图 书 馆
Recent Advances in Bayesian MethodsRecent Advances in Bayesian Methods |
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| 课程网址: | http://videolectures.net/acml2013_zhu_bayesian_methods/ |
| 主讲教师: | Jun Zhu |
| 开课单位: | 清华大学 |
| 开课时间: | 2014-03-27 |
| 课程语种: | 英语 |
| 中文简介: |  今年是贝叶斯定理250周年，它在统计应用中发挥着越来越重要的作用。现有的贝叶斯模型，尤其是非参数贝叶斯方法，在很大程度上依赖于专门构思的先验，以结合领域知识来发现改进的潜在表示。尽管先验可以通过贝叶斯定理影响后验分布，但最近的研究表明，施加后验正则化可以说更直接，在某些情况下可以更自然，更容易。本教程将包括两个部分。首先，我将回顾参数化和非参数贝叶斯方法的最新发展，并举例说明用于回归的高斯过程，用于聚类的Dirichlet过程以及用于潜在特征学习的Indian Buffet过程。在第二部分中，我将介绍贝叶斯定理和相对熵最小化原理之间的联系。特别是，我将介绍正则化贝叶斯推理（RegBayes），这是一种计算框架，用于对所需的后置数据后验分布进行正则化并进行后验推理。当由线性算子对后验分布进行凸正则化时，RegBayes可以用凸分析理论求解。此外，我将提供一些具体示例，包括MedLDA，用于学习区分性主题表示；无限潜在支持向量机，用于学习区分性潜在特征进行分类；所有这些模型都结合（非参数）贝叶斯模型探索了大余量思想，以发现预测性潜在表示。我将讨论变分方法和蒙特卡洛方法进行推理。 |
| 课程简介: | This year marks the 250th Anniversary of Bayes’ theorem, which is playing an increasingly important role in statistical applications. Existing Bayesian models, especially nonparametric Bayesian methods, rely heavily on specially conceived priors to incorporate domain knowledge for discovering improved latent representations. While priors can affect posterior distributions through Bayes' theorem, recent work has shown that imposing posterior regularization is arguably more direct and in some cases can be more natural and easier. This tutorial will consist of two parts. First, I will review the recent developments of parametric and nonparametric Bayesian methods, with examples of Gaussian processes for regression, Dirichlet processes for clustering, and Indian buffet processes for latent feature learning. In the second part, I will introduce the connections between Bayes’ theorem and the principle of relative entropy minimization. In particular, I will introduce regularized Bayesian inference (RegBayes), a computational framework to perform posterior inference with regularization on the desired post-data posterior distributions. When the convex regularization is induced from a linear operator on the posterior distributions, RegBayes can be solved with convex analysis theory. Furthermore, I will present some concrete examples, including MedLDA for learning discriminative topic representations; infinite latent support vector machines for learning discriminative latent features for classification; and others on social network analysis, matrix factorization, multi-task learning, etc. All these models explore the large-margin idea in combination with a (nonparametric) Bayesian model for discovering predictive latent representations. I will discuss both variational and Monte Carlo methods for inference. |
| 关 键 词: | 贝叶斯定理; 线性算子 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2020-11-16：zyk |
| 最后编审: | 2020-11-16：zyk |
| 阅读次数: | 26 |