Joint Learning of Smoothing and Model Parameters in GAM Frameworks

Monika Zimmermann, Universität Duisburg-Essen

Co-authors: Florian Ziel, University of Duisburg-Essen

Abstract: Embedding GAMs in FNNs to leverage their complementary strengths motivates the need for efficient learning of smoothing parameters jointly with model parameters. We propose a novel criterion for joint estimation, initially in a simple Gaussian additive model setting, that minimizes an AIC-type estimate using the joint rather than conditional likelihood in the Linear Mixed Model view. Gradient-based learning with this criterion yields results comparable to common methods. Unlike UBRE, which has a shallow score function near its minimum, this criterion results in pronounced and stable local minima for resampling. However, similarly to UBRE, it needs to be adapted to account for smoothing parameter uncertainty.