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

Xing YAN, Yonghua Su, Wenxuan Ma

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 P(y|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 intu-itions and interpretability. We seek an adaptive balance between the structural integrity and the flexibility for P(y|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 con-ditional 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.