论文标题
使用力矩匹配在数据中学习线性对称性
Learning Linear Symmetries in Data Using Moment Matching
论文作者
论文摘要
在机器学习和统计学中，使用从专家知识中得出的对称性来简化问题或使用数据增强或惩罚等方法来改善性能。在本文中，我们考虑了直接以无模型方式从数据中直接从数据中学习此类对称性的无监督和半监督的问题。我们表明，在最坏的情况下，这个问题与图形自动形态问题一样困难。但是，如果我们仅限于协方差矩阵具有独特特征值的情况，那么特征向量也将是对称转换的特征向量。如果我们进一步限制寻找正交对称性，那么特征值将为1或-1，并且问题减少到确定哪些特征向量为哪个。我们从理论和经验上开发和比较不同方法在对称转换中应具有特征值-1的不同方法的有效性，并讨论如何将此方法扩展到我们具有标签的非正交案例
It is common in machine learning and statistics to use symmetries derived from expert knowledge to simplify problems or improve performance, using methods like data augmentation or penalties. In this paper we consider the unsupervised and semi-supervised problems of learning such symmetries in a distribution directly from data in a model-free fashion. We show that in the worst case this problem is as difficult as the graph automorphism problem. However, if we restrict to the case where the covariance matrix has unique eigenvalues, then the eigenvectors will also be eigenvectors of the symmetry transformation. If we further restrict to finding orthogonal symmetries, then the eigenvalues will be either be 1 or -1, and the problem reduces to determining which eigenvectors are which. We develop and compare theoretically and empirically the effectiveness of different methods of selecting which eigenvectors should have eigenvalue -1 in the symmetry transformation, and discuss how to extend this approach to non-orthogonal cases where we have labels
