论文标题
预期的雅各布外生产：理论与经验
The Expected Jacobian Outerproduct: Theory and Empirics
论文作者
论文摘要
未知回归函数的预期梯度外生产（EGOP）是在多指数回归理论中产生的操作员，并且已知可以恢复与预测输出最相关的方向。但是，在包括其廉价估计器在内的EGOP上进行的工作仅限于回归设置。在这项工作中，我们将该操作员调整为多级设置，我们将预期的Jacobian Outerproduct（EJOP）配音。此外，我们提出了一个简单的EJOP粗略估计器，并表明在轻度假设下，它在统计学上保持一致。此外，我们表明特征值和特征空间也保持一致。最后，我们表明，估计的EJOP可以用作指标，以在现实世界中的非参数分类任务中得到改进：既通过用作度量标准，又是廉价的度量学习任务。
The expected gradient outerproduct (EGOP) of an unknown regression function is an operator that arises in the theory of multi-index regression, and is known to recover those directions that are most relevant to predicting the output. However, work on the EGOP, including that on its cheap estimators, is restricted to the regression setting. In this work, we adapt this operator to the multi-class setting, which we dub the expected Jacobian outerproduct (EJOP). Moreover, we propose a simple rough estimator of the EJOP and show that somewhat surprisingly, it remains statistically consistent under mild assumptions. Furthermore, we show that the eigenvalues and eigenspaces also remain consistent. Finally, we show that the estimated EJOP can be used as a metric to yield improvements in real-world non-parametric classification tasks: both by its use as a metric, and also as cheap initialization in metric learning tasks.
