Ensemble Multi-Quantiles: Adaptively Flexible Distribution Prediction for Uncertainty Quantification

TL;DR

This paper introduces EMQ, an adaptive ensemble multi-quantile method for distribution prediction in regression, which improves uncertainty quantification by balancing flexibility and structure, outperforming existing methods on UCI datasets.

Contribution

The paper presents EMQ, a novel data-driven ensemble approach that adaptively learns the conditional distribution for uncertainty quantification, surpassing traditional Gaussian and flexible quantile methods.

Findings

EMQ achieves state-of-the-art performance on UCI regression datasets.

The method effectively balances model flexibility and structural integrity.

Visualization confirms the advantages of the ensemble multi-quantile approach.

Abstract

We propose a novel, succinct, and effective approach for distribution prediction to quantify uncertainty in machine learning. It incorporates adaptively flexible distribution prediction of $\mathbb{P}(\mathbf{y}|\mathbf{X}=x)$ in regression tasks. This conditional distribution's quantiles of probability levels spreading the interval $(0,1)$ are boosted by additive models which are designed by us with intuitions and interpretability. We seek an adaptive balance between the structural integrity and the flexibility for $\mathbb{P}(\mathbf{y}|\mathbf{X}=x)$, while Gaussian assumption results in a lack of flexibility for real data and highly flexible approaches (e.g., estimating the quantiles separately without a distribution structure) inevitably have drawbacks and may not lead to good generalization. This ensemble multi-quantiles approach called EMQ proposed by us is totally data-driven, and can gradually depart from Gaussian and discover the optimal conditional distribution in the boosting. On extensive regression tasks from UCI datasets, we show that EMQ achieves state-of-the-art performance comparing to many recent uncertainty quantification methods. Visualization results further illustrate the necessity and the merits of such an ensemble model.