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I am confusing about the relationship between MI score and correlation score. I've searched for some information and know that: with Cov(𝑋,𝑌) we look at what non-independence does to their product, while in 𝐼(𝑋,𝑌) we look at what non-independence does to their joint probability distribution. (Mutual information versus correlation)

But when I plot the graph of MI score and correlation score, I am still confused. In the below graph, I am using the rolling window to continue plot the score between 'Topic' and 'Emotion' As you can see in the x-axis where the range between 140-160, the correlation(Pearson) score is quite low, whereas the same period in the MI graph, the score is no significant low or high

enter image description here

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  • $\begingroup$ Since MI and correlation are not measuring the same thing it would be surprising if they didn't behave differently. $\endgroup$ – Glen_b Dec 2 '19 at 0:43
  • $\begingroup$ So actually there is no relationship between MI score and correlation score? I thought there might have some contrast trend $\endgroup$ – Shin Yu Wu Dec 2 '19 at 0:59
  • $\begingroup$ It's not clear to me how you jumped from "not the same thing" to "no relationship". Correlation is a more specific kind of association. $\endgroup$ – Glen_b Dec 2 '19 at 1:05
  • $\begingroup$ oh! Because when I see the graph, there is no specific relationship between these two, that's why I am wondering if there is 'no relationship'. So in the case that I show above, can I say there is no correlation between the 'topic' and 'emotion'? Because the Pearson score is usually lower than 0.3. $\endgroup$ – Shin Yu Wu Dec 2 '19 at 1:11
  • $\begingroup$ I don't follow what you're asking. Lack of obvious relationship in a particular instance isn't necessarily any indication of lack of relationship in general. $\endgroup$ – Glen_b Dec 2 '19 at 2:15