论文标题
无限梯度提升的大型样本理论
A large sample theory for infinitesimal gradient boosting
论文作者
论文摘要
无穷小的梯度提升（Dombry和Duchamps，2021）被定义为从机器学习中流行的基于树的梯度增强算法的消失的学习率极限。它的特征是在无限二维函数空间中非线性普通微分方程的解，其中无穷小的增强操作员驱动动力学取决于训练样本。我们考虑模型在较大的样本限制中的渐近行为，并证明其收敛到确定性过程。该人口限制再次以差分方程为特征，该方程取决于人口分布。我们探讨了该人群限制的某些特性：我们证明了动态使测试误差减少，并且我们考虑其长时间行为。
Infinitesimal gradient boosting (Dombry and Duchamps, 2021) is defined as the vanishing-learning-rate limit of the popular tree-based gradient boosting algorithm from machine learning. It is characterized as the solution of a nonlinear ordinary differential equation in a infinite-dimensional function space where the infinitesimal boosting operator driving the dynamics depends on the training sample. We consider the asymptotic behavior of the model in the large sample limit and prove its convergence to a deterministic process. This population limit is again characterized by a differential equation that depends on the population distribution. We explore some properties of this population limit: we prove that the dynamics makes the test error decrease and we consider its long time behavior.
