# Difference between Validation Error on Learning Curve and Validation Error Calculation in Machine Learning Model

I am encountering a problem where the validation error I see on the learning curve of my machine learning model is different from the validation error I calculate using the mean squared error function. I am not sure if this is the expected behavior or if there is an error in my code. I am seeking advice on how to interpret and address this issue.

Here is my Random Forest model:

    # Define the model
rf_model = RandomForestRegressor(random_state=42)

# Define the parameter grid for pruning
param_grid = {
'max_depth': [5, 10, 15],
'min_samples_split': [2, 5, 10],
'min_samples_leaf': [1, 2, 3, 4],
}

# Perform a grid search to find the best hyperparameters
grid_search = GridSearchCV(estimator=rf_model, param_grid=param_grid, cv=5)
grid_search.fit(X_train, y_train)
best_rf_reg = grid_search.best_estimator_

# Train the model on the training set using the best hyperparameters
best_rf_reg.fit(X_train, y_train)

# Make predictions on the test set
y_pred = best_rf_reg.predict(X_test)

rf_r2 = r2_score(y_test, y_pred)
rf_mse = mean_squared_error(y_test, y_pred)
rf_mae = mean_absolute_error(y_test, y_pred)

print("Rˆ2 in random forest:", rf_r2)
print("MSE in random forest:", rf_mse)
print("MAE in random forest:", rf_mae)


And it's output:

• Rˆ2 in random forest: 0.788561260837054
• MSE in random forest: 171727.5491440435
• MAE in random forest: 284.4151697399289

And I use this code to get the validation and train errors for learning curve:

from sklearn.model_selection import learning_curve
import matplotlib.pyplot as plt

# Replace 'model' with the name of your model
train_sizes, train_scores, test_scores = learning_curve(best_rf_reg, X, y, cv=5, scoring = 'neg_mean_squared_error', shuffle = True)

train_scores_mean = -train_scores.mean(axis=1)
validation_scores_mean = -test_scores.mean(axis=1)
print('Mean training scores\n\n', pd.Series(train_scores_mean, index=train_sizes))
print('\n', '-' * 20)  # separator
print('\nMean validation scores\n\n', pd.Series(validation_scores_mean, index=train_sizes))


Mean training scores:

• 93050.572113
• 121290.780987
• 135467.911224
• 145831.052914
• 149380.086868

Mean validation scores:

• 274654.971506
• 226675.486281
• 214613.725089
• 212955.842776
• 212945.602182

Why in this output validation scores significantly higher that output from the model? It seems like there might be some confusion regarding the interpretation of the results. When looking at the learning curve, you are observing the mean training and validation scores at different training set sizes. These results show how your model performs with different amounts of training data.

On the other hand, when you calculate the performance metrics (R^2, MSE, MAE) after training your model on the full training set and testing it on the test set, you are getting an evaluation of your model's performance on unseen data (test set).

A key point to note is that the mean validation scores from the learning curve (which are calculated using cross-validation) are not directly comparable to the mean squared error (MSE) calculated for the test set. The learning curve validation scores are an estimate of how well the model generalizes to unseen data during the training process, while the MSE on the test set is an evaluation of how well the model generalizes to an entirely new dataset.

As for the discrepancy between the validation scores from the learning curve and the MSE from the test set, it is expected that the two values might be different. This is because they are calculated using different data samples and for different purposes.

The higher validation scores from the learning curve compared to the test set MSE could be due to various factors, such as differences in the distribution of data points in the cross-validation folds compared to the test set or the inherent randomness in the random forest model.

To better understand and address this issue, you can try these steps:

-Ensure that your data is properly shuffled and randomly split into training and test sets, as well as during cross-validation.

-Check if there is any data leakage, which might cause the model to perform better on the test set than during cross-validation.

-Analyze the learning curve for any indication of high bias (underfitting) or high variance (overfitting) in your model. This can help you fine-tune your model or preprocessing steps to improve its performance.

-Experiment with different models or hyperparameter settings to see if you can achieve better performance and consistency between the learning curve and test set results.