### Abstract

The mean square upper bound of the difference between the error probability of Bayesian decision and the decision error probability connected with some estimates of Bayesian decision function is known for two hypotheses testing problems. The convergence of the mean square minimization algorithm is also proved for weakly dependent labeled samples. This paper presents an improved upper bound given by the mean distances of Bayesian decision functions and their estimates for multihypotheses testing. A slight modification of this upper bound might actually be minimized over the space of given finite dimensional decision functions. It is an adaptive recursive algorithm, a version of stochastic approximation particularly suited to certain tasks in statistical pattern recognition and related control problems.

Original language | English |
---|---|

Title of host publication | Probl Control Inf Theory |

Pages | 449-457 |

Number of pages | 9 |

Volume | 5 |

Edition | 5-6 |

Publication status | Published - 1976 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Probl Control Inf Theory*(5-6 ed., Vol. 5, pp. 449-457)

**UPPER BOUND OF ERROR PROBABILITIES FOR MULTIHYPOTHESES TESTING AND ITS APPLICATION IN ADPATIVE PATTERN RECOGNITION.** / Györfi, L.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Probl Control Inf Theory.*5-6 edn, vol. 5, pp. 449-457.

}

TY - CHAP

T1 - UPPER BOUND OF ERROR PROBABILITIES FOR MULTIHYPOTHESES TESTING AND ITS APPLICATION IN ADPATIVE PATTERN RECOGNITION.

AU - Györfi, L.

PY - 1976

Y1 - 1976

N2 - The mean square upper bound of the difference between the error probability of Bayesian decision and the decision error probability connected with some estimates of Bayesian decision function is known for two hypotheses testing problems. The convergence of the mean square minimization algorithm is also proved for weakly dependent labeled samples. This paper presents an improved upper bound given by the mean distances of Bayesian decision functions and their estimates for multihypotheses testing. A slight modification of this upper bound might actually be minimized over the space of given finite dimensional decision functions. It is an adaptive recursive algorithm, a version of stochastic approximation particularly suited to certain tasks in statistical pattern recognition and related control problems.

AB - The mean square upper bound of the difference between the error probability of Bayesian decision and the decision error probability connected with some estimates of Bayesian decision function is known for two hypotheses testing problems. The convergence of the mean square minimization algorithm is also proved for weakly dependent labeled samples. This paper presents an improved upper bound given by the mean distances of Bayesian decision functions and their estimates for multihypotheses testing. A slight modification of this upper bound might actually be minimized over the space of given finite dimensional decision functions. It is an adaptive recursive algorithm, a version of stochastic approximation particularly suited to certain tasks in statistical pattern recognition and related control problems.

UR - http://www.scopus.com/inward/record.url?scp=0017246825&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0017246825&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:0017246825

VL - 5

SP - 449

EP - 457

BT - Probl Control Inf Theory

ER -