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This paper explores the application of quantum probability frameworks to statistical settings and machine learning, specifically proposing a model reduction technique inspired by partial least squares regression. The author argues that postulates from quantum foundations can provide valid Bayesian priors for certain experiments, bridging theoretical quantum mechanics with practical statistical inference. While it touches on machine learning, the core contribution lies in advancing quantum probability theory and its foundational arguments rather than introducing a new AI product or policy.
Quantum probability for statisticians; some new ideas
arXiv:2503.02658v4 Announce Type: replace Abstract: It is argued from several points of view that quantum probabilities might play a role in statistical settings. New approaches toward quantum foundations have postulates that appear to be equally valid in macroscopic settings. One such approach is described here in detail, while one other is briefly sketched. In particular, arguments behind the Born rule, which gives the basis for quantum probabilities, are given. A list of ideas for possible statistical applications of quantum probabilities is provided and discussed. A particular area is machine learning, where there exists substantial literature on links to quantum probability. Here, an idea about model reduction is sketched and is motivated from a quantum probability model. Quantum models can play a role in model reduction, where the partial least squares regression model is a special case. It is shown that for certain experiments, a Bayesian prior given by a quantum probability can be motivated. Quantum decision theory is an emerging discipline that can be motivated by this author's theory of quantum foundations.
Abstract:It is argued from several points of view that quantum probabilities might play a role in statistical settings. New approaches toward quantum foundations have postulates that appear to be equally valid in macroscopic settings. One such approach is described here in detail, while one other is briefly sketched. In particular, arguments behind the Born rule, which gives the basis for quantum probabilities, are given. A list of ideas for possible statistical applications of quantum probabilities is provided and discussed. A particular area is machine learning, where there exists substantial literature on links to quantum probability. Here, an idea about model reduction is sketched and is motivated from a quantum probability model. Quantum models can play a role in model reduction, where the partial least squares regression model is a special case. It is shown that for certain experiments, a Bayesian prior given by a quantum probability can be motivated. Quantum decision theory is an emerging discipline that can be motivated by this author's theory of quantum foundations.
arXiv:2503.02658 [quant-ph]
(or arXiv:2503.02658v4 [quant-ph] for this version)
From: Inge S. Helland [view email] [v1] Tue, 4 Mar 2025 14:18:49 UTC (28 KB) [v2] Thu, 27 Mar 2025 11:37:45 UTC (28 KB) [v3] Wed, 25 Jun 2025 13:32:47 UTC (29 KB) [v4] Wed, 7 Oct 2026 07:34:05 UTC (27 KB)
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