What is Gradient Boosting?

Gradient boosting builds an ensemble of weak models, typically decision trees, sequentially. Each new model focuses on correcting the errors of the previous model, leading to improved overall accuracy. Gradient boosting is sensitive to outliers and noise in the data, requiring preprocessing steps like feature scaling and missing value imputation. At each iteration, GBM calculates the negative gradient of the loss function with respect to its predictions. This gradient represents the direction of learning, guiding the new tree to fit these residuals better. The learning rate controls the step size taken along this gradient, affecting the influence of each individual tree.

Let’s understand the interplay between objective functions, and gradient calculations is crucial for effectively using and interpreting these models.

Objective Function:

The objective function combines the loss function with a regularization term to prevent overfitting. In gradient boosting, it often takes the form:

Objective = Loss(y_true, y_pred) + λ * Regularization(f)

where:

• y_true are the true values
• y_pred are the predicted values
• λ is the regularization hyperparameter
• Regularization(f) penalizes model complexity (e.g., number of trees in the ensemble)

The objective function helps the model find a balance between fitting the training data well and generalizing to unseen data.

Gradient Calculation

The core idea behind gradient boosting is to iteratively add new weak learners to the ensemble, each focusing on correcting the errors made by the previous learners. To do this, we need to calculate the gradient of the objective function with respect to the predictions of the current model. The gradient points in the direction of the steepest ascent of the objective function, indicating how much each prediction needs to change to minimize the objective. Mathematically, the gradient calculation involves taking the partial derivatives of the objective function with respect to the predicted values (ypred​). The negative gradient indicates the direction in which the predictions should be updated to minimize the objective function.

Gradient boosting algorithms (GBMs) are ensemble learning methods that excel in various machine learning tasks, from regression to classification. They work by iteratively adding decision trees that correct the mistakes of their predecessors. Each tree focuses on the errors left by the previous ones, gradually building a stronger collective predictor. In this article, we are going to learn the fundamentals of gradient boosting and demonstrate how can we tune the hyperparameters of Gradient Boosting Algorithm.