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通过分层核学习进行高维非线性变量选择

High-Dimensional Non-Linear Variable Selection through Hierarchical Kernel Learning
课程网址: http://videolectures.net/smls09_bach_hdnlv/  
主讲教师: Francis R. Bach
开课单位: INRIA研究机构
开课时间: 2009-05-06
课程语种: 英语
中文简介:
我们考虑了用于监督学习的高维非线性变量选择问题。我们的方法是基于在特征或正定核的数个定义明确的特征组之间执行线性选择,这些特征描述了原始变量之间的非线性相互作用。为了有效地从众多内核中进行选择,我们使用内核的自然分层结构将多内核学习框架扩展到可以嵌入有向无环图的内核。我们表明,然后可以通过多项式适应稀疏性归纳图的图形,在多项式时间内选择核的数量来执行核选择。此外,我们研究了高维环境中变量选择的一致性,表明在某些假设下,我们的正则化框架允许使用许多不相关的变量,这些变量在观察次数中次幂。
课程简介: We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many well-defined groups of features or positive definite kernels, that characterize non-linear interactions between the original variables. To select efficiently from these many kernels, we use the natural hierarchical structure of the kernels to extend the multiple kernel learning framework to kernels that can be embedded in a directed acyclic graph; we show that it is then possible to perform kernel selection through a graph-adapted sparsity-inducing norm, in polynomial time in the number of selected kernels. Moreover, we study the consistency of variable selection in high-dimensional settings, showing that under certain assumptions, our regularization framework allows a number of irrelevant variables which is sub-exponential in the number of observations.
关 键 词: 监督学习; 非线性变量; 自然分层结构
课程来源: 视频讲座网
最后编审: 2021-03-01:yumf
阅读次数: 51