2020/06/05 by Shubhendu Trivedi, J. Wang, Trivedi, Shubhendu +1 · 1 citation
Computer Science · #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Face and Expression Recognition #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms
paper · pdf · doi:10.48550/arxiv.2006.03550
openalex publication_date 2020/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.