数据增广求解贝叶斯Logistic回归模型的方法研究

Data Augmentation for Bayesian Logistic Models

贝叶斯Logistic回归模型是机器学习中一类被广泛应用的经典模型,然而由于其先验和似然间的非共轭性,Logistic回归模型的贝叶斯推理成为机器学习中的一个重要问题。数据增广方法是一种解决非共轭问题非常有效的方法,该方法通过引入增广变量来发掘模型中的隐藏结构,再通过采样的方法得到模型推理结果。本篇文章实现了两种不同的数据增广算法并通过在多个现实生活数据集上进行试验来对比算法的优越性。

In Machine Learning, Bayesian inference for logistic model is one of the classical model which has been widely used for years, but it has been considering as an intractable problem due to the non-conjugacy between the prior and the logistic likelihood. Data Augmentation is very effective in dealing with non-conjugacy problem, the idea is to introduce auxiliary variables to make the inference tractable conditioned on these variables and thus the data was 'augmented'. Then we can sample from the model to achieve the inference result. In the paper, we implemented two algorithms and check the algorithms under several statistical criterions.