Variational Bayesian Learning Theory
Variational Bayesian Learning Theory
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DOI：
10.1017/9781139879354
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发表时间：
2019-06
期刊：
影响因子：
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通讯作者：
Shinichi Nakajima;Kazuho Watanabe;Masashi Sugiyama
中科院分区：
文献类型：
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作者：
Shinichi Nakajima;Kazuho Watanabe;Masashi Sugiyama
变分贝叶斯学习是机器学习中最流行的方法之一。专为研究人员和研究生在机器学习，这本书总结了最近的发展，在非渐近和渐近理论的变分贝叶斯学习，并建议如何将这一理论应用于实践。作者开始通过开发一个基本框架，重点是共轭，这使读者能够推导出易处理的算法。其次，它总结了非渐近理论，虽然在双线性模型中的应用有限，精确地描述了变分贝叶斯解的行为，并揭示了其稀疏性诱导机制。最后，本文总结了渐近理论，该理论揭示了依赖于先验设置的相变现象，从而提供了如何为特定目的设置超参数的建议。详细的推导允许读者在没有贝叶斯学习特定数学技术的先验知识的情况下沿着进行。
Variational Bayesian learning is one of the most popular methods in machine learning. Designed for researchers and graduate students in machine learning, this book summarizes recent developments in the non-asymptotic and asymptotic theory of variational Bayesian learning and suggests how this theory can be applied in practice. The authors begin by developing a basic framework with a focus on conjugacy, which enables the reader to derive tractable algorithms. Next, it summarizes non-asymptotic theory, which, although limited in application to bilinear models, precisely describes the behavior of the variational Bayesian solution and reveals its sparsity inducing mechanism. Finally, the text summarizes asymptotic theory, which reveals phase transition phenomena depending on the prior setting, thus providing suggestions on how to set hyperparameters for particular purposes. Detailed derivations allow readers to follow along without prior knowledge of the mathematical techniques specific to Bayesian learning.