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simplify notation
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lisa-wm committed Nov 23, 2023
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7 changes: 3 additions & 4 deletions exercises/evaluation/ex_rnw/ex_of_uf.Rnw
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Assume a polynomial regression model with a continuous target variable $y$ and
a continuous, $p$-dimensional feature vector $\xv$ and polynomials of degree
$d$, i.e.,
$$\fxi = \sum_{j=1}^p \sum_{k=0}^d \theta_{j,k} (\xi_j)^k,$$ and
$\yi = \fxi + \epsi$ where the $\epsi$ are iid with $\var(\epsi)=\sigma^2 \
\forall i\in \{1, \dots, n\}$.
$$\fxi = \sum_{j=1}^p \sum_{k=0}^d \theta_{j,k} \left(\xi_j\right)^k,$$
$\forall i\in \{1, \dots, n\}$.

\begin{enumerate}[a)]
\item For each of the following situations, indicate whether we would
Expand All @@ -17,7 +16,7 @@ $\yi = \fxi + \epsi$ where the $\epsi$ are iid with $\var(\epsi)=\sigma^2 \
observations $n$ is small.
\item[(iii)] The true relationship between the features and the response is
highly non-linear.
\item[(iv)] The variance of the error terms, $\sigma^2$, is extremely high.
\item[(iv)] The data are very noisy.
\end{enumerate}
\item Are overfitting and underfitting properties of a learner or of a
fixed model? Explain your answer.
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