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Merged
bertdv merged 1 commit into from
Dec 18, 2025
Merged

Update Discriminative Classification.jl #273

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6 changes: 3 additions & 3 deletions lectures/Discriminative Classification.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -645,10 +645,10 @@ md"""

#### Discrimination boundaries (*)

Show that for logistic regression with ``p(y_n =1 \,|\, x_n, w) = \sigma(w^T x_n)``, the discrimination boundary, which can be computed by
Show that for logistic regression with ``p(y_n =1 \,|\, x_n) = \sigma(w^T x_n)``, the discrimination boundary, which can be computed by

```math
\frac{p(y_n\in\mathcal{C}_1|x_n)}{p(y_n\in\mathcal{C}_0|x_n)} \overset{!}{=} 1
\frac{p(y_n =1|x_n)}{p(y_n =0|x_n)} \overset{!}{=} 1
```

is a straight line.
Expand All @@ -660,7 +660,7 @@ md"""

```math
\begin{align}
\frac{ p(y_n \in \mathcal{C}_1 |x_n) }{ p(y_n\in\mathcal{C}_0|x_n) } &= \frac{ \sigma(w^T x_n)}{1 - \sigma(w^T x_n)} \\
\frac{ p(y_n =1 |x_n) }{ p(y_n =0|x_n) } &= \frac{ \sigma(w^T x_n)}{1 - \sigma(w^T x_n)} \\
&= \frac{ \frac{1}{1+\exp(-w^T x_n)} }{ 1 -\frac{1}{1+\exp(-w^T x_n)} } \\
&= \frac{1}{1+\exp(-w^T x_n) - 1} \\
&= \exp(w^T x)
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