Variational Treatment of Trial-by-Trial Drift-Diffusion Models of Behaviour

Abstract

The Full Drift Diffusion Model (DDM) is challenging to fit to behavioural data. Precision of the fits are usually poor for some if not all parameters, and computationally expensive to obtain. Moreover, inference at the trial level for each and every parameters, threshold included, has so far been considered as impossible. Most approaches rely on strong assumptions about the model structure, such as selection of the parameters that are subject to trial-to-trial variability or prior distribution of these parameters, that usually lack precise mathematical or empirical justifications. The fact that, in most versions of the DDM, the sequence of participants choices are considered as independent and identically distributed (i.i.d.), has been mainly overlooked so far. Our contribution to the field is threefold: first, we introduce Variational Bayes as a method to fit the full DDM. Second, we relax the i.i.d. assumption, and propose a data-driven algorithm based on a Recurrent Auto-Encoder, that estimates the local posterior probability of the DDM parameters at each trial based on the sequence of parameters and data preceding the data. Finally, we show that inference at the trial level can be achieved efficiently for each and every parameter of the DDM, threshold included. This data-driven approach is highly generic and self-contained, in the sense that no external input (e.g. regressors or physiological measure) is necessary to fit the data. Using simulations and real-world examples, we show that this method outperforms by several order of magnitude the i.i.d.-based ones, either Markov Chain Monte Carlo or i.i.d.-VB.