Ch 2, logic error?

[vkrepos]

To get a better understanding of the feature value as a multiplicative factor, 𝑥(i)(𝑗), let’s go through another simple example, where:
𝑦^(𝑖) = 1, 𝑦(𝑖) = 0, 𝜂 = 1
Let’s assume that 𝑥(i)(𝑗) = 1.5 and we misclassify this example as class 0.
...
For instance, if we have another example, 𝑥(i)(𝑗) = 2 , that is incorrectly classified as class 0

I believe it should be:

𝑦^(𝑖) = 0, 𝑦(𝑖) = 1, 𝜂 = 1

[Rekklessss]

@rasbt @vkrepos I think there’s a small wording/math mismatch in the example on p. 23 (the one with $y=1$, $\hat y=0$, $\eta=1$, $x_j=1.5$).

Using the update rule right above:

$$ \Delta w_j = \eta (y - \hat y) x_j = 1 \cdot (1-0) \cdot 1.5 = 1.5 $$

and

$$ \Delta b = \eta (y - \hat y) = 1 \cdot (1-0) = 1. $$

So the corresponding weight should increase by 1.5, not 2.5. The “2.5 in total” only makes sense if it’s referring to $\Delta w_j + \Delta b = 1.5 + 1 = 2.5$ (weight update + bias update), but the sentence currently reads like the weight itself is updated by 2.5.

Maybe rephrase to something like: “increase the corresponding weight by 1.5 and the bias by 1 (2.5 total parameter increment)”, or just explicitly state the two updates.