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arXiv · 2303.11536

Indeterminate Probability Theory

Tao Yang·Chuang Liu·Xiaofeng Ma·Weijia Lu·Ning Wu·Bingyang Li·Zhifei Yang·Peng Liu·Lin Sun·Xiaodong Zhang·Can Zhang
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Abstract

Complex continuous or mixed joint distributions (e.g., P(Y | z_1, z_2, ..., z_N)) generally lack closed-form solutions, often necessitating approximations such as MCMC. This paper proposes Indeterminate Probability Theory (IPT), which makes the following contributions: (1) An observer-centered framework in which experimental outcomes are represented as distributions combining ground truth with observation error; (2) The introduction of three independence candidate axioms that enable a two-phase probabilistic inference framework; (3) The derivation of closed-form solutions for arbitrary complex joint distributions under this framework. Both the Indeterminate Probability Neural Network (IPNN) model and the non-neural multivariate time series forecasting application demonstrate IPT's effectiveness in modeling high-dimensional distributions, with successful validation up to 1000 dimensions. Importantly, IPT is consistent with classical probability theory and subsumes the frequentist equation in the limit of vanishing observation error.

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Tao Yang, Chuang Liu, Xiaofeng Ma, Weijia Lu, Ning Wu, Bingyang Li, Zhifei Yang, Peng Liu, Lin Sun, Xiaodong Zhang, Can Zhang. 2023-03-21. Indeterminate Probability Theory. https://arxiv.org/abs/2303.11536

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