In defense of the maximum entropy inference process.

*(English)*Zbl 0939.68118Summary: This paper is a sequel to an earlier result of the authors that in making inferences certain probabilistic knowledge bases the maximum entropy inference process, ME, is the only inference process respecting “common sense.” This result was criticized on the grounds that the probabilistic knowledge bases considered are unnatural and that ignorance of dependence should not be identified with statistical independence. We argue against these criticisms and also against the more general criticism that ME is representation dependent. In a final section, however, we provide a criticism of our own of ME, and of inference processes in general, namely that they fail to satisfy compactness.

##### MSC:

68T37 | Reasoning under uncertainty in the context of artificial intelligence |

68T30 | Knowledge representation |

03B48 | Probability and inductive logic |

60A99 | Foundations of probability theory |

94A17 | Measures of information, entropy |

PDF
BibTeX
XML
Cite

\textit{J. Paris} and \textit{A. Vencovská}, Int. J. Approx. Reasoning 17, No. 1, 77--103 (1997; Zbl 0939.68118)

Full Text:
DOI

##### References:

[1] | Paris, J.; Vencovska, A., A note on the inevitability of maximum entropy, Internat. J. approx. reason., 4, 3, 183-224, (1990) · Zbl 0697.68089 |

[2] | Paris, J., The uncertain Reasoner’s companion—A mathematical perspective, (1994), Cambridge U.P · Zbl 0838.68104 |

[3] | Halpern, J.Y.; Koller, D., Representation dependence in probabilistic inference, Ijcai, 1853-1860, (1995) |

[4] | Jaeger, M., Representation independence of nonmonotonic inference relations, () |

[5] | Walley, P., Statistical reasoning with imprecise probabilities, (1991), Chapman and Hall · Zbl 0732.62004 |

[6] | Paris, J. and Vencovská, A., Some observations on the maximum entropy inference process,Tech. Report L1-96 Dept. of Mathematics, Manchester Univ., U.K. |

[7] | Maung, I., () |

[8] | Tversky, A.; Kahneman, D., Judgement under uncertainty: heuristics and biases, Science, 185, 1124-1131, (1974) |

[9] | Shore, J.E.; Johnson, R.W., Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy, IEEE trans. inform. theory, IT-26, 1, 26-37, (1980) · Zbl 0429.94011 |

[10] | Csiszár, I., Why least squares and maximum entropy? an axiomatic approach to inverse problems, () · Zbl 0753.62003 |

[11] | Paris, J.; Vencovská, A., Maximum entropy and inductive inference, (), 397-403 · Zbl 0691.03008 |

[12] | Aczel, J., Lectures on functional equations and their applications, (), Chapter 2 · Zbl 0139.09301 |

[13] | Hopcroft, J.E.; Ullman, J.D., Introduction to automata theory, languages and computation, (1979), Addison-Wesley · Zbl 0196.01701 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.