August 2015
Intermediate to advanced
272 pages
5h 46m
Japanese
Content preview from Think Stats 第2版 ―プログラマのための統計入門
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163
163
11.7 パラメータを推定する
11.7
パラメータを推定する
線形回帰と異なり、ロジスティック回帰には閉形式の解がないので、初期の解を推
量して、それを繰り返し改善することで解きます。
普通の目標は、最尤推定（
MLE
、
maximum-likelihood estimate
）、すなわち、デー
タの尤度を最大化するパラメータ集合を見出すことです。例えば、次のようなデータ
があったとします。
>>> y = np.array([0, 1, 0, 1])
>>> x1 = np.array([0, 0, 0, 1])
>>> x2 = np.array([0, 1, 1, 1])
最初の推量を、β
0
＝−
1.5,
β
1
＝
2.8,
β
2
＝
1.1
で始めます。
>>> beta = [-1.5, 2.8, 1.1]
各行について
log_o
を計算します。
>>> log_o = beta[0] + beta[1] * x1 + beta[2] * x2
[-1.5 -0.4 -0.4 2.4]
対数オッズから確率に変換します。
>>> o = np.exp(log_o)
[ 0.223 0.670 0.670 11.02 ]
>>> p = o / (o+1)
[ 0.182 0.401 0.401 0.916 ]
log_o
が
0
より大きいなら、
o
は
1
より大きく、
p
は
0.5
より大きいことに気を付
けてください。
結果の尤度は
y==1
のときに
p
で、
y==0
のときに
1-p
です。例えば、男の子の確率が
0.8
で結果が男の子なら、尤度は ...
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O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.