Distributed lag neural additive models improve nonlinear effect learning over time
Distributed Lag Neural Additive Models
Artificial IntelligenceMachine Learning
Summary
When analyzing how things change over time due to different influences, it's important to understand how past events affect current outcomes. The authors propose a new kind of model called Distributed Lag Neural Additive Models (DLNAMs) that uses neural networks to better capture these time-based effects. Unlike older methods that rely on fixed mathematical shapes, DLNAMs learn flexible patterns automatically and give clear, easy-to-understand results. Their tests show DLNAMs can more accurately and reliably understand how different factors influence results over time, especially with complex data.
What this means in practice
- •For environmental health analysts: Analyze how past exposure to pollutants affects health outcomes over time with improved accuracy and interpretability.
- •For financial risk modelers: Build models that capture delayed and nonlinear effects of market factors on risk, improving prediction fidelity.
Authors
Calle Helmersson, Shivang Pandey, Leonardo Olivetti, Elena Raffetti
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.