Linked Questions

18
votes
2answers
9k views

Kullback-Leibler divergence - interpretation [duplicate]

I have a question about the Kullback-Leibler divergence. Can someone explain why the "distance" between the blue density and the "red" density is smaller than the distance between the "green" curve ...
9
votes
1answer
1k views

Why is Kullback-Leilbler divergence a better metric for measuring distance between two probability distributions than squared error? [duplicate]

I know that KL-divergence is a metric that is more suitable when we want to measure the distance between numbers which a probability form. However, I am still confused what is the benefit of using KL-...
6
votes
2answers
822 views

textbook example of KL Divergence [duplicate]

I have read what KL Divergence is about: assess differences in probability distributions between two sets. I have also read, and digested, that it is emphatically not a true metric because of ...
5
votes
1answer
443 views

Where does the Kullback-Leibler come from? [duplicate]

Let $p(x)$ be some "true" distribution which we want to model using a simpler distribution $q(x)$. Why is the KL divergence $$KL(q||p)=\int q(x)\log{\frac{q(x)}{p(x)}}$$ a good way to represents the ...
4
votes
2answers
616 views

KL divergence vs Absolute Difference between two distributions? [duplicate]

Why should I use KL divergence over just giving the abs difference from two PDFs?
1
vote
0answers
104 views

Kullback-Leibler divergence with sample data likelihood [duplicate]

I'm trying to get my head around the KL divergence in the context of the sample likelihood under two competing hypotheses, one optimal $H_0$ and one suboptimal $H_1$. Roughly speaking, I want to see ...
41
votes
1answer
21k views

Why do we use Kullback-Leibler divergence rather than cross entropy in the t-SNE objective function?

In my mind, KL divergence from sample distribution to true distribution is simply the difference between cross entropy and entropy. Why do we use cross entropy to be the cost function in many machine ...
30
votes
2answers
3k views

Why should we use t errors instead of normal errors?

In this blog post by Andrew Gelman, there is the following passage: The Bayesian models of 50 years ago seem hopelessly simple (except, of course, for simple problems), and I expect the Bayesian ...
24
votes
4answers
2k views

Kullback-Leibler divergence WITHOUT information theory

After much trawling of Cross Validated, I still don't feel like I'm any closer to understanding KL divergence outside of the realm of information theory. It's rather odd as somebody with a Math ...
15
votes
3answers
5k views

What's the maximum value of Kullback-Leibler (KL) divergence

I am going to use KL divergence in my python code and I got this tutorial. On that tutorial, to implement KL divergence is quite simple. ...
19
votes
2answers
9k views

What is the difference Cross-entropy and KL divergence?

Both of Cross-entropy and KL divergence are tools to measure the distance between two probability distribution. What is the difference? $$ H(P,Q) = -\sum_x P(x)\log Q(x) $$ $$ KL(P | Q) = \sum_{x} P(...
15
votes
1answer
6k views

Qualitively what is Cross Entropy

This question gives a quantitative definition of cross entropy, in terms of it's formula. I'm looking for a more notional definition, wikipedia says: In information theory, the cross entropy ...
10
votes
2answers
8k views

Kullback-Leibler Divergence for two samples

I tried to implement a numerical estimate of the Kullback-Leibler Divergence for two samples. To debug the implementation draw the samples from two normal distributions $\mathcal N (0,1)$ and $\...
5
votes
2answers
5k views

Intuition of the Bhattacharya Coefficient and the Bhattacharya distance?

The Bhattacharyya distance is defined as $D_B(p,q) = -\ln \left( BC(p,q) \right)$, where $BC(p,q) = \sum_{x\in X} \sqrt{p(x) q(x)}$ for discrete variables and similarly for continuous random variables....
11
votes
1answer
6k views

Intuitively, why is cross entropy a measure of distance of two probability distributions?

For two discrete distributions $p$ and $q$, cross entropy is defined as $$H(p,q)=-\sum_x p(x)\log q(x).$$ I wonder why this would be an intuitive measure of distance between two probability ...

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