论文标题
解决高斯混合物的可靠学习性
Settling the Robust Learnability of Mixtures of Gaussians
论文作者
论文摘要
这项工作代表了两种重要工作线的自然合并：高斯学习混合物和算法稳定的统计数据。特别是，我们为学习任何恒定数量的高斯人学习混合物提供了第一种可证明的强大算法。我们只需要对混合权重（有界的分级性）进行温和的假设，并且组件之间的总变化距离远离零。我们算法的核心是一种新方法，用于通过将差异操作的精心选择的差分操作序列应用于某些生成函数，不仅编码我们想要学习的参数，而且我们希望求解的多种方程式。我们展示了我们得出的符号身份如何直接用于分析自然平方的松弛。
This work represents a natural coalescence of two important lines of work: learning mixtures of Gaussians and algorithmic robust statistics. In particular we give the first provably robust algorithm for learning mixtures of any constant number of Gaussians. We require only mild assumptions on the mixing weights (bounded fractionality) and that the total variation distance between components is bounded away from zero. At the heart of our algorithm is a new method for proving dimension-independent polynomial identifiability through applying a carefully chosen sequence of differential operations to certain generating functions that not only encode the parameters we would like to learn but also the system of polynomial equations we would like to solve. We show how the symbolic identities we derive can be directly used to analyze a natural sum-of-squares relaxation.
