Efficient simulation of diffusion-based choice RT models on CPU and GPU

Accelerating item factor analysis on GPU with Python package xifa

Item parameter estimation is a crucial step when conducting item factor analysis (IFA). From the view of frequentist estimation, marginal maximum likelihood (MML) seems to be the gold standard. However, fitting a high-dimensional IFA model by MML is still a challenging task. The current study demonstrates that with the help of a GPU (graphics processing unit) and carefully designed vectorization, the computational time of MML could be largely reduced for large-scale IFA applications. In particular, a Python package called xifa (accelerated item factor analysis) is developed, which implements a vectorized Metropolis-Hastings Robbins-Monro (VMHRM) algorithm. Our numerical experiments show that the VMHRM on a GPU may run 33 times faster than its CPU version. When the number of factors is at least five, VMHRM (on GPU) is much faster than the Bock-Aitkin expectation maximization, MHRM implemented by mirt (on CPU), and the importance-weighted autoencoder (on GPU). The GPU-implemented VMHRM is most appropriate for high-dimensional IFA with large data sets. We believe that GPU computing will play a central role in large-scale psychometric modeling in the near future.

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.

A flexible framework for simulating and fitting generalized drift-diffusion models

The drift-diffusion model (DDM) is an important decision-making model in cognitive neuroscience. However, innovations in model form have been limited by methodological challenges. Here, we introduce the generalized drift-diffusion model (GDDM) framework for building and fitting DDM extensions, and provide a software package which implements the framework. The GDDM framework augments traditional DDM parameters through arbitrary user-defined functions. Models are solved numerically by directly solving the Fokker-Planck equation using efficient numerical methods, yielding a 100-fold or greater speedup over standard methodology. This speed allows GDDMs to be fit to data using maximum likelihood on the full response time (RT) distribution. We demonstrate fitting of GDDMs within our framework to both animal and human datasets from perceptual decision-making tasks, with better accuracy and fewer parameters than several DDMs implemented using the latest methodology, to test hypothesized decision-making mechanisms. Overall, our framework will allow for decision-making model innovation and novel experimental designs.

Parallel probability density approximation

Probability density approximation (PDA) is a nonparametric method of calculating probability densities. When integrated into Bayesian estimation, it allows researchers to fit psychological processes for which analytic probability functions are unavailable, significantly expanding the scope of theories that can be quantitatively tested. PDA is, however, computationally intensive, requiring large numbers of Monte Carlo simulations in order to attain good precision. We introduce Parallel PDA (pPDA), a highly efficient implementation of this method utilizing the Armadillo C++ and CUDA C libraries to conduct millions of model simulations simultaneously in graphics processing units (GPUs). This approach provides a practical solution for rapidly approximating probability densities with high precision. In addition to demonstrating this method, we fit a piecewise linear ballistic accumulator model (Holmes, Trueblood, & Heathcote, 2016) to empirical data. Finally, we conducted simulation studies to investigate various issues associated with PDA and provide guidelines for pPDA applications to other complex cognitive models.