Quantum-Like Sampling

Andreas Wichert
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Andreas Wichert: Department of Informatics, INESC-ID/IST-University of Lisboa, 1000-029 Lisboa, Portugal

Mathematics, 2021, vol. 9, issue 17, 1-11

Abstract: Probability theory is built around Kolmogorov’s axioms. To each event, a numerical degree of belief between 0 and 1 is assigned, which provides a way of summarizing the uncertainty. Kolmogorov’s probabilities of events are added, the sum of all possible events is one. The numerical degrees of belief can be estimated from a sample by its true fraction. The frequency of an event in a sample is counted and normalized resulting in a linear relation. We introduce quantum-like sampling. The resulting Kolmogorov’s probabilities are in a sigmoid relation. The sigmoid relation offers a better importability since it induces the bell-shaped distribution, it leads also to less uncertainty when computing the Shannon’s entropy. Additionally, we conducted 100 empirical experiments by quantum-like sampling 100 times a random training sets and validation sets out of the Titanic data set using the Naïve Bayes classifier. In the mean the accuracy increased from 78.84 % to 79.46 % .

Keywords: quantum probabilities; sampling; quantum cognition; naïve bayes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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