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On the use of I-divergence for generating distribution approximations
1Electronics Laboratories, University of Kent at Canterbury, Kent CT2 7NT, England.
IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
Summary
An upper bound for error probability, related to I-divergences between distributions, is proven. This bound is monotonic and reaches Bayes error when divergences vanish, offering insights into classification accuracy.
Area of Science:
- Information Theory
- Statistical Learning Theory
- Pattern Recognition
Background:
- Assessing the closeness of probability distributions is crucial in statistical inference and machine learning.
- I-divergences quantify the difference between probability distributions.
- Error probability is a key metric in classification tasks.
Purpose of the Study:
- To establish an upper bound for error probability as a function of I-divergences.
- To analyze the behavior of this bound concerning I-divergences.
- To investigate the implications for two-class discrete measurement classification.
Main Methods:
- Theoretical analysis of error probability bounds.
- Mathematical derivation of the relationship between error probability and I-divergences.
- Examination of a specific two-class recognition problem.
Main Results:
- Existence of a monotonic nondecreasing upper bound for error probability based on I-divergences.
- The bound converges to the Bayes error probability as I-divergences approach zero.
- A constant upper bound of ¿ is identified for a specific two-class recognition problem.
Conclusions:
- The study provides a theoretical framework for understanding error probability bounds in relation to distribution divergence.
- The findings offer insights into the performance limits of classification systems with approximating distributions.
- The established bounds are valuable for designing and analyzing classification algorithms.
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