【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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