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具有高斯过程强度的泊松过程中的可跟踪非参数贝叶斯推断
Tractable Nonparametric Bayesian Inference in Poisson Processes with Gaussian Process Intensities |
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| 课程网址: |
http://videolectures.net/icml09_adams_tnbi/
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| 主讲教师: |
Ryan Prescott Adams
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| 开课单位: |
多伦多大学
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| 开课时间: |
2009-08-26
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| 课程语种: |
英语
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| 中文简介: |
非均匀泊松过程是一个点过程，其整个域（通常是时间或空间）具有不同的强度。对于非参数贝叶斯建模，高斯过程是一种在此强度上进行先验分布的有用方法。泊松过程和GP的组合被称为高斯Cox过程或双随机泊松过程。在这些模型中基于似然的推断需要在无限维随机函数上的难以求的积分。在本文中，我们提出了高斯Cox过程的第一种方法，其中可以在不引入近似或有限维代理分布的情况下执行推理。我们称我们的方法为Sigmoidal Gaussian Cox过程，该过程使用泊松数据的生成模型通过马尔可夫链蒙特卡罗实现易处理的推理。我们将我们的方法与合成数据的竞争方法进行比较，并将其应用于几个真实世界的数据集。
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| 课程简介: |
The inhomogeneous Poisson process is a point process that has varying intensity across its domain (usually time or space). For nonparametric Bayesian modeling, the Gaussian process is a useful way to place a prior distribution on this intensity. The combination of an Poisson process and GP is known as a Gaussian Cox process, or doubly-stochastic Poisson process. Likelihood-based inference in these models requires an intractable integral over an infinite-dimensional random function. In this paper we present the first approach to Gaussian Cox processes in which it is possible to perform inference without introducing approximations or finite-dimensional proxy distributions. We call our method the Sigmoidal Gaussian Cox Process, which uses a generative model for Poisson data to enable tractable inference via Markov chain Monte Carlo. We compare our methods to competing methods on synthetic data and also apply it to several real-world data sets.
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| 关 键 词: |
非均匀泊松过程; 非参数贝叶斯; 无限维随机函数
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| 课程来源: |
视频讲座网
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| 最后编审: |
2019-04-21：lxf
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| 阅读次数: |
99
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