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From Bayesian Inference to Logical Bayesian Inference

Abstract : Bayesian Inference (BI) uses the Bayes’ posterior whereas Logical Bayesian Inference (LBI) uses the truth function or membership function as the inference tool. LBI is proposed because BI is not compatible with the classical Bayes’ prediction and does not use logical probability and hence cannot express semantic meaning. In LBI, statistical probability and logical probability are strictly distinguished, used at the same time, and linked by the third kind of Bayes’ Theorem. The Shannon channel consists of a set of transition probability functions whereas the semantic channel consists of a set of truth functions. When a sample is large enough, we can directly derive the semantic channel from Shannon’s channel. Otherwise, we can use parameters to construct truth functions and use the Maximum Semantic Information (MSI) criterion to optimize the truth functions. The MSI criterion is equivalent to the Maximum Likelihood (ML) criterion, and compatible with the Regularized Least Square (RLS) criterion. By matching the two channels one with another, we can obtain the Channels’ Matching (CM) algorithm. This algorithm can improve multi-label classifications, maximum likelihood estimations (including unseen instance classifications), and mixture models. In comparison with BI, LBI (1) uses the prior P(X) of X instead of that of Y or θ and fits cases where the source P(X) changes, (2) can be used to solve the denotations of labels, and (3) is more compatible with the classical Bayes’ prediction and likelihood method. LBI also provides a confirmation measure between −1 and 1 for induction.
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https://hal.inria.fr/hal-02118825
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Submitted on : Friday, May 3, 2019 - 1:26:27 PM
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Chenguang Lu. From Bayesian Inference to Logical Bayesian Inference. 2nd International Conference on Intelligence Science (ICIS), Nov 2018, Beijing, China. pp.11-23, ⟨10.1007/978-3-030-01313-4_2⟩. ⟨hal-02118825⟩

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