如何选择高斯基函数超参数进行线性回归? [英] How to choose Gaussian basis functions hyperparameters for linear regression?

问题描述

我在机器学习环境中还很陌生，我正在尝试正确地理解一些基础概念.我的问题如下: 我有一组数据观察值和相应的目标值{ x ， t }.我正在尝试使用此数据训练一个函数，以便预测未观察到的数据的值，并且我试图通过使用最大后验(MAP)技术(以及贝叶斯方法)和高斯基础函数来实现此目的:

I'm quite new in machine learning environment, and I'm trying to understand properly some basis concept. My problem is the following: I have a set of data observation and the corresponding target values {x,t}. I'm trying to train a function with this data in order to predict the value of unobserved data and I'm trying to achieve this by using the maximum posterior (MAP) technique (and so Bayesian approach) with Gaussian basis function of the form:

\{Phi}Gaussian_{j}(x)=exp((x−μ_{j})^2/2*sigma_{j}^2)

我该如何选择

1)要使用的基础函数数(M)

1) The number of basis functions to use (M)

2)每个函数的平均值(μ_{j})

2) The mean for every function (μ_{j})

3)每个函数的方差(sigma_ {j})

3) The variance for every function (sigma_{j})

?

推荐答案

文献中有不同的方法.最常见的方法是对输入数据执行无监督的聚类(请参见"EMRBF:使用径向基函数进行过程控制" 和稳健的贝叶斯学习径向基网络" .

There are different approaches to this in the literature. The most common approach is to perform an unsupervised clustering of the input data (see the Netlab toolbox). Some other approaches are described in the papers "EMRBF: A Statistical Basis for Using Radial Basis Functions for Process Control" and "Robust Full Bayesian Learning for Radial Basis Networks".

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