[英]How do I solve this conditional probabilities problem with MATLAB?
If P( c j | x i ) are already known, where i=1,2,...n; 如果已知P(c j | x i ),则i = 1,2,... n; j=1,2,...k;
J = 1,2,...,K;
How do I calculate/estimate: P( c j | x l , x m , x n ) , where j=1,2,...k; 如何计算/估算: P(c j | x l ,x m ,x n ) ,其中j = 1,2,... k; l,m,n belongs to http://latex.mathoverflow.net/jsMath/fonts/cmsy10/alpha/120/char32.png {1,2,...n} ?
l,m,n 属于http://latex.mathoverflow.net/jsMath/fonts/cmsy10/alpha/120/char32.png {1,2,... n}吗?
EDIT2 (following the OP's comment) EDIT2 (在OP的评论之后)
From bayes rule we know that P(C|x1,x2,x3) ~ P(C)*P(x1,x2,x3|C)
and therefore for classification, you compute that expression for all C=j
and predict the most likely class ( MAP ). 根据贝叶斯规则,我们知道
P(C|x1,x2,x3) ~ P(C)*P(x1,x2,x3|C)
,因此对于分类,您可以针对所有C=j
计算该表达式并预测最大可能的类别( MAP )。
Now to compute P(x1,x2,x3|C)
, for iid observations, this can be written as: P(x1,x2,x3|C) = P(x1|C)*P(x2|C)*P(x3|C)
, which given a parametric model each could be computed easily. 现在要计算
P(x1,x2,x3|C)
,对于iid观测值,可以写成: P(x1,x2,x3|C) = P(x1|C)*P(x2|C)*P(x3|C)
,每个参数模型都可以轻松计算。
What you want to do is not possible without further information or simplifying assumptions. 如果没有更多信息或简化假设,您想做的事情是不可能的。
The conditional probability P(A|B,C) is not (completely/at all :) determined by P(A|B) and P(A|C). 条件概率P(A | B,C)并非(完全/完全:)由P(A | B)和P(A | C)确定。
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