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Quantum-Like Sampling

Author

Listed:
  • Andreas Wichert

    (Department of Informatics, INESC-ID/IST-University of Lisboa, 1000-029 Lisboa, Portugal)

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 % .

Suggested Citation

  • Andreas Wichert, 2021. "Quantum-Like Sampling," Mathematics, MDPI, vol. 9(17), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2036-:d:621012
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    References listed on IDEAS

    as
    1. Jérôme Busemeyer & Ariane Lambert-Mogiliansky & Zheng Wang, 2009. "Empirical Comparison of Markov and Quantum models of decision-making," PSE-Ecole d'économie de Paris (Postprint) halshs-00754332, HAL.
    2. V. Yukalov & D. Sornette, 2011. "Decision theory with prospect interference and entanglement," Theory and Decision, Springer, vol. 70(3), pages 283-328, March.
    3. Jérôme Busemeyer & Ariane Lambert-Mogiliansky & Zheng Wang, 2009. "Empirical Comparison of Markov and Quantum models of decision-making," Post-Print halshs-00754332, HAL.
    Full references (including those not matched with items on IDEAS)

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