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Indeterminate Probability Theory

arXiv 2303.11536 ↗First posted 21 Mar 2023cs.LG cs.AI cs.CVcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 16 of its 48 references that are in the map. First posted on arXiv 21 Mar 2023.

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References · 16

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4 more
  1. 2017Recent Advances in Zero-shot Recognitioncited by 28
  2. 2022Sparse Probabilistic Circuits via Pruning and Growingcited by 17
  3. 2018A Tutorial on Deep Latent Variable Models of Natural Languagecited by 10
  4. 2018Effectiveness of Hierarchical Softmax in Large Scale Classification Taskscited by 8

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