Distributed Lag Neural Additive Models
Abstract
We introduce Distributed Lag Neural Additive Models (DLNAMs), neural-additive analogues of Distributed Lag Non-linear Models (DLNMs) for learning nonlinear effects distributed over lags. DLNAMs replace a prespecified spline cross-basis with neural components that learn exposure--lag response surfaces, avoiding choices of basis family, dimension, and knot placement while preserving additive interpretability and familiar distributed-lag summaries. Exp-centered input layers, smooth activations, and learned subnetwork mixtures produce smooth, locally adaptive representations; pointwise uncertainty combines a conditional last-layer Laplace approximation with between-member ensemble variation. In simulations, DLNAMs generally outperformed DLNM comparators, including penalized and treed variants, in recovering known response functions, with lower bias, stronger boundary recovery, and better-calibrated cumulative intervals; gains were largest for more demanding functions. The architecture performed consistently across sample sizes, outcome families, lag horizons, and jointly fitted multi-exposure settings, retaining recovery performance as exposures were added; fit-specific changes were largely confined to optimization, and applications recovered established empirical patterns.
Versions
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BibTeX
@misc{helmersson2026distributed,
title = {{Distributed Lag Neural Additive Models}},
author = {Calle Helmersson and Shivang Pandey and Leonardo Olivetti and Elena Raffetti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07381},
eprint = {2609.07381},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07381},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Distributed Lag Neural Additive Models
AU - Calle Helmersson
AU - Shivang Pandey
AU - Leonardo Olivetti
AU - Elena Raffetti
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07381
UR - https://arxiv.org/abs/2609.07381
AB - We introduce Distributed Lag Neural Additive Models (DLNAMs), neural-additive analogues of Distributed Lag Non-linear Models (DLNMs) for learning nonlinear effects distributed over lags. DLNAMs replace a prespecified spline cross-basis with neural components that learn exposure--lag response surfaces, avoiding choices of basis family, dimension, and knot placement while preserving additive interpretability and familiar distributed-lag summaries. Exp-centered input layers, smooth activations, and learned subnetwork mixtures produce smooth, locally adaptive representations; pointwise uncertainty combines a conditional last-layer Laplace approximation with between-member ensemble variation. In simulations, DLNAMs generally outperformed DLNM comparators, including penalized and treed variants, in recovering known response functions, with lower bias, stronger boundary recovery, and better-calibrated cumulative intervals; gains were largest for more demanding functions. The architecture performed consistently across sample sizes, outcome families, lag horizons, and jointly fitted multi-exposure settings, retaining recovery performance as exposures were added; fit-specific changes were largely confined to optimization, and applications recovered established empirical patterns.
ER -