【0】涉及到的各种符号

Notation List

∀ ∃ ⊆ 包含 ⊂(或⫋) 真包含 另外,还有相应的⊄,⊈,⊉等 ∪ 集合的并运算 U(P)表示P的领域 ∩ 集合的交运算 -或\ 集合的差运算 ⊕集合的对称差运算

符号 含义
V (没搞懂怎么写) a calligraphic symbol typically denotes a set of random variables
dom(x) Domain of a variable
x=x (没搞懂怎么写) The variable x is in the state x
p(x = tr) probability of event/variable x being in the state true
p(x = fa) probability of event/variable x being in the state false
p(x, y) probability of x and y
p(x∩y) probability of x and y
p(x∪y) probability of x or y
p(x|y) y的情况下,x发生的概率
X ∐ Y|Z 在Z的条件下,X和Y独立
X ∏ Y|Z 在Z的条件下,X和Y不独立
∫x(x) continuous variables this is shorthand for ∫f(x)dx and for discrete variables means summation over the states of x, ∑xf(x)
II[S] Indicator : has value 1 if the statement S is true, 0 otherwise
pa (x) The parents of node x
ch (x) The children of node x
ne (x) Neighbours of node x
dim (x) For a discrete variable x, this denotes the number of states x can take
⟨f (x)⟩p(x) The average of the function f(x) with respect to the distribution p(x)
δ(a, b) Delta function. For discrete a, b, this is the Kronecker delta, δa,b and for continuous a, b the Dirac delta function δ(a − b)
dim x The dimension of the vector/matrix x
♯ (x = s, y = t) The number of times x is in state s and y in state t simultaneously
xy The number of times variable x is in state y
D Dataset
n Data index
N Number of dataset training points
S Sample Covariance matrix
σ(x) The logistic sigmoid 1/(1 + exp(−x))
erf(x) The (Gaussian) error function
xa:b xa,xa+1,…,xb ……………………………..
i∼j The set of unique neighbouring edges on a graph
Im The m×m identity matrix
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