二进制分类自适应提升中的量子加速
Quantum Speedup in Adaptive Boosting of Binary Classification
摘要：
在经典机器学习中，一组弱分类器可以自适应地组合成一个强分类器，以提高整体性能，这种技术称为自适应增强（或AdaBoost）。然而，为大数据集构造强分类器通常是消耗资源的。在这里，我们提出了一个量子扩展的AdaBoost，展示了一个量子算法，可以输出最佳的强分类器的查询的数量的二次加速。我们的研究结果还包括一个泛化的标准AdaBoost的情况下，每个分类器的输出可能是概率，即使是相同的输入。我们证明了非确定性分类器的更新规则和查询复杂度与确定性分类器相同，这可能是经典机器学习界独立感兴趣的。此外，AdaBoost算法也可以应用于以量子态形式编码的数据;我们展示了如何通过使用t-设计工具来简化训练集。我们的方法描述了一个量子机器学习模型，其中在寻找最佳分类器时实现了量子加速，然后可以将其应用于经典机器学习应用。
英文摘要：
In classical machine learning, a set of weak classifiers can be adaptively combined to form a strong classifier for improving the overall performance, a technique called adaptive boosting (or AdaBoost). However, constructing the strong classifier for a large data set is typically resource consuming. Here we propose a quantum extension of AdaBoost, demonstrating a quantum algorithm that can output the optimal strong classifier with a quadratic speedup in the number of queries of the weak classifiers. Our results also include a generalization of the standard AdaBoost to the cases where the output of each classifier may be probabilistic even for the same input. We prove that the update rules and the query complexity of the non-deterministic classifiers are the same as those of deterministic classifiers, which may be of independent interest to the classical machine-learning community. Furthermore, the AdaBoost algorithm can also be applied to data encoded in the form of quantum states; we show how the training set can be simplified by using the tools of t-design. Our approach describes a model of quantum machine learning where quantum speedup is achieved in finding the optimal classifier, which can then be applied for classical machine-learning applications.
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