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2007 NIPS NeurIPS 2007

How SVMs can estimate quantiles and the median

Abstract

We investigate quantile regression based on the pinball loss and the ǫ-insensitive loss. For the pinball loss a condition on the data-generating distribution P is given that ensures that the conditional quantiles are approximated with respect to k · k1. This result is then used to derive an oracle inequality for an SVM based on the pinball loss. Moreover, we show that SVMs based on the ǫ-insensitive loss estimate the conditional median only under certain conditions on P .

🌉 Interdisciplinary Bridge — Machine Learning and Mathematics & Optimization
📈 Trend Setter — Loss Functions
🧭 Keyword Pioneer — quantile regression
🐝 Cross-Pollinator — Artificial Intelligence, Computer Science, Computer Vision, Data Science & Analytics, Deep Learning, Healthcare & Medicine, Knowledge & Reasoning, Machine Learning, Mathematics & Optimization, Natural Language Processing, Reinforcement Learning, Robotics, Speech & Audio

Authors

Andreas Christmann , Ingo Steinwart

Topics

Machine Learning > Core Methods > Classification Machine Learning > Core Methods > Regression Machine Learning > Optimization & Theory > Loss Functions Mathematics & Optimization > Mathematics > Statistics Machine Learning > Learning Types > Metric Learning Machine Learning > Core Methods > Support Vector Machine Machine Learning > Learning Types > Regression

Keywords

oracle inequality quantile regression pinball loss median estimation epsilon-insensitive loss support vector machine
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