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베이즈 정리와 확신도

베이즈 정리와 확신도, 불확실성

베이즈 정리 & 확신도

불확실성의 원인

  • 약한 관련성의 지식
    • IF와 THEN의 연관성의 강도가 약하다
    • 약한 인과성이나 애매한 연관관계
    • 베이즈 정리, 확신도 사용 표현
  • 부정확한 언어 사용
    • 자연어는 모호하고 부정확
    • 자주 본다?
    • 퍼지이론 사용 표현
  • 불완전한 데이터에 기반한 지식
    • 알려지지 않은 것으로 간주하고, 근사적인 추론 진행
  • 상충되는 지식의 통합
    • 모순된 견해와 상충된 지식의 통합

베이즈 정리

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베이즈 정리 예시

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베이즈 추론

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  • 지식의 규칙 표현

사건 E가 일어났을 때 H가 일어날 확률

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단일 증거 E에 기반을 둔 다중 가설 H1, H2… Hm에 대한 식

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증거 E1, E2…Em과 가설 H1, H2, Hm….에 관한 식

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다른 증거 간의 조건부 독립성 (Naive Bayesian)

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Forecast-Bayesian Reasoing

LS (Likelihood of Sufficiency)

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  • 충분 가능성
  • 증거 E가 있을 때 가설 H를 신뢰하는 정도를 의미

LN (Likelihood of Necessity)

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  • 필요 가능성
  • 증거 E가 없을 때 (아닐 때) 가설 H를 불신하는 정도를 의미

예시

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확률을 이용한 규칙의 불확실성 표현

  • LS값이 크다 = 증거가 관찰되면 가설이 성립될 확률이 크다
  • LN값이 작다 = 증거가 없다면 (아니라면) 가설이 성립되지 않을 확률이 크다

사전 확률과 사후 확률

사전 확률

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  • 현재 가지고 있는 정보를 기초로 하여 정한 초기 확률
  • 확률 시행 전에 이미 가지고 있는 지식을 통해 부여한 확률
  • 예) 동전을 던져 앞면이 나올 확률

사후 확률

  • 사건 발생 후에 어떤 원인으로부터 일어난 것이라고 생각되어지는 확률
  • 추가된 정보로부터 사전 정보를 새롭게 수정한 확률
  • 베이즈 정리로부터 구할 수 있음

가설의 사후 확률을 얻는 방법

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확신도

  • 전문가가 제안하는 가설이 믿을만한가를 표시한 정도
  • -1~1 구간의 값으로 표현

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