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文件名称:Riemannian Geometry and Statistical Machine Learning
文件大小:3.28MB
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更新时间:2013-12-01 15:30:52
Riemannian Geometry Statistical Machine Learning
Statistical machine learning algorithms deal with the problem of selecting an appropriate
statistical model from a model space based on a training set {xi}N
i=1 ⊂ X or {(xi, yi)}N
i=1 ⊂ X × Y. In doing so they either implicitly or explicitly make assumptions on the geometries
of the model space and the data space X. Such assumptions are crucial to the success of
the algorithms as different geometries are appropriate for different models and data spaces.
By studying these assumptions we are able to develop new theoretical results that enhance our
understanding of several popular learning algorithms. Furthermore, using geometrical reasoning
we are able to adapt existing algorithms such as radial basis kernels and linear margin classifiers
to non-Euclidean geometries. Such adaptation is shown to be useful when the data space does
not exhibit Euclidean geometry. In particular, we focus in our experiments on the space of text
documents that is naturally associated with the Fisher information metric on corresponding
multinomial models.
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- 这是一篇CMU学生的博士论文。将统计学习和黎曼几何联系起来,想法比较新