文档介绍：Bayesian Models and Notation
Logistic Regression
• Random (= statistical = stochastic) vari-
able: upper-case letter, . V or X, or
upper-case string, . RAIN
Probability theory as basis for the construction
of classifiers:
• Binary variables: take one of two values,
X = true (abbreviated x) and X = false
• Multivariate probabilistic models (abbreviated ¬x)
• Conjunctions: (X = x) ∧(Y = y) as
• Independence assumptions
X = x, Y = y
• Naive Bayesian classifier • Templates: X, Y means X = x, Y = y, for
any value x, y, . the choice of the values
x and y does not really matter
• Forest-works (FANs)
• X P (X) = P (x) + P (¬x), where X is bi-
• Approximation: logistic regression
Pnary
Joint probability distribution Chain rule
Joint (= multivariate) distribution: Definition of conditional probability distribu-
tion:
P (X1, X2, . . . , Xn)
P (X1, X2, . . . , Xn)
Example of joint probability distribution: P (X1 | X2, . . . , Xn) =
P (X2, . . . , Xn)
P (X1, X2, X3) with:
P (x1, x2, x3) = ⇒ P (X1, X2, . . . , Xn) =
P (X | X , . . . , Xn)P (X , . . . , Xn)
P (¬x1, x2, x3) = 1 2 2
P (x , ¬x , x ) =
1 2 3 Furthermore,
P (x1, x2, ¬x3) =
( ) = 0 3
P ¬x1, ¬x2, x3 . P (X2, . . . , Xn) =
P (x1, ¬x2, ¬x3) = P (X2 | X3, . . . , Xn)P (X3, . . . , Xn)
. . .
P (¬x1, x2, ¬x3) = . . .
P (¬x1, ¬x2, ¬x3