Efficient estimation of bounded gradient-drift diffusion models for affect on CPU and GPU.

Computational modeling plays an important role in a gamut of research fields. In affect research, continuous-time stochastic models are becoming increasingly popular. Recently, a non-linear, continuous-time, stochastic model has been introduced for affect dynamics, called the Affective Ising Model (AIM). The drawback of non-linear models like the AIM is that they generally come with serious computational challenges for parameter estimation and related statistical analyses. The likelihood function of the AIM does not have a closed form expression. Consequently, simulation based or numerical methods have to be considered in order to evaluate the likelihood function. Additionally, the likelihood function can have multiple local minima. Consequently, a global optimization heuristic is required and such heuristics generally require a large number of likelihood function evaluations. In this paper, a Julia software package is introduced that is dedicated to fitting the AIM. The package includes an implementation of a numeric algorithm for fast computations of the likelihood function, which can be run both on graphics processing units (GPU) and central processing units (CPU). The numerical method introduced in this paper is compared to the more traditional Euler-Maruyama method for solving stochastic differential equations. Furthermore, the estimation software is tested by means of a recovery study and estimation times are reported for benchmarks that were run on several computing devices (two different GPUs and three different CPUs). According to these results, a single parameter estimation can be obtained in less than thirty seconds using a mainstream NVIDIA GPU.

Stimulus-Driven Affective Change: Evaluating Computational Models of Affect Dynamics in Conjunction with Input.

The way in which emotional experiences change over time can be studied through the use of computational models. An important question with regard to such models is which characteristics of the data a model should account for in order to adequately describe these data. Recently, attention has been drawn on the potential importance of nonlinearity as a characteristic of affect dynamics. However, this conclusion was reached through the use of experience sampling data in which no information was available about the context in which affect was measured. However, affective stimuli may induce some or all of the observed nonlinearity. This raises the question of whether computational models of affect dynamics should account for nonlinearity, or whether they just need to account for the affective stimuli a person encounters. To investigate this question, we used a probabilistic reward task in which participants either won or lost money at each trial. A number of plausible ways in which the experimental stimuli played a role were considered and applied to the nonlinear Affective Ising Model (AIM) and the linear Bounded Ornstein-Uhlenbeck (BOU) model. In order to reach a conclusion, the relative and absolute performance of these models were assessed. Results suggest that some of the observed nonlinearity could indeed be attributed to the experimental stimuli. However, not all nonlinearity was accounted for by these stimuli, suggesting that nonlinearity may present an inherent feature of affect dynamics. As such, nonlinearity should ideally be accounted for in the computational models of affect dynamics. Supplementary Information: The online version contains supplementary material available at 10.1007/s42761-022-00118-5.