Confrontare RMSE e root-mean-squared Relative Error

In questo esercizio mostrerai che applicare il logaritmo a un output monetario prima di modellare migliora l’errore relativo medio (ma aumenta la RMSE) rispetto al modellare direttamente l’output monetario. Confronterai i risultati di model.log dell’esercizio precedente con un modello (model.abs) che stima direttamente il reddito.

I dataset income_train e income_test sono già caricati, insieme al tuo modello model.log.

Sono inoltre disponibili:

model.abs: un modello che adatta direttamente il reddito agli input usando la formula

Income2005 ~ Arith + Word + Parag + Math + AFQT

Questo esercizio fa parte del corso

Supervised Learning in R: Regression

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Istruzioni dell'esercizio

Completa gli spazi vuoti per aggiungere a income_test le previsioni dei modelli.
- Non dimenticare di fare l’esponenziale delle previsioni di model.log per annullare la trasformazione log!
Completa gli spazi vuoti per eseguire pivot_longer() sulle previsioni e calcolare i residui e l’errore relativo.
Completa gli spazi vuoti per calcolare la RMSE e la RMSE relativa delle previsioni.
- Quale modello ha un errore assoluto maggiore? E un errore relativo maggiore?

Esercizio pratico interattivo

Prova a risolvere questo esercizio completando il codice di esempio.

# fmla.abs is available
fmla.abs

# model.abs is available
summary(model.abs)

# Add predictions to the test set
income_test <- income_test %>%
  mutate(pred.absmodel = ___(___, income_test),        # predictions from model.abs
         pred.logmodel = ___(___(___, income_test)))   # predictions from model.log

# pivot_longer the predictions and calculate residuals and relative error
income_long <- income_test %>% 
  pivot_longer(names_to = 'modeltype', values_to = 'pred', cols=c('pred.absmodel', 'pred.logmodel')) %>%
  mutate(residual = ___,   # residuals
         relerr   = ___)   # relative error

# Calculate RMSE and relative RMSE and compare
income_long %>% 
  group_by(modeltype) %>%      # group by modeltype
  summarize(rmse     = ___,    # RMSE
            rmse.rel = ___)    # Root mean squared relative error

Modifica ed esegui il codice

Questo esercizio fa parte del corso

Supervised Learning in R: Regression

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4.6+

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In this chapter we introduce the concept of regression from a machine learning point of view. We will present the fundamental regression method: linear regression. We will show how to fit a linear regression model and to make predictions from the model.

Exercise 1: Welcome and Introduction Exercise 2: Identify the regression tasks Exercise 3: Linear regression - the fundamental method Exercise 4: Code a simple one-variable regression Exercise 5: Examining a model Exercise 6: Predicting once you fit a model Exercise 7: Predicting from the unemployment model Exercise 8: Multivariate linear regression (Part 1)Exercise 9: Multivariate linear regression (Part 2)Exercise 10: Wrapping up linear regression

Now that we have learned how to fit basic linear regression models, we will learn how to evaluate how well our models perform. We will review evaluating a model graphically, and look at two basic metrics for regression models. We will also learn how to train a model that will perform well in the wild, not just on training data. Although we will demonstrate these techniques using linear regression, all these concepts apply to models fit with any regression algorithm.

Exercise 1: Evaluating a model graphically Exercise 2: Graphically evaluate the unemployment model Exercise 3: The gain curve to evaluate the unemployment model Exercise 4: Root Mean Squared Error (RMSE)Exercise 5: Calculate RMSE Exercise 6: R-squared Exercise 7: Calculate R-squared Exercise 8: Correlation and R-squared Exercise 9: Properly Training a Model Exercise 10: Generating a random test/train split Exercise 11: Train a model using test/train split Exercise 12: Evaluate a model using test/train split Exercise 13: Create a cross validation plan Exercise 14: Evaluate a modeling procedure using n-fold cross-validation

Before moving on to more sophisticated regression techniques, we will look at some other modeling issues: modeling with categorical inputs, interactions between variables, and when you might consider transforming inputs and outputs before modeling. While more sophisticated regression techniques manage some of these issues automatically, it's important to be aware of them, in order to understand which methods best handle various issues -- and which issues you must still manage yourself.

Exercise 1: Variabili categoriche in input Exercise 2: Esaminare la struttura degli input categorici Exercise 3: Modellare con input categorici Exercise 4: Interazioni Exercise 5: Modellare un'interazione Exercise 6: Modeling an interaction (2)Exercise 7: Trasformare la risposta prima della modellazione Exercise 8: Errore relativo Exercise 9: Modellare un output monetario trasformato con log Exercise 10: Confrontare RMSE e root-mean-squared Relative Error

Esercizio in corso

Exercise 11: Trasformare gli input prima della modellazione Exercise 12: Trasformazioni degli input: la "mazza da hockey"Exercise 13: Trasformazioni degli input: la "hockey stick" (2)

Now that we have mastered linear models, we will begin to look at techniques for modeling situations that don't meet the assumptions of linearity. This includes predicting probabilities and frequencies (values bounded between 0 and 1); predicting counts (nonnegative integer values, and associated rates); and responses that have a non-linear but additive relationship to the inputs. These algorithms are variations on the standard linear model.

Exercise 1: Logistic regression to predict probabilities Exercise 2: Fit a model of sparrow survival probability Exercise 3: Predict sparrow survival Exercise 4: Poisson and quasipoisson regression to predict counts Exercise 5: Poisson or quasipoisson Exercise 6: Fit a model to predict bike rental counts Exercise 7: Predict bike rentals on new data Exercise 8: Visualize the bike rental predictions Exercise 9: GAM to learn non-linear transforms Exercise 10: Writing formulas for GAM models Exercise 11: Writing formulas for GAM models (2)Exercise 12: Model soybean growth with GAM Exercise 13: Predict with the soybean model on test data

In this chapter we will look at modeling algorithms that do not assume linearity or additivity, and that can learn limited types of interactions among input variables. These algorithms are *tree-based* methods that work by combining ensembles of *decision trees* that are learned from the training data.

Exercise 1: The intuition behind tree-based methods Exercise 2: Predicting with a decision tree Exercise 3: Random forests Exercise 4: Build a random forest model for bike rentals Exercise 5: Predict bike rentals with the random forest model Exercise 6: Visualize random forest bike model predictions Exercise 7: One-Hot-Encoding Categorical Variables Exercise 8: vtreat on a small example Exercise 9: Novel levels Exercise 10: vtreat the bike rental data Exercise 11: Gradient boosting machines Exercise 12: Find the right number of trees for a gradient boosting machine Exercise 13: Fit an xgboost bike rental model and predict Exercise 14: Evaluate the xgboost bike rental model Exercise 15: Visualize the xgboost bike rental model