c) 2021 — 2025 Orange

This code is released under the GPL2 license. See the LICENSE.md file for more information.

Contact

• Homepage: opensource.orange.com
• e-mail: [email protected]

Link documents

• Contributors list