Likelihood approximation networks (LANs) for fast inference of simulation models in cognitive neuroscience

Abstract

In cognitive neuroscience, computational modeling can formally adjudicate between theories and affords quantitative fits to behavioral/brain data. Pragmatically, however, the space of plausible generative models considered is dramatically limited by the set of models with known likelihood functions. For many models, the lack of a closed-form likelihood typically impedes Bayesian inference methods. As a result, standard models are evaluated for convenience, even when other models might be superior. Likelihood-free methods exist but are limited by their computational cost or their restriction to particular inference scenarios. Here, we propose neural networks that learn approximate likelihoods for arbitrary generative models, allowing fast posterior sampling with only a one-off cost for model simulations that is amortized for future inference. We show that these methods can accurately recover posterior parameter distributions for a variety of neurocognitive process models. We provide code allowing users to deploy these methods for arbitrary hierarchical model instantiations without further training.

Humans reconfigure target and distractor processing to address distinct task demands

“…Our model also provides process-level insight into how attractor networks can account for the dynamics of attentional control, parsimoniously explaining both within-trial gain dynamics and, critically, how adaptation alters the initial conditions of these feature gains. Future research should directly fit this model to participants’ behavior, potentially leveraging recent advances in the efficient estimation of parameters for complex decision models (Fengler, Govindarajan, Chen, & Frank, 2021), allowing for finer grained comparisons between different accounts of dynamic attentional control.…”

Flexible and efficient simulation-based inference for models of decision-making

“…This version of the DDM is the ideal candidate for comparing the performance of different inference methods because the likelihood of an observation given the parameters, L ( x | θ ), can be calculated analytically (Navarro and Fuss, 2009, in contrast to more complicated versions of the DDM, e.g., Ratcliff and Rouder (1998); Usher and McClelland (2001); Reynolds and Rhodes (2009)). We evaluated MNLE’s performance, and compared against the publicly available pre-trained LAN neural networks (Fengler et al, 2021), based on the analytical likelihoods and the inferred posteriors of the DDM.…”

“…More recent approaches from the field simulation-based inference (SBI, Cranmer et al, 2020) have the potential to overcome these limitations by using machine learning algorithms such as neural networks. Recently, Fengler et al (2021) presented an SBI-algorithm for a specific problem in cognitive neuroscience—inference for drift-diffusion models (DDM). They introduced a new approach, called likelihood approximation networks (LANs), which uses neural networks to predict log-likelihoods from data and parameters.…”

“…Finally, supervised learning is used to train a neural network to predict log-likelihoods, by minimizing a loss function (the Huber loss) between the network-predicted log-likelihoods and the (log of) the empirically estimated likelihoods. Overall, LANs require a large number of model simulations such that the histogram-probability of each possible observed data and for each possible combination of input parameters, can be accurately estimated— N · M model simulations, e.g., 1.5 · 10 6 · 10 5 (150 billion) for the examples used in Fengler et al (2021). The extremely high number of model simulations will make it infeasible for most users to run this training themselves, so that there would need to be a repository from which users can download pre-trained LANs.…”

“…While most neural likelihood estimation methods target continuous data, MNLE works with mixed data types, as typically obtained in decision-making experiments (e.g., binary decisions and associated continuous reaction times). We demonstrate MNLE on the classical drift-diffusion model (DDM) and compare its performance to a recently proposed method for SBI on DDMs, called likelihood approximation networks (LAN, Fengler et al 2021). We show that MNLE is substantially more efficient than LANs, requiring up to six orders of magnitudes fewer model simulations to achieve comparable likelihood accuracy and evaluation time while providing the same level of flexibility.…”