There are 3 tuning parameters when using Boosting:

1. The number of trees, denoted by $$B$$. Cross-validation is used in order to select $$B$$. If the value of $$B$$ is too big, it may overfit the data, albeit slowly.
2. The shrinkage parameter ($$\lambda$$), which controls the rate at which the boosting learns. This value is typically a small positive value; if it is very small, a large $$B$$ value may be required for it to work well.
3. The number of splits in each tree, denoted by $$d$$. This value controls how complex the boosting will be. If $$d = 1$$, there is a single split, where each model has at most 1 variable (also known as a stump). It is also known as the 'interaction depth', which controls the interaction order.

University of Michigan - Ann Arbor

Google

Boosting is another approach that can be used for both classification and regression. Boosting improves predictions of a decision tree by learning slowly. Unlike bagging, boosting works sequentially, where each tree grown uses the information from those created before it, and works on modified versions of the original data set. Boosting combines a large number of trees ($\hat{f}^{1}, ...,  \hat{f}^{B}$). Decision trees are fitted based on the residuals of the model rather than the response (Y), then update the residuals by adding it to the fitted function. This means that each model created is slowly reducing the error of the previous ones. This causes an improvement of $\hat{f}$, particularly in places where it does not do as well as others. Decision trees using boosting tend to be very small.


Boosting

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

An Introduction to Statistical Learning with Applications in R

Tuning Parameters in Boosting

Boosting is heavily dependent on the trees formed before it, whereas in bagging, each tree is formed independently and varies instead based on the sample of predictors chosen. 

Boosting vs Bagging

Boosting algorithms are methods to help transform weak learners to stronger learners. There are 3 common boosting algorithms used in data science:

1. AdaBoosting (Adaptive Boosting)
2. GradientBoosting
3. XGBoost (Extreme Gradient Boosting)

Common Boosting algorithm

Below is a video that I found helpful in understanding boosting and how its used with decision trees. The coursera course the video is a part of may be useful as well.

[SAS]. Boosting [Video File]. Retrieved from [www.coursera.org/lecture/machine-learning-sas/boosting-2J0Df](https://www.coursera.org/lecture/machine-learning-sas/boosting-2J0Df) 

Coursera: Boosting with Decision Trees

https://quantdare.com/what-is-the-difference-between-bagging-and-boosting/

what is boosting

Below is a representation of under and overfitting of the boundaries of U.S. sates. The data comes from the US Census Bureau. In its original format, the data is a single Keyhole Markup Language (KML) file which contains latitude and longitude coordinates of the borders of US states. The necessary latitude, longitude, and label (state) data were parsed from the KML files using a simple Python script. The main idea here is to understand the bias-variance trade-off and how that relates to under and overfitting. 

Additionally there are two examples of ways they avoided under and overfitting and created a much more accurate map using (gradient) boosting and random forest classifiers.

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