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update ic class 1 (#1159)
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ludwigbothmann authored Nov 8, 2023
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Expand Up @@ -29,7 +29,7 @@ Given (2)$\;-\;$(4), she figures one could formulate the explicit ERM problem, b
\item[2)] Write down the explicit form of the ERM problem for estimating the parameter vector $\thetab$.
\end{enumerate}

Later, the research group trains the logistic regression model and receives a corresponding parameter estimate $\thetabh = (\thetah_0,\; \thetah_{age},\; \thetah_{blood\;pressure},\; \thetah_{weight})$. Researcher Son, who has worked all night on the research problem, finds a function scribbled on his personal notes. He remembers it was useful in the context of a logistic regression model, but does not recall how:
Later, the research group trains the logistic regression model and receives a corresponding parameter estimate $\thetabh = (\thetah_0,\; \thetah_{age},\; \thetah_{blood\;pressure},\; \thetah_{weight})$. Researcher Laetitia, who has worked all night on the research problem, finds a function scribbled on her personal notes. She remembers it was useful in the context of a logistic regression model, but does not recall how:
\begin{align}
h\left( \xv^{(i)} ~|~ \thetabh, \; \alpha \right) = \scalebox{1.2}{$\I_{[\alpha, 1]}$} \left( \frac{1}{1+\exp (- \thetabh^T \xi ) } \right), ~~~ \alpha \in \; (0,1)
\end{align}
Expand All @@ -38,7 +38,7 @@ h\left( \xv^{(i)} ~|~ \thetabh, \; \alpha \right) = \scalebox{1.2}{$\I_{[\alpha,
\item[3)] What purpose does the function serve in the case of a trained logistic regression model with estimated parameters $\thetabh$? Explain the role of the parameter $\alpha$.
\end{enumerate}

Researcher Son is curious about why the loss function of the logistic regression model in $(3)$ is called \textit{Bernoulli loss}. He seems certain that he can connect it to the Bernoulli distribution, which has the following probability mass function:
Researcher Laetitia is curious about why the loss function of the logistic regression model in $(3)$ is called \textit{Bernoulli loss}. She seems certain that she can connect it to the Bernoulli distribution, which has the following probability mass function:
\begin{align}
\P(Y=y) = \pi^y (1-\pi)^{1-y}, ~~~ y \in \setzo
\end{align}
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