自由能最小化：建模、推理、学习和优化的统一框架
Free Energy Minimization: A Unified Framework for Modelling, Inference, Learning,and Optimization
摘要：
这些课堂讲稿的目的是回顾自由能最小化问题，将其作为最大熵建模、广义贝叶斯推理、潜变量学习、泛化的统计学习分析和局部优化定义的统一框架。自由能最小化首先介绍，在这里和历史上，作为一个热力学原理。然后，它被数学描述的背景下，Fenchel对偶。最后，从基本原理开始，涵盖了建模，推理，学习和优化的应用。
英文摘要：
The goal of these lecture notes is to review the problem of free energy minimization as a unified framework underlying the definition of maximum entropy modelling, generalized Bayesian inference, learning with latent variables, statistical learning analysis of generalization,and local optimization. Free energy minimization is first introduced, here and historically, as a thermodynamic principle. Then, it is described mathematically in the context of Fenchel duality. Finally, the mentioned applications to modelling, inference, learning, and optimization are covered starting from basic principles.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
