# 쿨백-라이블러 발산

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## 노트

• One important thing to note is that the KL Divergence is an asymmetric measure (i.e. KL(P,Q) !
• As expected we see a smaller KL Divergence for distributions 1 & 2 than 1 & 3.
• And we also see the KL Divergence of a distribution with itself is 0.
• Finally, we comment on recent applications of KL divergence in the neural coding literature and highlight its natural application.
• Proposition Let and be two probability density functions such that their KL divergence is well-defined.
• This study also investigates a variety of applications of KL divergence in medical diagnostics.
• Graphically, KL divergence depicted through the information graph.
• It described an application of the KL divergence for discrete biomarkers.
• Section 2 describes preliminaries, including mathematical details of the KL divergence.
• Optimal encoding of information is a very interesting topic, but not necessary for understanding KL divergence.
• With KL divergence we can calculate exactly how much information is lost when we approximate one distribution with another.
• Now we can go ahead and calculate the KL divergence for our two approximating distributions.
• We can double check our work by looking at the way KL Divergence changes as we change our values for this parameter.
• It is a great post explaining the KL divergence, but felt some of the intricacies in the explanation can be explained in more detail.
• Let us now compute the KL divergence for each of the approximate distributions we came up with.
• First we will see how the KL divergence changes when the success probability of the binomial distribution changes.
• You can see that as we are moving away from our choice (red dot), the KL divergence rapidly increases.
• The SciPy library provides the kl_div() function for calculating the KL divergence, although with a different definition as defined here.
• It also provides the rel_entr() function for calculating the relative entropy, which matches the definition of KL divergence here.
• # example of calculating the kl divergence (relative entropy) with scipy from scipy .
• It uses the KL divergence to calculate a normalized score that is symmetrical.
• Relative entropy relates to " rate function " in the theory of large deviations .
• Relative entropy remains well-defined for continuous distributions, and furthermore is invariant under parameter transformations .
• Relative entropy is directly related to the Fisher information metric .