{ "id": "2211.14545", "version": "v1", "published": "2022-11-26T11:45:32.000Z", "updated": "2022-11-26T11:45:32.000Z", "title": "Ensemble Multi-Quantile: Adaptively Flexible Distribution Prediction for Uncertainty Quantification", "authors": [ "Xing Yan", "Yonghua Su", "Wenxuan Ma" ], "categories": [ "cs.LG" ], "abstract": "We propose a novel, succinct, and effective approach to quantify uncertainty in machine learning. It incorporates adaptively flexible distribution prediction for $\\mathbb{P}(\\mathbf{y}|\\mathbf{X}=x)$ in regression tasks. For predicting this conditional distribution, its 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 including Gaussian assumption-based, Bayesian methods, quantile regression-based, and traditional tree models, under the metrics of calibration, sharpness, and tail-side calibration. Visualization results show what we actually learn from the real data and how, illustrating the necessity and the merits of such an ensemble model.", "revisions": [ { "version": "v1", "updated": "2022-11-26T11:45:32.000Z" } ], "analyses": { "keywords": [ "uncertainty quantification", "ensemble multi-quantile", "emq achieves state-of-the-art performance", "real data", "regression tasks" ], "note": { "typesetting": "TeX", "pages": 0, "language": "en", "license": "arXiv", "status": "editable" } } }