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ベイズ統計学 | マサムネの部屋

ベイズ統計学

ベイズ関連の記事を置いてます。

ベイズ統計学

特徴量選択の話

機械学習において、特徴量エンジニアリングは、モデルを選ぶのと同じくらい重要な作業です。既にある特徴量の中から、いらないモノを捨てる手法を紹介します。主に、統計学の力を使う手法の紹介です。
ベイズ統計学

ベイズ主成分分析の話

次元の大きなデータの次元を圧縮する方法の一つに、主成分分析があります。確率論的に主成分分析を行う方法があり、同様にベイズ流に行う方法もあります。この記事では、簡単なモデルで、パラメーターの推定式を計算します。
Python R

PPCAで画像を圧縮してみる

確率論的主成分分析(PPCA)という手法があります。隠れ変数によってデータが生成されているモデルを考えて、小さな次元のデータから、元のデータを再現したり、似たデータを得る手法です。結果をまとめて、pythonで実装してみます。
ベイズ統計学

確率論的主成分分析(PPCA)の話

主成分分析(PCA))を、確率論的に行う事が出来ます。普通のPCAはデータの次元を削減したり。クラスタリングしたり出来ます。一方、確率論的主成分分析(PPCA)は、次元を削減するだけでなく、データを生成する事も出来ます。議論の流れと、パラメーターの決定方法を解説します。
ベイズ統計学

ベイズの定理の応用(検査ロボットの能力を測る)

ベイズの定理の現実への応用の記事です。モデルを二項分布として、パラメーターの事前分布にベータ分布を仮定すると、事後分布もベータ分布になる事を示します。その結果を使って、現実の問題への応用を考えます。
ベイズ統計学

東京都のコロナウイルス感染者は実は沢山いる?志村けんさんの感染から推定!

東京都の発表によると、2020年3月25日時点では、コロナウイルスへの感染者は200人程度だった。芸能人の志村けんさんが感染したという事で、本当の感染者はもっといるんじゃないかというtweetが回ってきたので確率論で検証した。
ベイズ統計学

ラプラス近似とベイズロジスティック回帰

ラプラス近似の説明をし、簡単な応用としてベイズ流のロジスティック回帰を定式化します。ついでにロジスティック回帰の説明もします。pythonでベイズロジスティック回帰を実装して、irisデータで試してみます。
Python R

ベイズ統計学でブログのアクセス数を解析する

ブログを始めて4か月くらい経ちました。 最初の1週間はTwitterでフォローしてくれた人が見るだけと言うサイトでしたが、現在は検索エンジンから殆どのユーザーがブログを見てくれています。なんとなく、あるタイミングからアクセス数が増えたな~...
Python R

変分推論をpythonで実装する

ポアソン混合モデルを変分推論で近似するクラスをpython で実装します。ELBOを監視して、計算を早めに止めるEMアルゴリズムちっくな手法も実装します。
ベイズ統計学

変分推論入門

ベイズ統計学に、変分推論という技があります。この技はEMアルゴリズムを知っていると分かりやすくなります。原理を解説し、ポアソン混合モデルに対して変分推論を適用します。 変分推論 未知の確率分布\(p\)があるとしましょう。この...
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