Uniform Convergence of Rank-weighted Learning
Justin Khim, Liu Leqi, Adarsh Prasad, Pradeep Ravikumar
Abstract
The decision-theoretic foundations of classical machine learning models have largely focused on estimating model parameters that minimize the expectation of a given loss function. However, as machine learning models are deployed in varied contexts, such as in high-stakes decision-making and societal settings, it is clear that these models are not just evaluated by their average performances. In this work, we study a novel notion of L-Risk based on the classical idea of rank-weighted learning. These L-Risks, induced by rank-dependent weighting functions with bounded variation, is a unification of popular risk measures such as conditional value-at-risk and those defined by cumulative prospect theory. We give uniform convergence bounds of this broad class of risk measures and study their consequences on a logistic regression example.
BibTeX
@InProceedings{pmlr-v119-khim20a,
title = {Uniform Convergence of Rank-weighted Learning},
author = {Khim, Justin and Leqi, Liu and Prasad, Adarsh and Ravikumar, Pradeep},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {5254--5263},
year = {2020},
editor = {III, Hal Daumé and Singh, Aarti},
volume = {119},
series = {Proceedings of Machine Learning Research},
month = {13--18 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v119/khim20a/khim20a.pdf},
url = {https://proceedings.mlr.press/v119/khim20a.html},
abstract = {The decision-theoretic foundations of classical machine learning models have largely focused on estimating model parameters that minimize the expectation of a given loss function. However, as machine learning models are deployed in varied contexts, such as in high-stakes decision-making and societal settings, it is clear that these models are not just evaluated by their average performances. In this work, we study a novel notion of L-Risk based on the classical idea of rank-weighted learning. These L-Risks, induced by rank-dependent weighting functions with bounded variation, is a unification of popular risk measures such as conditional value-at-risk and those defined by cumulative prospect theory. We give uniform convergence bounds of this broad class of risk measures and study their consequences on a logistic regression example.}
}