以少胜多：一种基于张量优化的集成方法
Achieving More with Less: A Tensor-Optimization-Powered Ensemble Method
AI总结：
本文提出一种基于张量优化的集成方法，引入置信张量评估基分类器在不同类别上的性能，结合光滑部分凸的带间隔目标函数，仅用少量基学习器即可获得更优分类与泛化性能。
摘要：
集成学习是利用弱学习器生成强学习器的方法，但获取大量基学习器需要消耗大量时间和计算资源，因此研究如何仅用少量基学习器达到通常由大量基学习器获得的性能具有重要意义。本文认为，要实现这一目标，需在集成过程中同时提升分类性能和泛化能力。为提高模型精度，需更高效地整合每个弱基学习器；研究发现，不同基学习器对不同类别的预测准确率存在差异，为此本文引入置信张量$\tilde{\boldsymbol{\theta}}$，其中$\tilde{\boldsymbol{\theta}}_{rst}$表示第$t$个基分类器将样本预测为类别$r$而样本实际属于类别$s$的置信度，据本文所知，这是首次提出对基分类器在不同类别上的性能进行评估，该置信张量可弥补每个基分类器在不同类别上的优缺点，使方法能用更少的基学习器获得更优结果。为提升泛化性能，本文设计了利用间隔概念的光滑且部分凸的目标函数，使强学习器更具判别性；此外，本文证明损失函数的梯度矩阵中每列元素之和为零，这使得可以使用基于梯度的方法求解带约束的优化问题。
英文摘要：
Ensemble learning is a method that leverages weak learners to produce a strong learner. However, obtaining a large number of base learners requires substantial time and computational resources. Therefore, it is meaningful to study how to achieve the performance typically obtained with many base learners using only a few. We argue that to achieve this, it is essential to enhance both classification performance and generalization ability during the ensemble process. To increase model accuracy, each weak base learner needs to be more efficiently integrated. It is observed that different base learners exhibit varying levels of accuracy in predicting different classes. To capitalize on this, we introduce confidence tensors $\tilde{\mathbfΘ}$, where $\tilde{\mathbfΘ}_{rst}$ signifies the degree of confidence that the $t$-th base classifier assigns the sample to class $r$ while it actually belongs to class $s$. To the best of our knowledge, this is the first time an evaluation of the performance of base classifiers across different classes has been proposed. The proposed confidence tensor compensates for the strengths and weaknesses of each base classifier in different classes, enabling the method to achieve superior results with a smaller number of base learners. To enhance generalization performance, we design a smooth and partially convex objective function that leverages the concept of margin, making the strong learner more discriminative. Furthermore, it is proved that in the gradient matrix of the loss function, the sum of each column's elements is zero, allowing us to solve a constrained optimization problem using gradient-based methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
