The Cauchy–Schwarz Divergence for Poisson Point Processes

In this paper, we extend the notion of Cauchy-Schwarz divergence to point processes and establish that the Cauchy-Schwarz divergence between the probability densities of two Poisson point processes is half the squared L2-distance between their intensity functions. Extension of this result to mixtures of Poisson point processes and, in the case where the intensity functions are Gaussian mixtures, closed form expressions for the Cauchy-Schwarz divergence are presented. Our result also implies that the Bhattacharyya distance between the probability distributions of two Poisson point processes is equal to the square of the Hellinger distance between their intensity measures. We illustrate the result via a sensor management application where the system states are modeled as point processes.

• Publication year

  2013

• Venue

  IEEE Transactions on Information Theory

• Publication date

  2013-12-21

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1109/TIT.2015.2441709arXiv 1312.6224
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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