دانلود رایگان مقاله انگلیسی آیا شبکه های بیزی کوانتومی قوی تر از شبکه های بیزی کلاسیک هستند؟ - الزویر 2018

abstract

Recent works in the literature have proposed quantum-like Bayesian networks as an alternative decision model to make predictions in scenarios with high levels of uncertainty. Despite its promising capabilities, there is still some resistance in the literature concerning the advantages of these quantum-like models towards classical ones. In this work, we developed a Classical Latent Bayesian network model and we compared it against its quantum counterpart: the quantum-like Bayesian network. The comparison was done using a well known Prisoner’s Dilemma game experiment from Shafir and Tversky (1992), in which the classical axioms of probability theory are violated during a decision, and consequently the game cannot be simulated by pure classical models. In the end, we concluded that it is possible to simulate these violations using the Classical Latent Variable model, but with an exponential increase in its complexity. Moreover, this classical model cannot predict both observed and unobserved conditions from Shafir and Tversky (1992) experiments. The quantum-like model, on the other hand, is shown to be able to accommodate both situations for observed and unobserved events in a single model, making it more suitable and more general for these types of decision problems.

7. Conclusion

The application of quantum principles to model decisionmaking scenarios emerged in the scientific literature as a way to explain and understand human behaviour in situations with high levels of uncertainty that lead to the violation of the classical laws of probability theory and logic. However, many researchers are still resistant in accepting the promising advantages of these quantumlike models towards modelling decision-making scenarios. Many times it is argued that classical models can simulate these decision scenarios under high levels of uncertainty adding extra variables to the model that are not directly observed through data. That is, by including extra latent (or hidden) variables it was believed that the model could represent uncertainty in the same way as in a quantum-like model, despite the complexity of the classical model.

In this work, we study this classical conception and make a mathematical comparison between a classical Bayesian network with Latent variables with the quantum-like Bayesian network previously proposed in the work of Moreira and Wichert (2016a). Latent Variables can be defined as variables that are not directly observed from data, but they can be inferred using the information of the variables that were recorded. For a complete dataset and given the full network structure, latent variables can be estimated by simply counting how many times they can be inferred from each assignment of the observed random variables.