Hi there,
The uploaded image is from the lecture “When to Change Dev/Test Sets and Metrics?” of Week 1. Even though Sir Andrew told us not to worry too much about how the cost function J has been defined, I am very confused whether it has been correctly defined here. Will this equation not result in the effect of w(i) being completely cancelled out? Or am I missing something here?
Hi Zeeshan,
At first glance it might seem like that but let’s take a quick example.
Let W(i) be [1, 2, 3] and the L(y^(i), y(i)) be [4, 5, 6], so ‘i’ basically goes from 1 to 3. The formula now becomes:
J = ( i=1Σ3 W(i) L(y^(i), y(i)) ) / i=1Σ3 W(i)
=> J = (1 * 4 + 2 * 5 + 3 * 6) / (1 + 2 + 3)
=> J = (4 + 10 + 18) / 6
=> J = 32 / 6
=> J = 16/3
If you had directly cancelled out the W(i)s then you would have had the answer as => 4+5+6 => 15
Hope this helps.
This clarifies the confusion. Thank you!
Thanks for your explanations but one thing is still confusing to me.
Assuming we have only one coefficient, say 10, for false-positive porn images, and we have a set of 3 false-positive examples, the error of each example would be 1 and we’ll have:
J non-porn = (1 + 1 + 1) / 3 = 1
J porn = (10 * 1 + 10 * 1 + 10 * 1) / (10 + 10 + 10) = 1 but in this case we’d want to have 10 instead of 1.
Is there a mistake in my reasoning?
