Artificial neural networks for model identification and parameter estimation in computational cognitive models

Computational cognitive models have been used extensively to formalize cognitive processes. Model parameters offer a simple way to quantify individual differences in how humans process information. Similarly, model comparison allows researchers to identify which theories, embedded in different models, provide the best accounts of the data. Cognitive modeling uses statistical tools to quantitatively relate models to data that often rely on computing/estimating the likelihood of the data under the model. However, this likelihood is computationally intractable for a substantial number of models. These relevant models may embody reasonable theories of cognition, but are often under-explored due to the limited range of tools available to relate them to data. We contribute to filling this gap in a simple way using artificial neural networks (ANNs) to map data directly onto model identity and parameters, bypassing the likelihood estimation. We test our instantiation of an ANN as a cognitive model fitting tool on classes of cognitive models with strong inter-trial dependencies (such as reinforcement learning models), which offer unique challenges to most methods. We show that we can adequately perform both parameter estimation and model identification using our ANN approach, including for models that cannot be fit using traditional likelihood-based methods. We further discuss our work in the context of the ongoing research leveraging simulation-based approaches to parameter estimation and model identification, and how these approaches broaden the class of cognitive models researchers can quantitatively investigate.


Reviewer #1:
The authors have responded well to many of the points of the reviewers.Although the paper does now refer more comprehensively to the wider simulation-based inference literature, it's a little underwhelming not to have implemented/tested alternatives from this stable as a clear alternative (giving extra features such as posteriors rather than point estimates).Nevertheless, the paper's worthwhile contribution is now appropriately hedged.
Thank you for your suggestion.We have added a section called "Uncertainty of Parameter Estimates" (lines 201-217) which presents results with the uncertainty estimates derived from incorporating evidential learning (as outlined by Amini et al.,2020) into our method.Our results show that our approach can be easily adapted to incorporate uncertainty estimation (see lines 694-706 for methods details), without loss to the point estimate (which is typically the goal for our target application), but with a somewhat higher computational cost.
Minor points: L275: "promise [in successfully arbitrating between competing cognitive models] [in model identification]" The content of only one pair of brackets was probably meant to be in that sentence.
Thank you for catching this.We adjusted the sentence.

L278 "any standard cognitive data set with [a] normal number of participants "
We added the "a".We have double-checked this, and are confident that this is correct.The change was due to a previous minor bug which artificially enhanced the results for this method.

Reviewer #2:
Thank you for your thorough response to my and the other reviewers' comments.The response fully addresses all of my concerns other than major comment #1, which it seems to misunderstand.I've tried to rephrase this comment below to unpack it a bit more.I've also described an analysis which represents one simple way of addressing it which I believe would be very straightforward to do.If the authors prefer some other way, including merely acknowledging the concern in the text, that's of course fine too.
Thank you for your positive comments and constructive explanation of your major comment #1.We considered that the previous model misspecification analysis we performed was meant to address it, but we now understand that you refer to a stronger form of model misspecification where the models are from a different family altogether.We hope we have now addressed your concern.

Major Comment
One major claim of this manuscript is that ANN-based parameter estimation is a reasonable substitute for MAP-based parameter estimation, and that this is a practical tool that might be useful for fitting models to real datasets generated by humans or animals.The manuscript does a great job of showing that this is true when estimating parameters from synthetic datasets where the generative process exactly matches the model being fit.But real data are never generated from exactly the model being fit (they're generated by a human or an animal), so it's important to check whether the ANN-based method returns similar results to MAP when applied to datasets generated by different models.For concreteness: one way to address this would be creating a plot like the new Figure S10, which compares parameter estimates produced by MAP and by the ANN, but using mis-specified models.For example panel A showing estimates of RL model parameters would analyze datasets produced by the Bayesian model, and panel B vice-versa.Or of course the revision might choose to address it in some other way.
Thank you for your suggestion.We have conducted the model misspecification analysis you suggested, and summarize the results below (these are now included as supplementary figures S11, S14, S15).
We simulated data from the Bayesian inference model, and then estimated RL parameters based on the data sequences by 1) fitting the RL model using MAP and 2) using the neural network trained to estimate RL model parameters.Here we show the correlation between true and estimated parameters for both MAP and GRU methods.The main takeaway from this misspecification analysis is that we observe extremely similar patterns of variance attribution across both methods, such that the impact of model misspecification is comparable across methods.
Figure 3B panel ABC, True T: put "rho=.5"annotation lower We have adjusted the figure.

Fig S3 :
Fig S3:The top right plot changed quite a bit (and is now terrible), maybe the authors just want to double-check this is correct?

Fig
Fig S6: the p-value should be spelled out as something like "p<1e-xx" We have adjusted the p-value in the figure.