Boosting algorithm

I am quite confused with XGBoost. As far as I understood from the lecture video, the boosting algorithms will take a weak learning algorithm like a decision tree initially and train the training data. From then on, the algorithm adds more weight to the misclassified examples of the previous tree.

What is adding more weight to the examples mean? Because we do not have weights as parameters as in neural networks for decision trees as far as I understood. What is the process of increasing weights mean? How does increasing weights for the misclassified training examples help the trees that are built further?

Hi @bhavanamalla Great question!!

You’re right that decision trees themselves don’t have weighted training examples like neural networks. The “weighting” in boosting algorithms like XGBoost refers to how much each tree in the ensemble focuses on the misclassified examples from earlier trees.

Specifically, XGBoost maintains a distribution of weights over the training examples. Initially, all examples get equal weight. Then after each decision tree is trained, it increases the weights of the examples that tree misclassified.

This makes later trees focus more on the hard examples for the current ensemble. Adding a tree that focuses on the mistakes of previous trees improves the overall ensemble performance.

So the “weights” are actually on the examples, not in the trees themselves. The trees just benefit from the updated weight distribution when training on the same data. This iterative process of reweighting and adding new trees is the essence of boosting.

In summary:

  • Trees don’t have weighted training examples themselves
  • Boosting maintains weights over the training data
  • Weights increase for misclassified examples after each tree
  • New trees focus more on the misclassified examples
  • This improves the ensemble performance over iterations

I hope this helps!

Hi @pastorsoto ,

When you say focusing on hard misclassified examples by adding weights to them, that means enabling the algorithm to pick these misclassified examples more often than the other correctly classified examples while sampling with replacement?

Yes, that’s exactly right! By increasing the weights on the misclassified examples, XGBoost makes those examples more likely to be sampled when creating the training data for the next tree.

So for example:

  • Tree 1 is trained on the full dataset
  • It misclassifies examples A, B and C
  • When sampling data for tree 2, A, B and C are given 2x higher weight
  • So there’s a higher chance of A, B, C being sampled for tree 2’s training data
  • Tree 2 therefore focuses more on classifying A, B, C correctly

This skews the sampling distribution towards the hard examples as more trees are added. It’s an elegant way to direct each tree towards the current model’s weaknesses.

The sample weights are proportional to the errors - so the most misclassified examples get the highest weights. This gradually improves performance on those tough cases.

I hope this helps!

Makes sense! Thanks again for taking the time to drill this down

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