TITLE: Can someone explain Dirac Distribution?
QUESTION [5 upvotes]: I have been reading book on Deep Learning and in the chapter of probability and information theory I found this topic "Dirac Distribution and Empirical Distribution". It says:
In some cases, we wish to specify that all the mass in a probability distribution clusters around a single point.
I don't understand what this means? And also how this is related to machine learning, what is the significance of it?
I can understand a bit of mathematics of this but unable to picturize the concept, if someone can help me in this(in a more simpler way) it will be a real help.
PS: If you can provide some other study material regarding this it will be really helpful.
Thanks

REPLY [5 votes]: In Machine Learning, you use the $\delta$ probability distribution (concentrated at one point) when the true labels in a supervised learning problems are deterministic. In that case, the conditional probability of $\{Y|X=x\}$ is a delta centered at the true value $y=f(x)$. In contrast, when you do not have a deterministic label but different possible values for $y$ at a given $x$, your conditional distribution has some positive variance (spread).