Benutzer:Alexander Brock

aus Wikipedia, der freien Enzyklopädie

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$e^{\ln{x}} = x, \forall x \in \mathbb{R}^{+}$

$\ln ({a \cdot b}) = \ln a + \ln b$

$\ln {a \over b} = \ln a - \ln b$

$P(w_i|C) = {N_{C, i} \over N_C}$

$P(A|B) = {{P(B|A) \cdot P(A)} \over {P(B)}}$

$P(w_1 , w_2 , ... , w_n|C) = P(w_1|C) \cdot P(w_2|C) \cdot ... \cdot P(w_n|C) = {\prod_{k=1}^n {N_{C, k} \over N_C}}$

$P(Spam|w_1 , w_2 , ... , w_n) = \frac{ {\prod_{k=1}^n { {{\color{Red}N_{\text{Spam}, k}}} \over {{\color{Brown}N_{\text{Spam}}}} } } \cdot P(Spam) } { P(w_1 , w_2 , ... , w_n) }$

$P(Ham|w_1 , w_2 , ... , w_n) = \frac{ {\prod_{k=1}^n { {{\color{OliveGreen}N_{\text{Ham}, k}}} \over {{\color{Blue}N_{\text{Ham}}}} } } \cdot P(Ham) } { P(w_1 , w_2 , ... , w_n) }$

$V = \frac{ {\prod_{k=1}^n { {{\color{Red}N_{\text{Spam}, k}}} \over {{\color{Brown}N_{\text{Spam}}}} } } \cdot P(Spam) } { P(w_1 , w_2 , ... , w_n) } \cdot \frac{ {\prod_{k=1}^n { {{\color{Blue}N_{\text{Ham}}}} \over {{\color{OliveGreen}N_{\text{Ham}, k}}} } } \cdot P(w_1 , w_2 , ... , w_n) } { P(Ham) }$

$V = \frac { P(Spam) } { P(Ham) } \cdot {\prod_{k=1}^n { {{\color{Red}N_{\text{Spam}, k}}} \over {{\color{Brown}N_{\text{Spam}}}} } } \cdot {\prod_{k=1}^n { {{\color{Blue}N_{\text{Ham}}}} \over {{\color{OliveGreen}N_{\text{Ham}, k}}} } }$

$V = { {{\color{Brown}N_{\text{Spam}}} \prod_{k=1}^n {{{\color{Red}N_{\text{Spam}, k}} \over {\color{Brown}N_\text{Spam}}}} \over {{\color{Blue}N_\text{Ham}} \prod_{k=1}^n {{\color{OliveGreen}N_{\text{Ham}, k}} \over {\color{Blue}N_\text{Ham}}}}} }$

${ { \prod_{k=1}^n {{{\color{Red}N_{\text{Spam}, k}} \over {\color{Brown}N_\text{Spam}}}} \over { \prod_{k=1}^n {{\color{OliveGreen}N_{\text{Ham}, k}} \over {\color{Blue}N_\text{Ham}}}}} }$

$V = { {{\color{Brown}N_\text{Spam}} \over {\color{Blue}N_\text{Ham}}} { \prod_{k=1}^n { { {\color{Red}N_{\text{Spam}, k}} \over {\color{OliveGreen}N_{\text{Ham}, k}} } } } { \prod_{k=1}^n { { {\color{Blue}N_\text{Ham}} \over {\color{Brown}N_\text{Spam}} } } } } \quad | \ln(...)$

$\ln(V) = { \ln({\color{Brown}N_\text{Spam}})-\ln({\color{Blue}N_\text{Ham}})+ \sum_{k=1}^n { \ln \left( { {\color{Red}N_{\text{Spam}, k}} \over {\color{OliveGreen}N_{\text{Ham}, k}} } \right) } + \sum_{k=1}^n { \ln \left( { {\color{Blue}N_\text{Ham}} \over {\color{Brown}N_\text{Spam}} } \right) } }$

$\ln(V) = { \Bigl( n-1 \Bigr) { \Bigl( \ln( {\color{Blue}N_\text{Ham}} ) -\ln( {\color{Brown}N_\text{Spam}} ) \Bigr) } + \sum_{k=1}^n { \Bigl( \ln( {\color{Red}N_{\text{Spam}, k}} ) -\ln( {\color{OliveGreen}N_{\text{Ham}, k}} ) \Bigr) } }$

$V = \exp \Biggl( { \Bigl( n-1 \Bigr) { \Bigl( \ln( {\color{Blue}N_\text{Ham}} ) -\ln( {\color{Brown}N_\text{Spam}} ) \Bigr) } + \sum_{k=1}^n { \Bigl( \ln( {\color{Red}N_{\text{Spam}, k}} ) -\ln( {\color{OliveGreen}N_{\text{Ham}, k}} ) \Bigr) } \Biggr) }$

$P(Spam) = \exp \bigl( { sum(ln) + (n-1) ( {\color{Blue}ham} - {\color{Brown}spam} ) \bigr) }$

$(n-1) ( \ln( {\color{Blue}N_\text{Ham}} ) -\ln( {\color{Brown}N_\text{Spam}} ) )$

$10 - 1500$

$\ln{N_{Spam, i} \over N_{Ham, i}}$

$s p a m = s p a m + Δ s p a m$

$ln(s p a m + Δ s p a m) - ln e (ln(s p a m) - l n), s p a m = s p a m + n$

Von „http://de.wikipedia.org../../../a/l/e/Benutzer%7EAlexander_Brock_ff30.html“

Benutzer:Alexander Brock

aus Wikipedia, der freien Enzyklopädie

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