The Variational Bayesian method (VB) is used to solve the probability distributions of latent variables with the minimum free energy criterion. This criterion is not easy to understand, and the computation is complex. For these reasons, this paper proposes the Semantic Variational Bayes' method (SVB). The Semantic Information Theory the author previously proposed extends the rate-distortion function R(D) to the rate-fidelity function R(G), where R is the minimum mutual information for given semantic mutual information G. SVB came from the parameter solution of R(G), where the variational and iterative methods originated from Shannon et al.'s research on the rate-distortion function. The constraint functions SVB uses include likelihood, truth, membership, similarity, and distortion functions. SVB uses the maximum information efficiency (G/R) criterion, including the maximum semantic information criterion for optimizing model parameters and the minimum mutual information criterion for optimizing the Shannon channel. For the same tasks, SVB is computationally simpler than VB. The computational experiments in the paper include 1) using a mixture model as an example to show that the mixture model converges as G/R increases; 2) demonstrating the application of SVB in data compression with a group of error ranges as the constraint; 3) illustrating how the semantic information measure and SVB can be used for maximum entropy control and reinforcement learning in control tasks with given range constraints, providing numerical evidence for balancing control's purposiveness and efficiency. Further research is needed to apply SVB to neural networks and deep learning.

翻译：变分贝叶斯方法（VB）以最小自由能准则求解潜变量的概率分布。该准则不易理解且计算复杂。为此，本文提出语义变分贝叶斯方法（SVB）。作者此前提出的语义信息理论将率失真函数R(D)扩展为率保真函数R(G)，其中R是在给定语义互信息G下的最小互信息。SVB源于R(G)的参数求解，其变分与迭代方法源自Shannon等人对率失真函数的研究。SVB使用的约束函数包括似然函数、真实函数、隶属函数、相似函数与失真函数。SVB采用最大信息效率（G/R）准则，包含优化模型参数的最大语义信息准则与优化香农信道的最小互信息准则。对于相同任务，SVB的计算复杂度低于VB。本文的计算实验包括：1）以混合模型为例，展示混合模型随G/R增大而收敛；2）以一组误差范围作为约束，演示SVB在数据压缩中的应用；3）说明语义信息度量与SVB如何用于给定范围约束下的最大熵控制与强化学习控制任务，为平衡控制的主动性与效率提供数值证据。将SVB应用于神经网络与深度学习仍需进一步研究。