Modella la crescita della soia con un GAM

In questo esercizio modellerai il peso medio delle foglie di una pianta di soia in funzione del tempo (dopo la semina). Come vedrai, la pianta di soia non cresce a un ritmo costante, ma ha un "picco di crescita" che poi rallenta. Per questo, il peso delle foglie non è ben descritto da un modello lineare.

Ricorda che puoi indicare quale variabile vuoi modellare in modo non lineare in una formula con la funzione s() (docs):

y ~ s(x)

Ricorda anche che gam() (docs) del pacchetto mgcv ha la seguente interfaccia di chiamata

gam(formula, family, data)

Per la regressione standard, usa family = gaussian (il valore predefinito).

I dati di training sulla soia, soybean_train, sono già stati caricati. Hanno due colonne: l'output weight e la variabile Time. Per confronto, è già stato caricato anche il modello lineare model.lin, stimato usando la formula weight ~ Time.

Questo esercizio fa parte del corso

Supervised Learning in R: Regression

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Prova a risolvere questo esercizio completando il codice di esempio.

# soybean_train is available
summary(soybean_train)

# Plot weight vs Time (Time on x axis)
ggplot(soybean_train, aes(x = ___, y = ___)) + 
  geom_point()

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Questo esercizio fa parte del corso

Supervised Learning in R: Regression

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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: Categorical inputs Exercise 2: Examining the structure of categorical inputs Exercise 3: Modeling with categorical inputs Exercise 4: Interactions Exercise 5: Modeling an interaction Exercise 6: Modeling an interaction (2)Exercise 7: Transforming the response before modeling Exercise 8: Relative error Exercise 9: Modeling log-transformed monetary output Exercise 10: Comparing RMSE and root-mean-squared Relative Error Exercise 11: Transforming inputs before modeling Exercise 12: Input transforms: the "hockey stick"Exercise 13: Input transforms: the "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: Regressione logistica per prevedere probabilità Exercise 2: Adatta un modello per la probabilità di sopravvivenza dei passeri Exercise 3: Prevedi la sopravvivenza dei passeri Exercise 4: Regressione di Poisson e quasipoisson per prevedere conteggi Exercise 5: Poisson o quasipoisson Exercise 6: Adatta un modello per prevedere i conteggi di noleggio bici Exercise 7: Prevedi i noleggi di bici su nuovi dati Exercise 8: Visualizza le previsioni di noleggio bici Exercise 9: GAM per apprendere trasformazioni non lineari Exercise 10: Scrivere formule per modelli GAM Exercise 11: Scrivere formule per modelli GAM (2)Exercise 12: Modella la crescita della soia con un GAM

Esercizio in corso

Exercise 13: Fai previsioni con il modello della soia sui dati di test

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