# Calibrated Multiple-Output Quantile Regression with Representation Learning

**Authors:** Shai Feldman, Stephen Bates, Yaniv Romano  
**arXiv:** [2110.00816](https://arxiv.org/abs/2110.00816)  
**Date:** 2021-10-02  
**Summary page:** https://www.summarizepaper.com/en/paper/2110.00816v2/

## Key points

- Authors introduce a novel method for generating predictive regions encompassing a multivariate response variable
- Methodology consists of two key components: deep generative model and existing multiple-output quantile regression techniques
- Approach yields flexible and informative regions capable of assuming arbitrary shapes
- Extension of conformal prediction tailored to the multivariate response context is proposed
- Experimental results show that the method constructs significantly smaller regions compared to established techniques, demonstrating efficacy and potential for practical applications

## Summary

In their paper titled "Calibrated Multiple-Output Quantile Regression with Representation Learning," authors Shai Feldman, Stephen Bates, and Yaniv Romano introduce a novel method for generating predictive regions that encompass a multivariate response variable with a specified probability. The methodology consists of two key components: a deep generative model to acquire a representation of the response characterized by a unimodal distribution, and the application of existing multiple-output quantile regression techniques to this learned representation. This innovative approach yields flexible and informative regions capable of assuming arbitrary shapes - a feature lacking in conventional methodologies. Additionally, the authors propose an extension of conformal prediction tailored to the multivariate response context. This enables any method to output sets with predetermined coverage levels, providing theoretical assurance of achieving the desired coverage in finite-sample scenarios across all distributions. This enhances the robustness and reliability of their approach. Through experiments conducted on both real-world and synthetic datasets, it was demonstrated that their method constructs significantly smaller regions compared to established techniques. This underscores its efficacy and potential for practical applications in predictive modeling and uncertainty quantification.