Information Theory: Kullback-Leibler Divergence
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Questions and Answers

What does the Kullback-Leibler divergence measure?

  • How one probability distribution differs from another. (correct)
  • The total probability of the distributions combined.
  • The average of two probability distributions.
  • The similarity between two probability distributions.

    • In the formula for KL divergence, what does the term $ ext{log}_2 K$ represent?

  • The logarithmic transformation of the total components in the distribution. (correct)
  • The number of distinct outcomes in probability distribution p.
  • The scaling factor for the average probability.
  • The maximum value of the probability components.

    • What is represented by $p_k$ in the formula?

  • The value of the k-th component in probability distribution p. (correct)
  • The index of the probability distribution.
  • The total probability of all components in p.
  • The reference distribution value in q.

    • Which statement about the values of KL divergence is correct?

    <p>A larger value suggests a greater difference between the distributions.</p> Signup and view all the answers

    Why is $ ext{log}_2$ used in the KL divergence formula?

    <p>It allows for comparisons to be made on a binary scale.</p> Signup and view all the answers

    What do the two terms in the KL divergence formula collectively evaluate?

    <p>The sum of probabilities and the overall difference from max distribution.</p> Signup and view all the answers

    What role does the variable K play in KL divergence?

    <p>It defines the total number of components in the two distributions.</p> Signup and view all the answers

    Which of the following best describes the relationship between p and q in terms of KL divergence?

    <p>p is compared against a reference distribution q.</p> Signup and view all the answers

    Study Notes

    Information Theory - Kullback-Leibler Divergence

    • The Kullback-Leibler Divergence (KLD) is a measure of the difference between two probability distributions
    • D(p || q) is how much more likely the distribution p is than q.
    • It's also called the relative entropy
    • The expression D(p || q) represents the Kullback-Leibler divergence between distributions p and q.
    • The expression involves a summation over k from 0 to K-1.
    • p<sub>k</sub> represents the probability of event k in distribution p.
    • log₂ p<sub>k</sub> represents the base-2 logarithm of p<sub>k</sub>
    • log₂ K represents the base-2 logarithm of K
    • K is the total number of possible events.
    • ∑ is the summation operator.
    • p<sub>k</sub>is summed over all possible events from 0 to K–1 in distribution q.

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    Description

    Explore the concept of Kullback-Leibler Divergence (KLD), a key measure in information theory that quantifies the difference between two probability distributions. Learn how to compute KLD using its mathematical representation and gain insights into its applications and significance in statistics and machine learning.

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