Restricted Boltzmann machines modeling human choice
We extend the multinomial logit model to represent some of the empirical phenomena that are frequently observed in the choices made by humans. These phenomena include the similarity effect, the attraction effect, and the compromise effect. We formally quantify the strength of these phenomena that can be represented by our choice model, which illuminates the flexibility of our choice model. We then show that our choice model can be represented as a restricted Boltzmann machine and that its parameters can be learned effectively from data. Our numerical experiments with real data of human choices suggest that we can train our choice model in such a way that it represents the typical phenomena of choice.
This paper presents how restricted Boltzmann machines can be used to learn human choice preferences. Because restricted Boltzmann machines do not force choices to be independent of the set of alternatives, the RBM model can represent typical human choice phenomena that cannot be modeled by the multinomial logistic models that are used as a standard model of human choice. The work proves that the RBM choice model can model several standard features of human choices, and that RBMs can flexibly model a range of strengths of these features. The evaluation includes synthetic data (in the supplementary material) as well as a comparison of RBM versus MLM models for a dataset on real human choices. Overall, the model seems technically sound and is indeed able to model typical human choice phenomena. One concern I had was whether the model is too flexible: are there features of human choices that this model would not be able to model, or parameter values that we might expect to share across datasets to constrain the learned parameters? The presentation does not seem to suggest that RBMs can be used as a cognitive model, but simply that they can predict human choices; this may make the concern about falsifiability less pressing, but it seems like some discussion of whether flexibility could be a negative feature of the model would be helpful.The theorems that are proven do demonstrate that given only a single hidden unit, the choice phenomena can be represented up to a particular range of strengths, but the evaluation is not restricted to using a single hidden unit and performance on test with a single hidden unit does not appear to be much better than not using a hidden unit. Since the theorems only show that a single typical choice phenomenon can be represented using one hidden unit, it makes sense that more hidden units may be required in the simulations (thank you for this clarification in the rebuttal). However, it seems that the discussion should then connect the theoretical and empirical work to make sense of what we can learn about human choice and how much we can generalize to new choices given the extreme flexibility of the actual models used in the simulations. One of my concerns related to the flexibility of the model was whether the RBM choice model could be used to predict choices about new items based on their features. This is addressed in the discussion with the sentence "The focus of this paper is in designing the fundamental structure of the RBM choice model and analyzing its fundamental properties, and the study about the RBM choice model with attributes is reported elsewhere." Thank you to the authors for clarifying that this is work in progress/not yet published - I think this sentence could be re-worded to make it more clear, but my concern about this paper standing on its own given the existence of the other work has been addressed. I do wonder, though, if it really makes sense to separate the two pieces of research. In the evaluation, I would have appreciated more qualitative explanation of the meaning of the hidden units in the RBM (i.e., why here 4 hidden units is approximately equivalent in performance to 16); such explanation might be helpful in understanding whether we can draw any conclusions about human choices based on the learned RBM model or if the model is only descriptive. To me, it seems like learning something about human choices (rather than just describing them computationally) needs to be a key outcome of this paper, especially given the flexibility of RBMs that the authors note.The qualitative clarification about generalizability in the rebuttal is helpful. I still believe it would strengthen the paper substantially to do more detailed testing than leave one out. In particular, it would strengthen the submission to more closely examine the effects of training set size and characteristics on test performance. Overall, my main concern about this paper is on its focus: computationally describing human choice phenomena and predicting a new choice from existing choices without looking at what we might learn about choices from this model or how much overfitting is a problem. Learning about choices from the model seems likely to be most interesting to computational cognitive scientists, but the current paper doesn't address this issue; I think it could be addressed using the current work, and I would appreciate seeing discussion of it. The overfitting concern seems to be most relevant for the broader machine learning community, which might be interested mainly in the applications. I think the paper could be substantially strengthened by addressing these issues or by explaining why they are not in scope; this concern is why I think presenting this work with the attribute work might result in more impact.Minor notes:line 18 (and later): "the choice made by humans" is used several times in the paper - I think this should read "the choices made by humans", but maybe this is a specialized use?line 375: Maglve20 -> Maglev20line 377: such attraction effect ->  such attraction effectsline 431: from given choice set -> from a given choice set