The goal of this lecture note is to review the problem of free energy minimization as a unified framework underlying the definition of maximum entropy modeling, generalized Bayesian inference, learning with latent variables, the 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 applications to modeling, inference, learning, and optimization are covered, starting from basic principles.

中文翻译：

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自由能源的最小化：建模，推理，学习和优化的统一框架[讲义]

本讲义的目的是将自由能最小化问题作为一个统一的框架进行回顾，该框架以最大熵建模，广义贝叶斯推断，潜变量学习，泛化的统计学习分析和局部优化为基础。在这里和历史上，首先将自由能最小化作为热力学原理进行了介绍。然后，在芬切尔对偶性的上下文中对其进行数学描述。最后，从基本原理开始，介绍了建模，推理，学习和优化的应用程序。