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. (A)</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. (A)</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. (C)</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. (C)</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. (B)</p> Signup and view all the answers

Flashcards

Kullback-Leibler (KL) Divergence

A value that indicates how much one probability distribution diverges from another. Higher KL divergence means greater difference.

Probability Distribution p

One of the distributions being compared in the KL divergence calculation.

Probability Distribution q

The reference distribution used to compare with the first distribution (p) in the KL divergence calculation.

k

An index representing the specific component being examined in the probability distributions.

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K

The total number of components (items) present in the probability distributions.

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p_k

The probability of the kth component in probability distribution p.

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Summation of individual differences

The part of the KL divergence formula that measures the average difference between the two probability distributions.

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Difference from the Maximum Distribution

The part of the KL divergence formula that represents the difference between the distributions from the maximum distribution.

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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.
  • logâ‚‚ p<sub>k</sub> represents the base-2 logarithm of p<sub>k</sub>
  • logâ‚‚ 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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