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Summer of Math Exposition

Entropy of a Mixture

Audience: undergraduate

How can you interpret the entropy of a mixture of probability distributions?



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6.5 Overall score*
18 Rank
10 Votes
5 Comments

Comments

6.9

Overall, I really liked the “cleanness” of the presentation. Your piece gives a nice introduction to the concept of entropy for mixed probability distributions. However, I feel that you could have motivated the piece a bit more (e.g., what is entropy for a probability distribution and why is it important?; what are some of the symbols you’re using?- though some of these are very common and standard). I would have also liked a little bit more exposition regarding the intuition behind some of these ideas. Overall, I think this is a very good piece. Including some of the above elements would transform this into a really great exposition. Keep up the great job!

5.4

The style and color scheme of the article are very pleasing such that reading it is easy on the eye. However, the article could use more motivation in what the purpose of the article is and why its content is important or for what it can be used. The author mentions that the entropy of the linear combination can tell you a lot about the distributions but maybe this motivation should come earlier. It was interesting to read about “proclivity” and the image of the square with KL divergence was quite unexpected to me.

6.5

The layout is perfect - great interactive visuals too. But there could be more motivation given for topics introduced.

6.8

This is a short and clear article, thank you. I hadn’t known H(p_sublambda) had such applications. Some tertiary feedback is some readers may not know what JSD divergence, KL divergence, Bernoulli vairable, or χ 2 divergence, so perhaps linking a resource may improve upon the paper. I’ve set your Ranking score as an average of these individual scores, good luck: Motivation: 9 Clarity: 5 Novelty: 5 Memorability: 8

6.5

Great interactive graphics! Could have used more space on background and defining variables clearer.