Error in Problem Set 1 2e?

[RylanSchaeffer]

I think there may be an error in Problem Set 1 2e:

Specifically, x = phi(h), whereas the integrand term has phi(x). If this is a mistake, the problem is carried forward to

[cinjon]

Thanks Rylan, which curriculum is this?

[RylanSchaeffer]

http://www.depthfirstlearning.com/2020/Resurrecting-Sigmoid

[RylanSchaeffer]

@cinjon bump?

[cinjon]

Sorry for the delay, and thanks for the bump! I'm not so familiar with this one, will ping the authors right now.

[RylanSchaeffer]

Thank you!

Cheers, Rylan Schaeffer

On Thu, Jul 23, 2020 at 12:26 PM cinjon notifications@github.com wrote:

Sorry for the delay, and thanks for the bump! I'm not so familiar with this one, will ping the authors right now.

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[ramasesh]

Hi Ryan, Thanks for the question! I think I see the confusion. Though I think the expression is still correct, we used bad notation in writing $x$ as the variable of integration. In the equation with integration over $x$, this $x$ is just a dummy variable, not the same $x$ as $x^{l-1}_i$.

Does this clear things up? If so, we should probably change that expression to give the dummy variable a different name, maybe $h$.

Cheers, Vinay

[RylanSchaeffer]

Ok thank you for clarifying! I'm still a bit confused by the notation $p_{h^{l-1}}(x)$ inside the integral. What does this notation for a density mean?

[ramasesh]

Oh, I see. Yeah, good question, let me try and explain. In this notation, $p{h^{l-1}}(x)$ means "the probability density function of the random variable $h^{l-1}$, evaluated at value $x$". So $h^{l-1}$ is the random variable, and the probability of it taking on a value between, say, $4$ and $4 + \epsilon$ is $p{h^{l-1}}(4)\times\epsilon$. Does this help?

[RylanSchaeffer]

Yep! Thank you for clarifying!