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@karino2
Created February 2, 2017 13:41
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{"cells":[{"cell_type":"markdown","metadata":{},"source":["# Fig 8.51のSum Product具体例\n\nPRML 8.4.4の例を通してsum productを具体的に見てみる。"]},{"cell_type":"code","execution_count":1,"metadata":{"collapsed":false},"outputs":[{"data":{"image/jpeg":"/9j/4QC8RXhpZgAATU0AKgAAAAgABgEaAAUAAAABAAAAVgEbAAUAAAABAAAAXgEoAAMAAAABAAIA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object>"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["MeatPieImage()"]},{"cell_type":"markdown","metadata":{},"source":["まずファクターグラフの定義より、このにあるランダム変数の同時確率は、unnormarize measure で以下のように書ける。"]},{"cell_type":"code","execution_count":1,"metadata":{"collapsed":false},"outputs":[{"data":{"image/jpeg":"/9j/4QC8RXhpZgAATU0AKgAAAAgABgEaAAUAAAABAAAAVgEbAAUAAAABAAAAXgEoAAMAAAABAAIA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\nUUUUAf/Z\n","text/plain":["<IPython.core.display.Image object>"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["MeatPieImage()"]},{"cell_type":"markdown","metadata":{},"source":["ここで$x_3$をルートに選んでsum productを実行する場合を考える。"]},{"cell_type":"markdown","metadata":{},"source":["## グラフ関係無く普通に計算する場合\n\n同時確率が分かれば、足し算する事でマージナルは出せる。\n$x_3$のマージナルは、$x_1$, $x_2$, $x_4$で和を取れば良い。\n\nすると求める答えは以下の式になる。"]},{"cell_type":"code","execution_count":1,"metadata":{"collapsed":false},"outputs":[{"data":{"image/jpeg":"/9j/4QC8RXhpZgAATU0AKgAAAAgABgEaAAUAAAABAAAAVgEbAAUAAAABAAAAXgEoAAMAAAABAAIA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\nSpvdBCQx/wAFH/8Ag38+Gf7QP7F/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lnfbHGvLMK9Xr82fCF/b/ET/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object>"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["MeatPieImage()"]},{"cell_type":"markdown","metadata":{},"source":["## sum productを実行してみる\n\n次にsum productで実際に計算して結果が合うか見てみる。 \n$x_3$までの経路を考える。 \nリーフからのメッセージは全て1。"]},{"cell_type":"code","execution_count":1,"metadata":{"collapsed":false},"outputs":[{"data":{"image/jpeg":"/9j/4QC8RXhpZgAATU0AKgAAAAgABgEaAAUAAAABAAAAVgEbAAUAAAABAAAAXgEoAAMAAAABAAIA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\npX4gf8GSv7Q3wg1b9nD4sfsqaf4Pg07xto3ie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yRs3/LOBFQySy4O1BgBnZFYA+n6K/lR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object>"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["MeatPieImage()"]},{"cell_type":"markdown","metadata":{},"source":["ファクターからランダム変数までのメッセージは、8.66に従い、入ってくるメッセージを掛けて、さらに自身のファクターを掛けた物を、入ってくるランダム変数のノードに対して足し合わせる。\n\nこの場合は$f_a$と$f_b$に入ってくるメッセージは1なので、これに自身のファクターを掛けて入ってくるノードの変数で足せば良い。 \n例えば$f_a$は、"]},{"cell_type":"code","execution_count":1,"metadata":{"collapsed":false},"outputs":[{"data":{"image/jpeg":"/9j/4QC8RXhpZgAATU0AKgAAAAgABgEaAAUAAAABAAAAVgEbAAUAAAABAAAAXgEoAAMAAAABAAIA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\nuW6aX5AtpC0TWyPJExmlCIoePYCP0Yr42/4Ls/8ABTG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object>"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["MeatPieImage()"]},{"cell_type":"markdown","metadata":{},"source":["というふうになる。$f_b$も同様。\n\nで、次に$x_2$からのメッセージという事になるが、これは8.69の通り、入ってくるメッセージの単なる積。"]},{"cell_type":"markdown","metadata":{},"source":["こうして端から順番に計算していける。\n順番に計算すると以下。"]},{"cell_type":"code","execution_count":1,"metadata":{"collapsed":false},"outputs":[{"data":{"image/jpeg":"/9j/4QC8RXhpZgAATU0AKgAAAAgABgEaAAUAAAABAAAAVgEbAAUAAAABAAAAXgEoAAMAAAABAAIA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\n8NBjq/xD+IN+1jYRAfxytvigs1wQR51xuYMPlXpXqP8Awct/sof8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N+K/8Aglx/wTA8H+Jv21/jb4i+Ov7TXx0WTxn4O+GSx5u9Mh1OOJrKykWMFrSzHyuqbd5a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\nzo0Z4WhVjyVP3UnKPPGE2uSrKD+KUZOKbV778UMpzShSUaco2bUmtt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object>"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["MeatPieImage()"]},{"cell_type":"markdown","metadata":{},"source":["ここまでで$x_3$のマージナルを求める事は出来た。"]},{"cell_type":"markdown","metadata":{},"source":["## その他のマージナル($x_2$を例に)\n\n次に$x_3$から逆向きのメッセージを計算していく。そして各エッジに結果のメッセージを両方の向きで覚えていく。\n\nそれがひとたび終われば、マージナルの欲しいノードの周辺のメッセージだけ考えればすぐに求めるマージナルが出る。\n\n例えば$x_2$のマージナルが欲しければ、$x_2$の回りのファクターからのメッセージの積で良くて、それは8.86のようになってる。答えもちゃんと普通に求めた場合と同じ式になってる。"]}],"metadata":{"kernelspec":{"display_name":"Python 2","language":"python","name":"python2"},"lanbuage_info":{"codemirror_mode":{"name":"ipython","version":2},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython2","version":"2.7.11"}},"nbformat":4,"nbformat_minor":0}
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