I don’t claim that the human brain is Bayesian in the strictest sense. The performance of our neural model doesn’t match the optimal Bayesian curve, but is closer to the human- level performance. Recall from section 2.6 that one of the open questions in the field of neurally plausible Bayesian computations is whether these computations are optimal. The results from my model suggest that they are probably suboptimal when realized in the brain due to the following reasons:
1. Limited resources: Figure 5.6 shows that the neural model provides a better match to the human predictions than an ideal Bayesian model byGriffiths and Tenenbaum
(2006). This is due to fitting of the neural tuning curves in the neural populations. Given a large number of neurons, the neural model is able to replicate the ideal Bayesian results. Thus, I predict that the suboptimal performance results from limited neural resources in the brain.
2. Improperly learned beliefs: Second source of sub-optimality is the prior when used during the learning phase. If the predictions are obtained from the neural model using the incompletely learned priors, that introduces another source of error in the predictions. In this case, the predictions won’t provide a good match to the human behavioral data. However, as mentioned in section 6.1, developmental studies might provide human data that can be fairly compared to the neural model predictions during the learning phase.
3. Approximate computations: Third source of sub-optimality is the dimensionality reduction of probability distributions for their efficient representation in neural pop- ulations. Though figure 5.5shows that the low-dimensional embedding doesn’t cause any error in the life span inference task, I expect that it can be a source of error if the distributions to be represented are more complex.
One can only claim that the brain is Bayesian if one believes that a “general-purpose theory of cognition” exists. However, given that our brain is arguably the most complex machine known to us as of today, and given our limited understanding of it, it is yet to be determined whether the goal of finding such a general-purpose theory to explain the brain even makes sense. Nonetheless, calling the brain Bayesian would require answering many foundational questions: How well can Bayesian theories account for irrationality in human cognition? Does the brain actually use Bayesian rules? Does it do so optimally or through approximate descriptions? Do Bayesian theories require an implausibly uniform view of
the mind? What kind of prior knowledge do we bring to bear on a particular learning or inference task? How does that knowledge interact with the examples we observe to guide our generalizations?
I haven’t attempted to answer all of these questions and do not intend to make the claim that the brain is Bayesian. However, I believe that that certain computations in the brain may be Bayesian (though probably not optimal), and I have shown their neural plausibility by proposing neural mechanisms for them, and comparing the results to human predictions.
In section 2.1, I mentioned that besides the Bayes’ theorem, the Bayesian Framework has been expanded to include other methods for approximate inference that are out of the scope of this thesis, e.g., variational Bayesian methods and Markov chain Monte Carlo methods. Statisticians commonly use these approximate inference methods to deal with very high dimensional problems, usually at a high computational cost. However, whether these approximate methods are neurally plausible, and whether the human brain employs them, are open questions. In this thesis, I do not make any claims about the neural plausibility of these methods.
Furthermore, I do not claim that humans are rational. There is a large body of literature on human decision making which suggests that humans do not make decisions according to ‘rational’ rules and do not follow models based on the utility theory (Mongin, 1997). For instance, the Ellsberg paradox (Segal, 1987) explains why most humans don’t take risks and settle for the mediocre i.e., humans exhibit a strong aversion to ambiguity and uncertainty, and have an inherent preference for the known over the unknown. In the face of ambiguity in the probabilities of the outcomes, humans may formulate a vague probability of possible outcomes which may be biased. For example, most humans avoid risk, and many assume that if they are not told the probability of a certain event in a real-life scenario,
it is to deceive them. This and other assumptions may affect their decisions, and hence their decisions may not follow models based on classical probability. Thus, I suggest that the probability distributions that humans represent may not always be accurate i.e., they may be biased. However in this thesis, I have given a neurally plausible account of how humans may represent probability distributions, regardless of whether these probabilities are accurate or biased, and how these representations can be used in meaningful ways to perform inference in a human-like way (which may not be optimal).