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  1. Wikipedia
    https://en.wikipedia.org/wiki/Kullback–Leibler_divergence

    Kullback–Leibler divergence - Wikipedia

    • In mathematical statistics, the Kullback–Leibler (KL) divergence (also called relative entropy and I-divergence ), denoted , is a type of statistical distance: a measure of how one reference probability distribution P is different from a second probability distribution Q. Mathematically, it is defined as A simple interpretation of the KL divergence of P from Q is the expected e… See more

    Introduction and context

    Consider two probability distributions P and Q. Usually, P represents the data, the observations, or a measured probability distribution. Distribution Q represents instead a theory, a model, a description or an approxi… See more

    Definition

    For discrete probability distributions P and Q defined on the same sample space, the relative entropy from Q to P is defined to be
    which is equivalent to
    In other words, it is the expectation of the logarithmic … See more

    KL Divergence – What is it and mathematical details explained
    At its core, KL (Kullback-Leibler) Divergence is a statistical measure that quantifies the dissimilarity between two probability distributions. Think of it like a mathematical ruler that tells us the “dis…
    Machine Learning Plus · https://www.machinele…
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    Table of Contents
    Introduction and context
    Definition
     
  1. The Kullback–Leibler (K-L) divergence is the sum KL (f, g) = Σ x f (x) log (f (x)/g (x)) where the sum is over the set of x values for which f (x) > 0. (The set {x | f (x) > 0} is called the support of f.) The K-L divergence measures the similarity between the distribution defined by g and the reference distribution defined by f.

    The Kullback–Leibler divergence between discrete probability ...

    blogs.sas.com/content/iml/2020/05/26/kullback-leibler-divergence-discrete.html
    blogs.sas.com/content/iml/2020/05/26/kullback-leibler-divergence-discrete.html
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  2. People also ask
    What is KL divergence?
    A simple interpretation of the KL divergence of P from Q is the expected excess surprise from using Q as a model instead of P when the actual distribution is P. While it is a measure of how different two distributions are, and in some sense is thus a "distance", it is not actually a metric, which is the most familiar and formal type of distance.

    Kullback–Leibler divergence - Wikipedia

    en.wikipedia.org
    What is the formula for KL divergence?
    The formula for KL Divergence is: KL (P∣∣Q) = ∑P (i)×log (Q (i)/P (i)) Where: P is the true probability distribution. Q is the probability distribution of the model. However, P and Q need not necessarily be True vs model probability distributions. It can be any two probability distributions in a different context.

    KL Divergence – What is it and mathematical details explained

    machinelearningplus.com
    How do you prove KL divergence?
    Proof: The KL divergence for a continuous random variable is given by which, applied to the normal distributions in \eqref {eq:norms}, yields Using the probability density function of the normal distribution, this becomes: Because the expected value is a linear operator, the expectation can be moved into the sum:

    Kullback-Leibler divergence for the normal distribution

    statproofbook.github.io
    What is KL (p q) divergence?
    The KL (p,q) divergence between distributions p (.) and q (.) has an intuitive information theoretic interpretation which you may find useful. Suppose we observe data x generated by some probability distribution p (.). A lower bound on the average codelength in bits required to state the data generated by p (.) is given by the entropy of p (.).

    How to interpret KL divergence quantitatively? - Cross Validated

    stats.stackexchange.com
    What is mutual information according to KL -divergence?
    If we let P ⊥ (x, y) = P X (x) ⋅ P Y (y) be the factorization of P, then I P (X, Y ) = D (P, P ⊥). Thus, according to KL -divergence, mutual information measures the dissimilarity of a joint distribution from its factorization.

    Kullback-Leibler Divergence - SpringerLink

    link.springer.com
    What is a KL-divergence?
    I finally took the time to take a detailed look at this topic. The KL-divergence is a measure of how similar (or different) two probablity distributions are. When having a discrete probability distribution P P and another probability distribution Q Q the KL-divergence for a set of points X X is defined as:

    Kullback-Leibler Divergence - Anna-Lena Popkes

    alpopkes.com
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  3. Springer
    https://link.springer.com/referenceworkentry/10...

    Kullback-Leibler Divergence - SpringerLink

  4. Cross Validated
    https://stats.stackexchange.com/questions/1028/how...

    distributions - How to interpret KL divergence quantitatively?

  5. Machine Learning Plus
    https://www.machinelearningplus.com/m…

    KL Divergence – What is it and mathematical details …

    Oct 2, 2023 · At its core, KL (Kullback-Leibler) Divergence is a statistical measure that quantifies the dissimilarity between two probability distributions. Think of it like a mathematical ruler that tells us the “distance” or difference between two …

  6. arXiv.org
    https://arxiv.org/abs/1404.2000

    [1404.2000] Notes on Kullback-Leibler Divergence and Likelihood

  8. The Book of Statistical Proofs
    https://statproofbook.github.io/P/norm-kl.html

    Kullback-Leibler divergence for the normal distribution

  9. CMU Statistics
    https://www.stat.cmu.edu/~cshalizi/754/2006/notes/lecture-28.pdf
    [PDF]

    Shannon Entropy and Kullback-Leibler Divergence

  10. MIT - Massachusetts Institute of Technology
    http://web.mit.edu/jstang/www/papers/quantization_isit2021.pdf
    [PDF]

    Quantization of Random Distributions under KL Divergence

  11. Statlect
    https://statlect.com/.../Kullback-Leibler …

    Kullback-Leibler divergence - Statlect

    We are going to give two separate definitions of Kullback-Leibler (KL) divergence, one for discrete random variables and one for continuous variables.

  12. alpopkes.com
    https://alpopkes.com/posts/machine_learning/kl_divergence

    Kullback-Leibler Divergence - Anna-Lena Popkes