Local Mixture Model in Hilbert Space

Mixture Models;Differential Geometry;Convex Geometry;Hilbert Space;Statistics

Zhiyue, Huang

University of Waterloo

关键词: Mixture Models;    Differential Geometry;    Convex Geometry;    Hilbert Space;    Statistics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/5007/1/Huang_Zhiyue.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

In this thesis, we study local mixture models with a Hilbert space structure. First, we consider the fibre bundle structure of local mixture models in a Hilbert space. Next, the spectral decomposition is introduced in order to construct local mixture models. We analyzethe approximation error asymptotically in the Hilbert space. After that, we will discuss the convexity structure of local mixture models. There are two forms of convexity conditions to consider,first due to positivity in the $-1$-affine structure and the second by points having to lie inside the convex hull of a parametricfamily. It is shown that the set of mixture densities is located inside the intersection of the sets defined by these two convexities. Finally, we discuss the impact ofthe approximation error in the Hilbert space when the domain of mixing variablechanges.