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Hi so I've got this problem for university and I just can't see how I'm supposed to rewrite this expression: $\dfrac{\exp(\mathbf{w^{t}x} + w_{0})}{\exp{(\mathbf{w^{t}x}} + w_{0}) + 1}$ into this: $\dfrac{1}{1 + \exp(-a)}$ where $\textit{a}$ can be any value.

I first tried simplifying the expression which lead to: $1 - \dfrac{1}{1 + \exp(\mathbf{w^tx} + w_{0})}$, this almost looks like what is required, $\textit{a}$ would then obviously be: $-\mathbf{w^{t}x} + w_{0}$. But I don't really know how to get rid of the 1 at the beginning of the resulting expression, nor do I see how I could otherwise rewrite/simplify it.

Any help is appreciated.

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Guide:

  • Divide both the numerator and the denominator by $\exp(w^Tx + w_0)$
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  • $\begingroup$ Thanks for the help, that I did not see that. (I feel dumb :P) $\endgroup$ – PEREZje Dec 8 '18 at 14:18

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