[3] Explicit regression gradient boosting algorithms were subsequently developed, by Jerome H. Friedman,[4][2] (in 1999 and later in 2001) simultaneously with the more general functional gradient boosting perspective of Llew Mason, Jonathan Baxter, Peter Bartlett and Marcus Frean.
A generalization of this idea to loss functions other than squared error, and to classification and ranking problems, follows from the observation that residuals
for a given model are proportional to the negative gradients of the mean squared error (MSE) loss function (with respect to
at each step for an arbitrary loss function L is a computationally infeasible optimization problem in general.
is finite[clarification needed], we choose the candidate function h closest to the gradient of L for which the coefficient γ may then be calculated with the aid of line search on the above equations.
Note that this approach is a heuristic and therefore doesn't yield an exact solution to the given problem, but rather an approximation.
number of iterations M. Algorithm: Gradient boosting is typically used with decision trees (especially CARTs) of a fixed size as base learners.
For this special case, Friedman proposes a modification to gradient boosting method which improves the quality of fit of each base learner.
Generic gradient boosting at the m-th step would fit a decision tree
, chosen using line search so as to minimize the loss function, and the model is updated as follows: Friedman proposes to modify this algorithm so that it chooses a separate optimal value
of terminal nodes in the trees is a parameter which controls the maximum allowed level of interaction between variables in the model.
Fitting the training set too closely can lead to degradation of the model's generalization ability, that is, its performance on unseen examples.
Several so-called regularization techniques reduce this overfitting effect by constraining the fitting procedure.
An optimal value of M is often selected by monitoring prediction error on a separate validation data set.
An important part of gradient boosting is regularization by shrinkage which uses a modified update rule: where parameter
) yields dramatic improvements in models' generalization ability over gradient boosting without shrinking (
[1] However, it comes at the price of increasing computational time both during training and querying: lower learning rate requires more iterations.
Soon after the introduction of gradient boosting, Friedman proposed a minor modification to the algorithm, motivated by Breiman's bootstrap aggregation ("bagging") method.
[2] Specifically, he proposed that at each iteration of the algorithm, a base learner should be fit on a subsample of the training set drawn at random without replacement.
introduce randomness into the algorithm and help prevent overfitting, acting as a kind of regularization.
Out-of-bag estimates help avoid the need for an independent validation dataset, but often underestimate actual performance improvement and the optimal number of iterations.
It is used in the tree building process by ignoring any splits that lead to nodes containing fewer than this number of training set instances.
At the Large Hadron Collider (LHC), variants of gradient boosting Deep Neural Networks (DNN) were successful in reproducing the results of non-machine learning methods of analysis on datasets used to discover the Higgs boson.
[16] Gradient boosting decision tree was also applied in earth and geological studies – for example quality evaluation of sandstone reservoir.
[4] Mason, Baxter et al. described the generalized abstract class of algorithms as "functional gradient boosting".
[5][6] Friedman et al. describe an advancement of gradient boosted models as Multiple Additive Regression Trees (MART);[18] Elith et al. describe that approach as "Boosted Regression Trees" (BRT).
[19] A popular open-source implementation for R calls it a "Generalized Boosting Model",[11] however packages expanding this work use BRT.
[20] Yet another name is TreeNet, after an early commercial implementation from Salford System's Dan Steinberg, one of researchers who pioneered the use of tree-based methods.
[22] For example, if a gradient boosted trees algorithm is developed using entropy-based decision trees, the ensemble algorithm ranks the importance of features based on entropy as well with the caveat that it is averaged out over all base learners.
[22][1] While boosting can increase the accuracy of a base learner, such as a decision tree or linear regression, it sacrifices intelligibility and interpretability.