Using recurrent neural network to estimate irreducible stochasticity in human choice-behavior

Reviewer #1 (Public Review):

Summary:
Ger and colleagues address an issue that often impedes computational modeling: the inherent ambiguity between stochasticity in behavior and structural mismatch between the assumed and true model. They propose a solution to use RNNs to estimate the ceiling on explainable variation within a behavioral dataset. With this information in hand, it is possible to determine the extent to which "worse fits" result from behavioral stochasticity versus failures of the cognitive model to capture nuances in behavior (model misspecification). The authors demonstrate the efficacy of the approach in a synthetic toy problem and then use the method to show that poorer model fits to 2-step data in participants with low IQ are actually due to an increase in inherent stochasticity, rather than systemic mismatch between model and behavior.

Strengths:
Overall I found the ideas conveyed in the paper interesting and the paper to be extremely clear and well-written. The method itself is clever and intuitive and I believe it could be useful in certain circumstances, particularly ones where the sources of structure in behavioral data are unknown. In general, the support for the method is clear and compelling. The flexibility of the method also means that it can be applied to different types of behavioral data - without any hypotheses about the exact behavioral features that might be present in a given task.

Weaknesses:
That said, I have some concerns with the manuscript in its current form, largely related to the applicability of the proposed methods for problems of importance in computational cognitive neuroscience. This concern stems from the fact that the toy problem explored in the manuscript is somewhat simple, and the theoretical problem addressed in it could have been identified through other means (for example through the use of posterior predictive checking for model validation), and the actual behavioral data analyzed were interpreted as a null result (failure to reject that the behavioral stochasticity hypothesis), rather than actual identification of model-misspecification. I expand on these primary concerns and raise several smaller points below.

A primary question I have about this work is whether the method described would actually provide any advantage for real cognitive modeling problems beyond what is typically done to minimize the chance of model misspecification (in particular, post-predictive checking). The toy problem examined in the manuscript is pretty extreme (two of the three synthetic agents are very far from what a human would do on the task, and the models deviate from one another to a degree that detecting the difference should not be difficult for any method). The issue posed in the toy data would easily be identified by following good modeling practices, which include using posterior predictive checking over summary measures to identify model insufficiencies, which in turn would call for the need for a broader set of models (See Wilson & Collins 2019). Thus, I am left wondering whether this method could actually identify model misspecification in real world data, particularly in situations where standard posterior predictive checking would fall short. The conclusions from the main empirical data set rest largely on a null result, and the utility of a method for detecting model misspecification seems like it should depend on its ability to detect its presence, not just its absence, in real data.

Beyond the question of its advantage above and beyond data- and hypothesis-informed methods for identifying model misspecification, I am also concerned that if the method does identify a model-insufficiency, then you still would need to use these other methods in order to understand what aspect of behavior deviated from model predictions in order to design a better model. In general, it seems that the authors should be clear that this is a tool that might be helpful in some situations, but that it will need to be used in combination with other well-described modeling techniques (posterior predictive checking for model validation and guiding cognitive model extensions to capture unexplained features of the data). A general stylistic concern I have with this manuscript is that it presents and characterizes a new tool to help with cognitive computational modeling, but it does not really adhere to best modeling practices (see Collins & Wilson, eLife), which involve looking at data to identify core behavioral features and simulating data from best-fitting models to confirm that these features are reproduced. One could take away from this paper that you would be better off fitting a neural network to your behavioral data rather than carefully comparing the predictions of your cognitive model to your actual data, but I think that would be a highly misleading takeaway since summary measures of behavior would just as easily have diagnosed the model misspecification in the toy problem, and have the added advantage that they provide information about which cognitive processes are missing in such cases.

As a more minor point, it is also worth noting that this method could not distinguish behavioral stochasticity from the deterministic structure that is not repeated across training/test sets (for example, because a specific sequence is present in the training set but not the test set). This should be included in the discussion of method limitations. It was also not entirely clear to me whether the method could be applied to real behavioral data without extensive pretraining (on >500 participants) which would certainly limit its applicability for standard cases.

The authors focus on model misspecification, but in reality, all of our models are misspecified to some degree since the true process-generating behavior almost certainly deviates from our simple models (ie. as George Box is frequently quoted, "all models are wrong, but some of them are useful"). It would be useful to have some more nuanced discussion of situations in which misspecification is and is not problematic.

Reviewer #2 (Public Review):

SUMMARY:
In this manuscript, Ger and colleagues propose two complementary analytical methods aimed at quantifying the model misspecification and irreducible stochasticity in human choice behavior. The first method involves fitting recurrent neural networks (RNNs) and theoretical models to human choices and interpreting the better performance of RNNs as providing evidence of the misspecifications of theoretical models. The second method involves estimating the number of training iterations for which the fitted RNN achieves the best prediction of human choice behavior in a separate, validation data set, following an approach known as "early stopping". This number is then interpreted as a proxy for the amount of explainable variability in behavior, such that fewer iterations (earlier stopping) correspond to a higher amount of irreducible stochasticity in the data. The authors validate the two methods using simulations of choice behavior in a two-stage task, where the simulated behavior is generated by different known models. Finally, the authors use their approach in a real data set of human choices in the two-stage task, concluding that low-IQ subjects exhibit greater levels of stochasticity than high-IQ subjects.

STRENGTHS:
The manuscript explores an extremely important topic to scientists interested in characterizing human decision-making. While it is generally acknowledged that any computational model of behavior will be limited in its ability to describe a particular data set, one should hope to understand whether these limitations arise due to model misspecification or due to irreducible stochasticity in the data. Evidence for the former suggests that better models ought to exist; evidence for the latter suggests they might not.

To address this important topic, the authors elaborate carefully on the rationale of their proposed approach. They describe a variety of simulations - for which the ground truth models and the amount of behavioral stochasticity are known - to validate their approaches. This enables the reader to understand the benefits (and limitations) of these approaches when applied to the two-stage task, a task paradigm commonly used in the field. Through a set of convincing analyses, the authors demonstrate that their approach is capable of identifying situations where an alternative, untested computational model can outperform the set of tested models, before applying these techniques to a realistic data set.

WEAKNESSES:
The most significant weakness is that the paper rests on the implicit assumption that the fitted RNNs explain as much variance as possible, an assumption that is likely incorrect and which can result in incorrect conclusions. While in low-dimensional tasks RNNs can predict behavior as well as the data-generating models, this is not *always* the case, and the paper itself illustrates (in Figure 3) several cases where the fitted RNNs fall short of the ground-truth model. In such cases, we cannot conclude that a subject exhibiting a relatively poor RNN fit necessarily has a relatively high degree of behavioral stochasticity. Instead, it is at least conceivable that this subject's behavior is generated precisely (i.e., with low noise) by an alternative model that is poorly fit by an RNN - e.g., a model with long-term sequential dependencies, which RNNs are known to have difficulties in capturing.

These situations could lead to incorrect conclusions for both of the proposed methods. First, the model misspecification analysis might show equal predictive performance for a particular theoretical model and for the RNN. While a scientist might be inclined to conclude that the theoretical model explains the maximum amount of explainable variance and therefore that no better model should exist, the scenario in the previous paragraph suggests that a superior model might nonetheless exist. Second, in the early-stopping analysis, a particular subject may achieve optimal validation performance with fewer epochs than another, leading the scientist to conclude that this subject exhibits higher behavioral noise. However, as before, this could again result from the fact that this subject's behavior is produced with little noise by a different model. Admittedly, the existence of such scenarios *in principle* does not mean that such scenarios are common, and the conclusions drawn in the paper are likely appropriate for the particular examples analyzed. However, it is much less obvious that the RNNs will provide optimal fits in other types of tasks, particularly those with more complex rules and long-term sequential dependencies, and in such scenarios, an ill-advised scientist might end up drawing incorrect conclusions from the application of the proposed approaches.

In addition to this general limitation, the paper also makes a few additional claims that are not fully supported by the provided evidence. For example, Figure 4 highlights the relationship between the optimal epochs and agent noise. Yet, it is nonetheless possible that the optimal epoch is influenced by model parameters other than inverse temperature (e.g., learning rate). This could again lead to invalid conclusions, such as concluding that low-IQ is associated with optimal epoch when an alternative account might be that low-IQ is associated with low learning rate, which in turn is associated with optimal epoch. Yet additional factors such as the deep double-descent (Nakkiran et al., ICLR 2020) can also influence the optimal epoch value as computed by the authors.

An additional issue is that Figure 4 reports an association between optimal epoch and noise, but noise is normalized by the true minimal/maximal inverse-temperature of hybrid agents (Eq. 23). It is thus possible that the relationship does not hold for more extreme values of inverse-temperature such as beta=0 (extremely noisy behavior) or beta=inf (deterministic behavior), two important special cases that should be incorporated in the current study. Finally, even taking the association in Figure 4 at face value, there are potential issues with inferring noise from the optimal epoch when their correlation is only r~=0.7. As shown in the figures, upon finding a very low optimal epoch for a particular subject, one might be compelled to infer high amounts of noise, even though several agents may exhibit a low optimal epoch despite having very little noise.

APPRAISAL AND DISCUSSION:
Overall, the authors propose a novel method that aims to solve an important problem, but whose generality might be limited only to special cases. In the future, it would be beneficial to test the proposed approach in a broader setting, including simulations of different tasks, different model classes, different model parameters, and different amounts of behavioral noise. Nonetheless, even without such additional work, the proposed methods are likely to be used by cognitive scientists and neuroscientists interested in assessing the quality and limits of their behavioral models.