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One reason this function might seem more "natural" than others is that it happens to be the inverse of the canonical parameter of the Bernoulli distribution: \begin{align} f(y) &= p^y (1 - p)^{1 - y} \\ &= (1 - p) \exp \left \{ y \log \left ( \frac{p}{1 - p} \right ) \right \} . \end{align} (The function of $p$ within the exponent is called the canonical parameter.)

Maybe a more compelling justification comes from information theory, where the logisticsigmoid function can be derived as a maximum entropy model. Roughly speaking, the logisticsigmoid function assumes minimal structure and reflects our general state of ignorance about the underlying model.

One reason this function might seem more "natural" than others is that it happens to be the inverse of the canonical parameter of the Bernoulli distribution: \begin{align} f(y) &= p^y (1 - p)^{1 - y} \\ &= (1 - p) \exp \left \{ y \log \left ( \frac{p}{1 - p} \right ) \right \} . \end{align} (The function of $p$ within the exponent is called the canonical parameter.)

Maybe a more compelling justification comes from information theory, where the logistic function can be derived as a maximum entropy model. Roughly speaking, the logistic function assumes minimal structure and reflects our general state of ignorance about the underlying model.

One reason this function might seem more "natural" than others is that it happens to be the inverse of the canonical parameter of the Bernoulli distribution: \begin{align} f(y) &= p^y (1 - p)^{1 - y} \\ &= (1 - p) \exp \left \{ y \log \left ( \frac{p}{1 - p} \right ) \right \} . \end{align} (The function of $p$ within the exponent is called the canonical parameter.)

Maybe a more compelling justification comes from information theory, where the sigmoid function can be derived as a maximum entropy model. Roughly speaking, the sigmoid function assumes minimal structure and reflects our general state of ignorance about the underlying model.

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One reason this function might seem more "natural" than others is that it happens to be the inverse of the canonical parameter of the Bernoulli distribution: \begin{align} f(y) &= p^y (1 - p)^{1 - y} \\ &= (1 - p) \exp \left \{ y \log \left ( \frac{p}{1 - p} \right ) \right \} . \end{align} (The function of $p$ within the exponent is called the canonical parameter.)

Maybe a more compelling justification comes from information theory, where the logistic function can be derived as a maximum entropy model. Roughly speaking, the logistic function assumes minimal structure and reflects our general state of ignorance about the underlying model.