# Auxiliary Quantile Forecasting with Linear Networks

arXiv: https://arxiv.org/abs/2212.02578 · HTML: https://mlsanity.com/paper/2212.02578/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 11 references that are in the map.
- First posted on arXiv 5 Dec 2022.

## Builds on (most cited first, 9 of 9)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecasting](https://mlsanity.com/paper/2111.06581/) (2021)
- [Probabilistic Time Series Forecasting with Implicit Quantile Networks](https://mlsanity.com/paper/2107.03743/) (2021)

## Abstract (arXiv)

We propose a novel multi-task method for quantile forecasting with shared Linear layers. Our method is based on the Implicit quantile learning approach, where samples from the Uniform distribution U(0, 1) are reparameterized to quantile values of the target distribution. We combine the implicit quantile and input time series representations to directly forecast multiple quantile estimations for multiple horizons jointly. Prior works have adopted a Linear layer for the direct estimation of all forecasting horizons in a multi-task learning setup. We show that following similar intuition from multi-task learning to exploit correlations among forecast horizons, we can model multiple quantile estimates as auxiliary tasks for each of the forecast horizon to improve forecast accuracy across the quantile estimates compared to modeling only a single quantile estimate. We show learning auxiliary quantile tasks leads to state-of-the-art performance on deterministic forecasting benchmarks concerning the main-task of forecasting the 50th percentile estimate.