결정계수(R2)와 설명분산점수 (Explained Variance Score)

  • sklearn.metrics 라이브러리를 까보면, 흔히쓰는 R스퀘어 (결정계수)말고도 비슷한 개념의 metrics가 한개가 더있다. 바로 설명분산점수(Explained Variance Score)인데 사실 R제곱 자체가
    • 1 – (Sum of Squared Residuals / Total Variance)
  • 로 정의되어있기 때문에, 이게 도대체 뭔 측정도구인지 싶을때가 있다. 코드를 까보면 아래와같이 설정되어있다.
    • Explained Variance Score = 1 – ( (Sum of Squared Residuals – Mean Error) / Total Variance )
  • 유일한 차이는 SSR에 Mean Error를 뺀다는것이다. 만약 모델이 얼추 제대로 맞추고 모델에서 나오는 오차는 별 트렌드없이 0을 기준으로 왔다갔다 한다면 둘의 값은 거의 비슷할것이다. 다만, 에러가 한쪽에 쏠려 있다거나 한다면 일단은 모델이 좀 편향되게 (잘못) 피팅이 되었다는 것이고 이는 Mean Error가 0에 가까운 값이 아닌 – 나 +를 띄게 된다.
  • R제곱과 설명분산점수가 다르게 나온다면 에러에 편향이 있다는것이고, 피팅이 잘못되었다는것을 뜻한다.
  • 굳이 부각되지 않은것은 어차피 잔차에 편향이 존재하지 않아야 회귀분석이 제대로 이뤄진것을 가정하기 때문이다.
  • 직관적으로 이해하자면, 설명분산점수는 결정계수와 다르게 경향성도 제거하기 때문에 눈꼽만큼 나은 지표지만, 실질적인 이득은 없어보인다.

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