文档介绍：Bayesian Reasoning and Machine Learning
David Barber c 2007,2008,2009,2010,2011,2012
Notation List
a calligraphic symbol typically denotes a set of random variables . . . . . . . . 7
V
dom(x) Domain of a variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
x = x The variable x is in the state x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
p(x = tr) probability of event/variable x being in the state true . . . . . . . . . . . . . . . . . . . 7
p(x = fa) probability of event/variable x being in the state false . . . . . . . . . . . . . . . . . . . 7
p(x, y) probability of x and y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
p(x y) probability of x and y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
∩
p(x y) probability of x or y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
∪
p(x y) The probability of x conditioned on y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
|
Variables are independent of variables conditioned on variables . 11
X ⊥⊥Y|Z X Y Z
Variables are dependent on variables conditioned on variables . . 11
X >>Y|Z X Y Z
R
R For continuous variables this is shorthand for f(x)dx and for discrete vari-
x f(x) P
ables means summation over the states of x, x f(x) . . . . . . . . . . . . . . . . . . 17
I [S] Indicator : has value 1 if the statement S is true, 0 otherwise . . . . . . . . . . 19
pa (x) The parents of node x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
ch (x) The children of node x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
ne (x) Neighbours of node x . . . . . . . . . . . . . . . . . .