In this  post, we will take a look at gradient boosting for regression. Gradient boosting simply makes sequential models that try to explain any examples that had not been explained by previously models. This approach makes gradient boosting superior to AdaBoost.

Regression trees are mostly commonly teamed with boosting. There are some additional hyperparameters that need to be set  which includes the following

• number of estimators
• learning rate
• subsample
• max depth

We will deal with each of these when it is appropriate. Our goal in this post is to predict the amount of weight loss in cancer patients based on the independent variables. This is the process we will follow to achieve this.

1. Data preparation
2. Baseline decision tree model
3. Hyperparameter tuning
4. Gradient boosting model development

Below is some initial code

from sklearn.ensemble import GradientBoostingRegressor
from sklearn import tree
from sklearn.model_selection import GridSearchCV
import numpy as np
from pydataset import data
import pandas as pd
from sklearn.model_selection import cross_val_score
from sklearn.model_selection import KFold

Data Preparation

The data preparation is not that difficult in this situation. We simply need to load the dataset in an object and remove any missing values. Then we separate the independent and dependent variables into separate datasets. The code is below.

df=data('cancer').dropna()
X=df[['time','sex','ph.karno','pat.karno','status','meal.cal']]
y=df['wt.loss']

We can now move to creating our baseline model.

Baseline Model

The purpose of the baseline model is to have something to compare our gradient boosting model to. Therefore, all we will do here is create  several regression trees. The difference between the regression trees will be the max depth. The max depth has to with the number of nodes python can make to try to purify the classification.  We will then decide which tree is best based on the mean squared error.

The first thing we need to do is set the arguments for the cross-validation. Cross validating the results helps to check the accuracy of the results. The rest of the code  requires the use of for loops and if statements that cannot be reexplained in this post. Below is the code with the output.

crossvalidation=KFold(n_splits=10,shuffle=True,random_state=1)

for depth in range (1,10):
tree_regressor=tree.DecisionTreeRegressor(max_depth=depth,random_state=1)
if tree_regressor.fit(X,y).tree_.max_depth<depth:
break
score=np.mean(cross_val_score(tree_regressor,X,y,scoring='neg_mean_squared_error', cv=crossvalidation,n_jobs=1))
print(depth, score)

 1 -193.55304528235052
 2 -176.27520747356175
 3 -209.2846723461564
 4 -218.80238479654003
 5 -222.4393459885871
 6 -249.95330609042858
 7 -286.76842138165705
 8 -294.0290706405905
 9 -287.39016236497804

You can see that a max depth of 2 had the lowest amount of error. Therefore, our baseline model has a mean squared error of 176. We need to improve on this in order to say that our gradient boosting model is superior.

However, before we create our gradient boosting model. we need to tune the hyperparameters of the algorithm.

Hyperparameter Tuning

Hyperparameter tuning has to with setting the value of parameters that the algorithm cannot learn on its own. As such, these are constants that you set as the researcher. The problem is that you are not any better at knowing where to set these values than the computer. Therefore, the process that is commonly used is to have the algorithm use several combinations  of values until it finds the values that are best for the model/. Having said this, there are several hyperparameters we need to tune, and they are as follows.

• number of estimators
• learning rate
• subsample
• max depth

The number of estimators is show many trees to create. The more trees the more likely to overfit. The learning rate is the weight that each tree has on the final prediction. Subsample is the proportion of the sample to use. Max depth was explained previously.

What we will do now is make an instance of the GradientBoostingRegressor. Next, we will create our grid with the various values for the hyperparameters. We will then take this grid and place it inside GridSearchCV function so that we can prepare to run our model. There are some arguments that need to be set inside the GridSearchCV function such as estimator, grid, cv, etc. Below is the code.

GBR=GradientBoostingRegressor()
search_grid={'n_estimators':[500,1000,2000],'learning_rate':[.001,0.01,.1],'max_depth':[1,2,4],'subsample':[.5,.75,1],'random_state':[1]}
search=GridSearchCV(estimator=GBR,param_grid=search_grid,scoring='neg_mean_squared_error',n_jobs=1,cv=crossvalidation)

We can now run the code and determine the best combination of hyperparameters and how well the model did base on the means squared error metric. Below is the code and the output.

search.fit(X,y)
search.best_params_
Out[13]: 
{'learning_rate': 0.01,
 'max_depth': 1,
 'n_estimators': 500,
 'random_state': 1,
 'subsample': 0.5}

search.best_score_
Out[14]: -160.51398257591643

The hyperparameter results speak for themselves. With this tuning we can see that the mean squared error is lower than with the baseline model. We can now move to the final step of taking these hyperparameter settings and see how they do on the dataset. The results should be almost the same.

Gradient Boosting Model Development

Below is the code and the output for the tuned gradient boosting model

GBR2=GradientBoostingRegressor(n_estimators=500,learning_rate=0.01,subsample=.5,max_depth=1,random_state=1)
score=np.mean(cross_val_score(GBR2,X,y,scoring='neg_mean_squared_error',cv=crossvalidation,n_jobs=1))
score
Out[18]: -160.77842893572068

These results were to be expected. The gradient boosting model has a better performance than the baseline regression tree model.

Conclusion

In this post, we looked at how to  use gradient boosting to improve a regression tree. By creating multiple models. Gradient boosting will almost certainly have a better performance than other type of algorithms that rely on only one model.