A Decision Theory Approach to the Approximation of Discrete Probability Densities
- 1 January 1980
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. PAMI-2 (1) , 61-67
- https://doi.org/10.1109/tpami.1980.4766971
Abstract
The problem of approximating a probability density function by a simpler one is considered from a decision theory viewpoint. Among the family of candidate approximating densities, we seek the one that is most difficult to discriminate from the original. This formulation leads naturaliy to the density at the smallest Bhattacharyya distance. The resulting optimization problem is analyzed in detail.Keywords
This publication has 12 references indexed in Scilit:
- Linear transformation of binary random vectors and its application to approximating probability distributionsIEEE Transactions on Information Theory, 1978
- Minimum Hellinger Distance Estimates for Parametric ModelsThe Annals of Statistics, 1977
- Sharper lower bounds for discrimination information in terms of variation (Corresp.)IEEE Transactions on Information Theory, 1975
- Consistency of an estimate of tree-dependent probability distributions (Corresp.)IEEE Transactions on Information Theory, 1973
- The Reliability of Linear Feature ExtractorsIEEE Transactions on Computers, 1971
- Approximating discrete probability distributionsIEEE Transactions on Information Theory, 1969
- Approximating discrete probability distributions with dependence treesIEEE Transactions on Information Theory, 1968
- On the best finite set of linear observables for discriminating two Gaussian signalsIEEE Transactions on Information Theory, 1967
- Approximating probability distributions to reduce storage requirementsInformation and Control, 1959
- Decision Rules, Based on the Distance, for Problems of Fit, Two Samples, and EstimationThe Annals of Mathematical Statistics, 1955