We study one-way matching of a pair of datasets with low rank signals. Under a stylized model, we first derive information-theoretic limits of matching. We then show that linear assignment with projected data achieves fast rates of convergence and sometimes even minimax rate optimality for this task. The theoretical error bounds are corroborated by simulated examples. Furthermore, we illustrate practical use of the matching procedure on two single-cell data examples.

翻译：我们研究一对数据集与低级信号的单向匹配。 在一种标准化模型下, 我们首先得出匹配的信息理论极限。 然后我们显示, 与预测数据的线性分配可以实现快速的趋同率, 有时甚至最小速率最佳化 。 模拟的例子证实了理论错误界限。 此外, 我们用两个单细胞数据示例来说明匹配程序的实际使用 。