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Relationship between KL divergence, JS divergence, and MMD?

What kind of relationship is there between the KL (Kullback-Leibler) divergence, JS (Jensen-Shannon) divergence, and MMD (maximum mean discrepancy)? I know that they all share a global minimum at $P=...
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0answers
14 views

How to measure the “variability” across a set of many (>>2) probability distributions?

Given a set of many of discrete probability distributions, is there a way I can efficiently calculate a metric that quantifies how different the entire set of these probability distributions are to ...
5
votes
1answer
3k views

Can KL-Divergence ever be greater than 1?

I've been working on building some test statistics based on the KL-Divergence, \begin{equation} D_{KL}(p \| q) = \sum_i p(i) \log\left(\frac{p(i)}{q(i)}\right), \end{equation} And I ended up with a ...
3
votes
0answers
86 views

Name of an $f$-divergence

The term divergence means a function $D$, which, given two probability distributions $P,Q$, assigns a non-negative real number $D(P,Q)$ such that $D(P,Q) = 0$ iff $P(x)=Q(x) \forall x$. The relative ...
2
votes
0answers
36 views

Approximation of objective based on statistical distance

I am a computer science researcher (mostly theoretical) currently in midst of statistics and not able to figure out how to proceed. At an abstract level, I have a hypothesis for an unknown ...
4
votes
1answer
3k views

Kullback-Leibler divergence of two normal distributions

I was recently trying to find a way to compute the KL-divergence between 2 populations that are normally distributed using the mean and variance of each population. But I found several different ...
1
vote
2answers
4k views

Bhattacharyya distance for histograms

One of the ways to measure the similarity of two discrete probability distributions is the Bhattacharyya distance. In computer vision, for example, it is used to evaluate the degree of similarity ...
35
votes
2answers
7k views

Kullback–Leibler vs Kolmogorov-Smirnov distance

I can see that there are a lot of formal differences between Kullback–Leibler vs Kolmogorov-Smirnov distance measures. However, both are used to measure the distance between distributions. Is there a ...