Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecasting

by   Youngsuk Park, et al.

Quantile regression is an effective technique to quantify uncertainty, fit challenging underlying distributions, and often provide full probabilistic predictions through joint learnings over multiple quantile levels. A common drawback of these joint quantile regressions, however, is quantile crossing, which violates the desirable monotone property of the conditional quantile function. In this work, we propose the Incremental (Spline) Quantile Functions I(S)QF, a flexible and efficient distribution-free quantile estimation framework that resolves quantile crossing with a simple neural network layer. Moreover, I(S)QF inter/extrapolate to predict arbitrary quantile levels that differ from the underlying training ones. Equipped with the analytical evaluation of the continuous ranked probability score of I(S)QF representations, we apply our methods to NN-based times series forecasting cases, where the savings of the expensive re-training costs for non-trained quantile levels is particularly significant. We also provide a generalization error analysis of our proposed approaches under the sequence-to-sequence setting. Lastly, extensive experiments demonstrate the improvement of consistency and accuracy errors over other baselines.



There are no comments yet.


page 1

page 2

page 3

page 4


Non-crossing convex quantile regression

Quantile crossing is a common phenomenon in shape constrained nonparamet...

Multivariate Quantile Function Forecaster

We propose Multivariate Quantile Function Forecaster (MQF^2), a global p...

Deep Quantile Aggregation

Conditional quantile estimation is a key statistical learning challenge ...

Solution to the Non-Monotonicity and Crossing Problems in Quantile Regression

This paper proposes a new method to address the long-standing problem of...

Regularization Strategies for Quantile Regression

We investigate different methods for regularizing quantile regression wh...

Dynamic Connected Neural Decision Classifier and Regressor with Dynamic Softing Pruning

In the regression problem, L1, L2 are the most commonly-used loss functi...

A Multi-Level Simulation Optimization Approach for Quantile Functions

Quantile is a popular performance measure for a stochastic system to eva...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.