Metrics optimization
学習目標
- Describe the role of correct metric optimization method in a competition
- Analyze new metrics
- Create constant baselines
- Recall the most important classification and regression metrics
- Describe what libraries can be used to optimize a particular metric
Regression metrics review II
今回対象のメトリクス
- ®MSPE, MAPE
- ®MSLE
MSPE: Mean Square Percentage Error
$$ MSPE = \frac{100\%}{N}\sum_{i=1}^N(\frac{y_i - \hat{y_i}}{y_i})^2 $$
最適な定数は加重平均
MAPE: Mean Absolute Percentage Error
$$ MSPE = \frac{100\%}{N}\sum_{i=1}^N|\frac{y_i - \hat{y_i}}{y_i}| $$
最適な定数は加重中央値
®MSLE: Root Mean Square Logarithmic Error
対数スケールで計算された RMSE
$$ RMSLE = \sqrt{\frac{1}{N}\sum_{i=1}^N (log({y_i}+1) - log(\hat{y_i} + 1))^2} $$
$$ = RMSE(log({y_i}+1), log(\hat{y_i} + 1) = \sqrt{MSE(log({y_i}+1), log(\hat{y_i} + 1)} $$
対数空間で RMSE の定数を見つけ、対数空間から逆変換する必要がある