Gradient Boosting - Ankit Tomar

As we continue our journey into ML algorithms, in this post, we’ll go deeper into gradient boosting — how it works, what’s happening behind the scenes mathematically, and why it performs so well.

🌟 What is gradient boosting?

Gradient boosting is an ensemble method where multiple weak learners (usually shallow decision trees) are combined sequentially. Each new tree corrects the errors (residuals) of the combined previous trees.

🧠 How does it actually work?

Initial prediction: Start with a simple model, like predicting the mean target value.
Compute residuals: Find the difference between true values and current predictions.
Fit a new tree: Train a tree to predict these residuals (i.e., the model’s mistakes).
Update: Add this new tree’s output to the current prediction, scaled by a learning rate.
Repeat: Build many such trees iteratively.

The final prediction is the sum of all trees.

🧮 Why is it called “gradient” boosting?

At each step, instead of just predicting residuals, the algorithm fits to the negative gradient of the loss function (how error changes as predictions change). This is a form of numerical optimization: we take steps in the direction that most quickly reduces error.

For example, with mean squared error (MSE):

The negative gradient is simply the residuals (actual – predicted).
But for log loss (classification), the gradient is different.

This makes gradient boosting very flexible — it can optimize almost any differentiable loss function.

✏️ How does it pick the best split in each tree?

When building each tree:

For each feature and threshold, it computes how much splitting at that point reduces the chosen loss (e.g., MSE or log loss).
It picks the split with the highest improvement.

Efficient calculation: Libraries like XGBoost and LightGBM use clever tricks (histograms, sampling) to make this faster even with large datasets.

📐 Formulas that help in interviews

Gini impurity:

Entropy:

In regression, the typical objective is to minimize mean squared error:

And the negative gradient tells us how to adjust predictions to reduce this error.

⚙️ Why is gradient boosting powerful?

Focuses learning on hard-to-predict data.
Works with different loss functions.
Builds complex nonlinear models.
Can handle numerical and categorical data.

But it can overfit, so tuning is essential.

🛡️ How to control overfitting

Reduce tree depth.
Use lower learning rate.
Add subsampling (random rows or columns).
Add regularization like shrinkage.

We will discuss XGboost, Catboost and LightGBM in upcoming blogs.

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Machine Learning