# A Functional Extension of Semi-Structured Networks

arXiv: https://arxiv.org/abs/2410.05430 · HTML: https://mlsanity.com/paper/2410.05430/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 62 references that are in the map.
- First posted on arXiv 7 Oct 2024.

## Builds on (most cited first, 21 of 21)

- [Wide & Deep Learning for Recommender Systems](https://mlsanity.com/paper/1606.07792/) (2016)
- [InceptionTime: Finding AlexNet for Time Series Classification](https://mlsanity.com/paper/1909.04939/) (2019)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [NODE-GAM: Neural Generalized Additive Model for Interpretable Deep Learning](https://mlsanity.com/paper/2106.01613/) (2021)
- [Neural Basis Models for Interpretability](https://mlsanity.com/paper/2205.14120/) (2022)
- [Semi-Structured Distributional Regression -- Extending Structured Additive Models by Arbitrary Deep Neural Networks and Data Modalities](https://mlsanity.com/paper/2002.05777/) (2020)
- [Deep Conditional Transformation Models](https://mlsanity.com/paper/2010.07860/) (2020)
- [Deep Learning with Functional Inputs](https://mlsanity.com/paper/2006.09590/) (2020)
- [Semi-Structured Deep Piecewise Exponential Models](https://mlsanity.com/paper/2011.05824/) (2020)
- [Non-linear Functional Modeling using Neural Networks](https://mlsanity.com/paper/2104.09371/) (2021)
- [DeepPAMM: Deep Piecewise Exponential Additive Mixed Models for Complex Hazard Structures in Survival Analysis](https://mlsanity.com/paper/2202.07423/) (2022)
- [Modern Non-Linear Function-on-Function Regression](https://mlsanity.com/paper/2107.14151/) (2021)
- [A New PHO-rmula for Improved Performance of Semi-Structured Networks](https://mlsanity.com/paper/2306.00522/) (2023)
- [A Non-linear Function-on-Function Model for Regression with Time Series Data](https://mlsanity.com/paper/2011.12378/) (2020)
- [Functional Autoencoder for Smoothing and Representation Learning](https://mlsanity.com/paper/2401.09499/) (2024)
- [Boosting Factor-Specific Functional Historical Models for the Detection of Synchronisation in Bioelectrical Signals](https://mlsanity.com/paper/1609.06070/) (2016)
- [Deep Function Machines: Generalized Neural Networks for Topological Layer Expression](https://mlsanity.com/paper/1612.04799/) (2016)
- [Change-point Detection for Sparse and Dense Functional Data in General Dimensions](https://mlsanity.com/paper/2205.09252/) (2022)
- [Feature selection in functional data classification with recursive maxima hunting](https://mlsanity.com/paper/1806.02922/) (2018)
- [How Inverse Conditional Flows Can Serve as a Substitute for Distributional Regression](https://mlsanity.com/paper/2405.05429/) (2024)
- [Gaussian Process for Functional Data Analysis: The GPFDA Package for R](https://mlsanity.com/paper/2102.00249/) (2021)

## Abstract (arXiv)

Semi-structured networks (SSNs) merge the structures familiar from additive models with deep neural networks, allowing the modeling of interpretable partial feature effects while capturing higher-order non-linearities at the same time. A significant challenge in this integration is maintaining the interpretability of the additive model component. Inspired by large-scale biomechanics datasets, this paper explores extending SSNs to functional data. Existing methods in functional data analysis are promising but often not expressive enough to account for all interactions and non-linearities and do not scale well to large datasets. Although the SSN approach presents a compelling potential solution, its adaptation to functional data remains complex. In this work, we propose a functional SSN method that retains the advantageous properties of classical functional regression approaches while also improving scalability. Our numerical experiments demonstrate that this approach accurately recovers underlying signals, enhances predictive performance, and performs favorably compared to competing methods.