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第8回 Dirichlet分布のパラメータ推定

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Avatar for Taichi Aida Taichi Aida
February 27, 2019

 第8回 Dirichlet分布のパラメータ推定

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Taichi Aida

February 27, 2019
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  1. 9 2 8B D 3 0( ) / 1 

        
  2.  h o~ _a c eW l ypf iv u

    _a c eW l ypf iv j / H : C dbR s , MMM C 8H 8 A H : C 08 8 2 68CC8: /8L 2 D - H M 2:.8CC D 5 1/-, 6 N 4H H 28 H , H : C M8CC8: H w t iv , MMM : 98 H8 8: A P M8 8 1 : 3- 8 k r mk j zng , MMM 8 : 8: A 8 8 2 A :
  3.   ! " #$ % • &$,( " )

    &$,( ~Multi(123,456 ) • 8$,( " ) 8$,( ~Multi(9$ ) • 16 8$,( = ; 16 ~Dir(>) • 9$ " 9$ ~Dir(?) • ? > 2 5
  4.   ! " #$ % • &$,( " )

    &$,( ~Multi(123,456 ) • 8$,( " ) 8$,( ~Multi(9$ ) • 16 8$,( = ; 16 ~Dir(>) • 9$ " 9$ ~Dir(?) • ? > 2 6
  5.   • !(#, %, &|(, ), *) 2 •

    2 • 2 • 1 • 1 •
  6.  • K !(#, %, &|(, ), *) ), *

    1 ,(#, %, &) L 2 2 -.[,(#, %, &)||! #, %, & (, ), * ] → 234 2 K 5 . log !((|), *)
  7.  L 5 !, # 7 54 $[&((, ), *|!,

    #)] !, # . 4 .$[&((, ), *|!, #)] .! = 0, .$[&((, ), *|!, #)] .# = 0 • .1 • • D A D
  8.    • ! " = 0 8 "

    = %(") 5] . "( 8 ")*+ = % ") , - = 0,1,2, …2 81 • . [ . 3
  9.   • ] ! " = 0 D "%D

    A ! " "& 1 ]y = ! "& ]D 3 ] D"&() 5A L 9 • 2 A . 9A [2 A