[prml] パターン認識と機械学習（第1章：序論）
TRANSCRIPT
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1
1
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2
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3
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1.1 1.2
1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.6
1.3 1.4
4
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1.5
1.5.1 1.5.2 1.5.3 1.5.4 1.5.5
1.6 1.6.1
5
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1.1
6
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y(x,w)x = (x , ...,x )
y(x,w) = w x
M :
wM
1 nT
j=0
M
jj
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wy(x,w)
ex.
E w = y(x ,w) t
0
( )21
n=1
N
( n n)
8
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9
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w = y(x ,w) t + w
...1.3
E~( )
21
n=1
N
( n n) 2 2
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1.2
p(B)
FB
p(BF )
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p(X) = p(X,Y )
p X,Y = p(Y X)p(X)
Y
( )
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DH
p HD =
( )p(D)
p DH p(H)( )
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1.2.1 x (x,x+ x) p(x) 0 p(x)x p(x)
p(x (a, b)) = p(x)dx
2
p(x) 0
p(x)dx = 1
a
b
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P (x) = p(x)dx
x
z
15
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1.2.2
f(x)p(x)
E[f ] = p(x)f(x)dx
f(x)E[f(x)]
var[f ] = E (f(x) E[f(x)])
[ 2]
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1.2.3
wD
Dw
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22
1 2
30 20
10 20
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P H D =
P H D 1
P DH 1
P (H ) 1
P (D)
( 1 )P (D)
P DH P (H )( 1) 1
( 1 )
( 1)
1
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11
1
0.5 0.75 0.600
2
0.5 0.5 0.400
P (H D) = 0.6
0.50.75+0.50.51
0.50.75+0.50.51
1
20
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2n n+ 1
1
0.6 0.75 0.692
2
0.4 0.5 0.308
P (H D) = 0.692
0.60.75+0.40.51
0.60.75+0.40.51
1
21
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1.2.4
N (x, ) = exp (x )
:https://ja.wikipedia.org/wiki/
2
(2 )2 21
1 (221 2)
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https://ja.wikipedia.org/wiki/%E6%AD%A3%E8%A6%8F%E5%88%86%E5%B8%83
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N (x, ) > 0, N (x, )dx = 1
E[x] = , var[x] =
2
2
2
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0
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p(x, ) = N (x , )
2
n=1
N
n2
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ln p(x, ) = (x ) ln ln(2)2221
n=1
N
n2
2N 2
2N
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0
= x
= (x )
MLN
1
n=1
N
n
2
ML2
N
1
n=1
N
n ML
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1.2.5 = y(x,w) t
p(tx,w,) = N ty(x,w),
p(tx,w,) = N t y(x ,w),
w ,
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( 1)
n=1N ( n n 1)
ML ML
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w
p(w) = N (w0, I)
: , I:
w
p(wx, t,,) p(tx,w,)p(w)
1
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MAPw
y(x ,w) t + w w2
n=1
N
{ n n}2 2
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1.2.6 w
To Be Continue;
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1.3 1LOO: Leaveoneoutmethod
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1.3 1
AIC: Akaike information criterionBayesian information criterion
w
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1.4 DMD
ex.
y(x,w) = w + w x + w x x
M
0
i=1
D
i i
i=1
D
j=1
D
ij i j
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1.5 t
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1.5.1 K
p(true) = p(x,C )dxk=1
K
Rk
k
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1.5.2
E(L) = L p(c x)
L
k
kj k
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1.5.3 p(x,C )
p(C x)x
k
k
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1.5.4
http://s0sem0y.hatenablog.com/entry/2017/06/08/010513
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http://s0sem0y.hatenablog.com/entry/2017/06/08/010513
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xf(w,x)
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GAN
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1.6 x
H[x] = p(x) log p(x)
to be continue
x
2
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