Advanced neural models improve analysis of time delayed effects
Distributed Lag Neural Additive Models
Artificial IntelligenceMachine Learning
Summary
Sometimes, things that happen now can affect outcomes later, but it's hard to understand exactly how these effects spread out over time. The researchers created a new type of computer model that can learn these delayed effects more flexibly and accurately than older methods. Their model uses neural networks that adapt to the data without needing lots of fixed assumptions, making it better at capturing complex patterns. Tests showed this new approach could recover the hidden relationships more precisely and handle different scenarios well.
neural networksdistributed lag modelsnonlinear effectsadditive modelstime series analysisspline basisuncertainty estimationlagged responsemachine learningensemble methods
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.