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ゼロから作るDeep Learning ❺ ―生成モデル編
book

ゼロから作るDeep Learning ❺ ―生成モデル編

by 斎藤 康毅
April 2024
Intermediate to advanced
336 pages
3h 27m
Japanese
O'Reilly Japan, Inc.
Content preview from ゼロから作るDeep Learning ❺ ―生成モデル編

付録C階層型VAEの理論と実装✪

ここでは「階層型VAE」について説明します。ただし単純さを優先して、図C-1で表される2階層の潜在変数に限定して話を進めます。

2階層VAEのモデル図

図C-1 2階層VAEのモデル図

[注記]

以降の議論は潜在変数がT個の場合でも流れは同じです。興味のある方は、潜在変数の数をTとして、以降の数式を展開してみましょう。

C.1 2階層VAEの構成要素

図C-1の2階層VAEは、単純なVAEの場合と学習方法は同じです。どちらのケースもELBOを目的関数とします。復習になりますが、VAEのELBOは次の式で表されます。

2階層VAEのELBOは、上の式のにを代入することで得られます。数式では次のように表されます。

上の式のELBOには2つの確率分布——と——が登場します。それらは階層型VAEの確率の乗法定理とマルコフ性により、次のように分解して表すことができます。 ...

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Publisher Resources

ISBN: 9784814400591Publisher Website