KL divergence on different domains

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SUMMARY

The discussion focuses on the application of Kullback-Leibler (KL) divergence for comparing two distributions derived from Kernel Smoothing Density Estimates (KSDensity) in MATLAB. The primary concern is the differing domains of the distributions, which affects the validity of using KL divergence. It is established that while the support of the distributions may differ, one can redefine the domain to include values where the density is zero, allowing for the application of KL divergence. The conversation emphasizes the importance of aligning the domains of the distributions for accurate distance measurement.

PREREQUISITES
  • Understanding of Kullback-Leibler divergence
  • Familiarity with Kernel Smoothing Density Estimates (KSDensity) in MATLAB
  • Knowledge of probability distribution support
  • Basic concepts of statistical distance measurement
NEXT STEPS
  • Research methods for aligning the domains of probability distributions
  • Explore alternative distance metrics for distributions with differing supports
  • Learn about MATLAB's KSDensity function and its parameters
  • Investigate the implications of zero-density values in probability distributions
USEFUL FOR

Data scientists, statisticians, and researchers involved in statistical analysis and distribution comparison, particularly those using MATLAB for density estimation.

flatlinez
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Hallo,


I'm trying to compare the distance between two distributions that I got from a Kernel smoothing density estimate (ksdensity in matlab). I was thinking of using the kullback leibler divergence, but I realized that the domains of my distributions are different (see attached).
Can I find a way to use the KLdivergence or i need to find another way?

Thank you
 

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flatlinez said:
Hallo,
I'm trying to compare the distance between two distributions

What is the goal of doing this comparison? If you measure a "distance" between the distribution then what are you comparing that distance to?

the domains of my distributions are different

It is the "support" of the distributions that are different. You can define the "domain" to be the same. A domain for a probability distribution can include values where the density is zero.
 

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