Re:Cross Entropy
by patall on Wednesday May 23, 2018 @02:42PM
(#17136839)
What I always wondered about is that this generally assumes that classes are assigned with an equal (human level) error probability. While this is certainly the case in heavily curated example dataset, many real world scenarios only consist of a considerably labeled positive set while the negative set is often drawn randomly from the background. Is there anything on how this can be taken into account (Besides weighting, obviously)?
"Cross-entropy is defined as the difference between the following two probability distributions"
Huh? No this is a mathematically imprecise statement (and not correct either). Most explanations use references to information theory, where a perfect knowledge of the desired probability distribution leads to a perfect allocation of bits in a binary encoding. The entropy is the expected number of bits when this allocation is done using the incorrect distribution, and obviously the goal is to minimize this, hence why it is suitable for use as a loss function.
Re:Cross Entropy
by tziki on Wednesday May 23, 2018 @03:50PM
(#17137560)
> The entropy is the expected number of bits when this allocation is done using the incorrect distribution
Is there any source that would derive and/or explain this more in-depth? I've been trying to develop an intuition for this, but haven't come across a good explanation.
The other reply mentioning "kullback-leibler divergence" (aka KL divergence) is what you need to understand as this is the fundamental concept. Minimizing this quantity is equivalent to minimizing the given "cross-entropy loss" expression. More generally to understand where this comes from, you'll want to read about information theory.
Re:Cross Entropy
by pixelpoet on Wednesday May 23, 2018 @02:54PM
(#17137005)
Aside: I'm always surprised how few people notice that e.g. "cos" is rendered differently to "\cos" in TeX; for a discipline largely characterised by attention to detail, almost no programmers seem to notice.
Huh? No this is a mathematically imprecise statement (and not correct either). Most explanations use references to information theory, where a perfect knowledge of the desired probability distribution leads to a perfect allocation of bits in a binary encoding. The entropy is the expected number of bits when this allocation is done using the incorrect distribution, and obviously the goal is to minimize this, hence why it is suitable for use as a loss function.
Is there any source that would derive and/or explain this more in-depth? I've been trying to develop an intuition for this, but haven't come across a good explanation.
I found this which seems much better
also lookup kullback-leibler divergence