Poisson o quasipoisson

Una delle assunzioni della regressione di Poisson per predire conteggi è che l’evento che stai contando sia distribuito secondo Poisson: il conteggio medio per unità di tempo è uguale alla varianza del conteggio. In pratica, “uguale” significa che media e varianza dovrebbero avere un ordine di grandezza simile.

Quando la varianza è molto maggiore della media, l’assunzione di Poisson non vale e una soluzione è usare la regressione quasipoisson, che non assume che \(variance = mean\).

Per ognuna delle seguenti situazioni, decidi se la regressione di Poisson sarebbe adatta o se dovresti usare la regressione quasipoisson.

Per quali situazioni puoi usare la regressione di Poisson?

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Supervised Learning in R: Regression

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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

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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 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