Ahmad
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What is the interpretation of mutual information for events?
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Mutual information is linked to the concept of entropy of a random variable that quantifies the expected "amount of information" held in a random variable, or the amount of uncertainty about ...

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If $P(x \mid y)$ is high, then does this imply that $P(y \mid x)$ is also high?
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Let's review the conditional probability of both $P(x|y)$ and $P(y|x)$: $$P(x|y) = \frac{P(x \cap y)}{P(y)}$$ and $$P(y|x) = \frac{P(x \cap y)}{P(x)}$$ The common thing in both is their joint ...

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Can two events be strongly or weakly dependent?
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Pointwsei mutual information is a measure of association between two single events. $$\operatorname{pmi}(x;y) \equiv \log\frac{p(x,y)}{p(x)p(y)} = \log\frac{p(x|y)}{p(x)} = \log\frac{p(y|x)}{p(y)}$$ ...

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What is the difference between "likelihood" and "probability"?
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If we put the conditional probability interpretation aside, you can think it in this way: In probability you usually want to find the probability of a possible event based on a model/parameter/...

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VC dimension of a rectangle
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Consider it like a game between you and an opponent. You choose the location of points and the opponent label them anyway he likes. If he wins by finding a labeling that can not be shattered, then ...

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