update book
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@@ -59,24 +59,15 @@ that $\vert\vert \bm{\beta}\vert\vert_2^2\le t$, where $t$ is
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a finite number larger than zero. We will not implement that here.
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=== a) Expression for Ridge regression ===
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Show that the optimal parameters
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!bt
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\[
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\hat{\bm{\beta}}_{\mathrm{Ridge}} = \left(\bm{X}^T\bm{X}+\lambda\bm{I}\right)^{-1}\bm{X}^T\bm{y},
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\]
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!et
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with $\bm{I}$ being a $p\times p$ identity matrix.
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with $\bm{I}$ being a $p\times p$ identity matrix,
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with the constraint that
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!bt
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\[
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\sum_{i=0}^{p-1} \beta_i^2 \leq t,
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\]
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!et
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with $t$ a finite positive number. In the optimization, we will not require that the latter is satisfied.
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The ordinary least squares result is
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!bt
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