The St. Petersburg paradox is a centuries-old puzzle concerning a lottery with infinite expected payoff on which people are only willing to pay a small amount to play. Despite many attempts and several proposals, no generally-accepted resolution is yet at hand. In a recent paper, we show that this paradox can be understood in terms of the mind optimally using its limited computational resources (Nobandegani et al. 2019). Specifically, we show that the St. Petersburg paradox can be accounted for by a variant of normative expected-utility valuation which acknowledges cognitive limitations: sample-based expected utility (Nobandegani et al. 2018). SbEU provides a unified, algorithmic explanation of major experimental findings on this paradox. We conclude by discussing the implications of our work for algorithmically understanding human cognition and for developing human-like artificial intelligence.

Deductive logic and its variants enjoy the common property of monotonicity. For tasks such as inductive reasoning and belief revision, this was eventually deemed a serious flaw, prompting attempts to construct non-monotonic versions of logic. With the introduction of the idea of probabilistic reasoning to AI, particularly with the advent of Bayesian networks (BNs), the aforementioned monotonicity was no longer an issue: Probability is inherently non-monotonic. In this work, we introduce the notion of relevance effect which bears on exploiting BNs to generate realizations of relevant variables to be used for potentially improving the performance of a learning model on a supervised classification task. We explore the potential of using the relevance effect in the context of Deep Belief Networks (DBNs) with a focus on relational domains. We show that although the idea is at odds with the non-monotonicity of probabilistic reasoning, we attain an improvement in learning performance in different simulations on both synthetic and real-world scenarios. The observation that adopting this notion has improved the performance of a powerful model like DBNs hints to its potential to be practiced so as to enhance the performance of supervised learning methods in general. We furthermore highlight the connections as well as the implications of our work to the psychology literature.