On a New Class of Bounds on Bayes Risk in Multihypothesis Pattern Recognition
- 1 January 1974
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Computers
- Vol. C-23 (1) , 70-80
- https://doi.org/10.1109/t-c.1974.223779
Abstract
An important measure concerning the use of statistical decision schemes is the error probability associated with the decision rule. Several methods giving bounds on the error probability are presently available, but, most often, the bounds are loose. Those methods generally make use of so-cailed distances between statistical distributions. In this paper a new distance is proposed which permits tighter bounds to be set on the error probability of the Bayesian decision rule and which is shown to be closely related to several certainty or separability measures. Among these are the nearest neighbor error rate and the average conditional quadratic entropy of Vajda. Moreover, our distance bears much resemblance to the information theoretic concept of equivocation. This relationship is discussed. Comparison is made between the bounds on the Bayes risk obtained with the Bhattacharyya coefficient, the equivocation, and the new measure which we have named the Bayesian distance.Keywords
This publication has 6 references indexed in Scilit:
- Comments on "The Divergence and Bhattacharyya Distance Measures in Signal Selection"IEEE Transactions on Communications, 1972
- Theoretical Comparison of a Class of Feature Selection Criteria in Pattern RecognitionIEEE Transactions on Computers, 1971
- The Divergence and Bhattacharyya Distance Measures in Signal SelectionIEEE Transactions on Communications, 1967
- Nearest neighbor pattern classificationIEEE Transactions on Information Theory, 1967
- A simple derivation of the coding theorem and some applicationsIEEE Transactions on Information Theory, 1965
- InequalitiesPublished by Springer Nature ,1961