From Wikipedia, the free encyclopedia
Chain rule may refer to:
d
y
d
x
=
d
y
d
u
⋅
d
u
d
x
.
{\displaystyle {\frac {\mathrm {d} y}{\mathrm {d} x}}={\frac {\mathrm {d} y}{\mathrm {d} u}}\cdot {\frac {\mathrm {d} u}{\mathrm {d} x}}.}
(
∂
x
∂
y
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z
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∂
y
∂
z
)
x
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∂
z
∂
x
)
y
=
−
1.
{\displaystyle \left({\frac {\partial x}{\partial y}}\right)_{z}\left({\frac {\partial y}{\partial z}}\right)_{x}\left({\frac {\partial z}{\partial x}}\right)_{y}=-1.}
P
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X
1
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x
1
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…
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X
n
=
x
n
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=
∏
i
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1
n
P
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X
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=
x
i
∣
X
i
+
1
=
x
i
+
1
,
…
,
X
n
=
x
n
)
{\displaystyle \mathrm {P} (X_{1}=x_{1},\ldots ,X_{n}=x_{n})=\prod _{i=1}^{n}\mathrm {P} (X_{i}=x_{i}\mid X_{i+1}=x_{i+1},\ldots ,X_{n}=x_{n})}
K
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X
,
Y
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=
K
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X
)
+
K
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Y
|
X
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+
O
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log
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K
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X
,
Y
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)
)
{\displaystyle K(X,Y)=K(X)+K(Y|X)+O(\log(K(X,Y)))}
H
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X
,
Y
)
=
H
(
X
)
+
H
(
Y
|
X
)
{\displaystyle H(X,Y)=H(X)+H(Y|X)}
Topics referred to by the same term
