Performance metrics for regression trees

Machine Learning with Tree-Based Models in R

Sandro Raabe

Data Scientist

How to measure performance?

Classification problems: accuracy (confusion matrix)
Regression problems: "correct" is relative, no binary correctness

$\Rightarrow$ Measure how far predictions are away from truth

Common metrics for regression

Mean Absolute Error (MAE)
Root Mean Square Error (RMSE)

MAE intuition:

plot of mean differences

MAE = average length of the red bars

Formulas and intuition

$$MAE = \frac{1}{n} \sum_{i=1}^n\left| actual_i - predicted_i \right|$$

"Sum of absolute deviations divided by the number of predictions"

$$\quad MSE = \quad \frac{1}{n} \sum_{i=1}^n\left( actual_i - predicted_i \right)^2$$

"Mean squared error"

Formulas and intuition

$$MAE = \frac{1}{n} \sum_{i=1}^n\left| actual_i - predicted_i \right|$$

"Sum of absolute deviations divided by the number of predictions"

$$RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^n\left( actual - predicted \right)^2}$$

"Root of the mean squared error"
Large errors get higher weight

Coding: predictions

# parsnip and yardstick are included in tidymodels
library(tidymodels)

# Make predictions and add to test data
predictions <- predict(model, new_data = chocolate_test) %>%

  bind_cols(chocolate_test)

# A tibble: 358 x 7
   .pred final_grade review_date cocoa_percent company_location
   <dbl>       <dbl>       <int>         <dbl> <fct>           
 1  2.5         2.75        2013          0.7  France          
 2  3.64        3.25        2014          0.8  France          
 3  3.3         3.5         2012          0.7  France          
 4  3.25        3.5         2011          0.72 Fiji            
# ... with 354 more rows, and 2 more variables: bean_type <fct>, broad_bean_origin <fct>

Coding: mae() and rmse()

# Evaluate using mae()
mae(predictions,

    estimate = .pred,

    truth = final_grade)

# A tibble: 1 x 2
  .metric   .estimate
  <chr>         <dbl>
1 mae           0.363

# Evaluate using rmse()
rmse(predictions,
     estimate = .pred,
     truth = final_grade)

# A tibble: 1 x 2
  .metric   .estimate
  <chr>         <dbl>
1 rmse          0.457

Let's evaluate!

Machine Learning with Tree-Based Models in R