Deconvolutional Time Series Regression: A Technique for Modeling Temporally Diffuse Effects

Researchers in computational psycholinguistics frequently use linear models to study time series data generated by human subjects. However, time series may violate the assumptions of these models through temporal diffusion, where stimulus presentation has a lingering influence on the response as the rest of the experiment unfolds. This paper proposes a new statistical model that borrows from digital signal processing by recasting the predictors and response as convolutionally-related signals, using recent advances in machine learning to fit latent impulse response functions (IRFs) of arbitrary shape. A synthetic experiment shows successful recovery of true latent IRFs, and psycholinguistic experiments reveal plausible, replicable, and fine-grained estimates of latent temporal dynamics, with comparable or improved prediction quality to widely-used alternatives.