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

• URL: http://arxiv.org/abs/2211.14545v3
• Date: Mon, 29 May 2023 04:24:24 GMT
• Title: Ensemble Multi-Quantiles: Adaptively Flexible Distribution Prediction for Uncertainty Quantification
• Authors: Xing Yan, Yonghua Su, Wenxuan Ma
• Abstract summary: We propose a novel, succinct, and effective approach for distribution prediction to quantify uncertainty in machine learning. It incorporates adaptively flexible distribution prediction of $mathbbP(mathbfy|mathbfX=x)$ in regression tasks. On extensive regression tasks from UCI datasets, we show that EMQ achieves state-of-the-art performance.
• Score: 4.728311759896569
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

Related papers

• Score-based generative models are provably robust: an uncertainty quantification perspective [4.396860522241307]
  We show that score-based generative models (SGMs) are provably robust to the multiple sources of error in practical implementation. Our primary tool is the Wasserstein uncertainty propagation (WUP) theorem. We show how errors due to (a) finite sample approximation, (b) early stopping, (c) score-matching objective choice, (d) score function parametrization, and (e) reference distribution choice, impact the quality of the generative model.
  arXiv  Detail & Related papers  (2024-05-24T17:50:17Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• Sample Complexity of Variance-reduced Distributionally Robust Q-learning [17.96094201655567]
  This paper presents two novel model-free algorithms, namely the distributionally robust Q-learning and its variance-reduced counterpart, that can effectively learn a robust policy despite distributional shifts. A series of numerical experiments confirm the theoretical findings and the efficiency of the algorithms in handling distributional shifts.
  arXiv  Detail & Related papers  (2023-05-28T19:40:46Z)
• Scalable Dynamic Mixture Model with Full Covariance for Probabilistic Traffic Forecasting [16.04029885574568]
  We propose a dynamic mixture of zero-mean Gaussian distributions for the time-varying error process. The proposed method can be seamlessly integrated into existing deep-learning frameworks with only a few additional parameters to be learned. We evaluate the proposed method on a traffic speed forecasting task and find that our method not only improves model horizons but also provides interpretabletemporal correlation structures.
  arXiv  Detail & Related papers  (2022-12-10T22:50:00Z)
• Distributional Gradient Boosting Machines [77.34726150561087]
  Our framework is based on XGBoost and LightGBM. We show that our framework achieves state-of-the-art forecast accuracy.
  arXiv  Detail & Related papers  (2022-04-02T06:32:19Z)
• Multivariate Probabilistic Regression with Natural Gradient Boosting [63.58097881421937]
  We propose a Natural Gradient Boosting (NGBoost) approach based on nonparametrically modeling the conditional parameters of the multivariate predictive distribution. Our method is robust, works out-of-the-box without extensive tuning, is modular with respect to the assumed target distribution, and performs competitively in comparison to existing approaches.
  arXiv  Detail & Related papers  (2021-06-07T17:44:49Z)
• Probabilistic Circuits for Variational Inference in Discrete Graphical Models [101.28528515775842]
  Inference in discrete graphical models with variational methods is difficult. Many sampling-based methods have been proposed for estimating Evidence Lower Bound (ELBO) We propose a new approach that leverages the tractability of probabilistic circuit models, such as Sum Product Networks (SPN) We show that selective-SPNs are suitable as an expressive variational distribution, and prove that when the log-density of the target model is aweighted the corresponding ELBO can be computed analytically.
  arXiv  Detail & Related papers  (2020-10-22T05:04:38Z)
• Mean-Field Approximation to Gaussian-Softmax Integral with Application to Uncertainty Estimation [23.38076756988258]
  We propose a new single-model based approach to quantify uncertainty in deep neural networks. We use a mean-field approximation formula to compute an analytically intractable integral. Empirically, the proposed approach performs competitively when compared to state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-06-13T07:32:38Z)
• A Precise High-Dimensional Asymptotic Theory for Boosting and Minimum-$\ell_1$-Norm Interpolated Classifiers [3.167685495996986]
  This paper establishes a precise high-dimensional theory for boosting on separable data. Under a class of statistical models, we provide an exact analysis of the universality error of boosting. We also explicitly pin down the relation between the boosting test error and the optimal Bayes error.
  arXiv  Detail & Related papers  (2020-02-05T00:24:53Z)
• Distributionally Robust Bayesian Quadrature Optimization [60.383252534861136]
  We study BQO under distributional uncertainty in which the underlying probability distribution is unknown except for a limited set of its i.i.d. samples. A standard BQO approach maximizes the Monte Carlo estimate of the true expected objective given the fixed sample set. We propose a novel posterior sampling based algorithm, namely distributionally robust BQO (DRBQO) for this purpose.
  arXiv  Detail & Related papers  (2020-01-19T12:00:33Z)
• CatBoostLSS -- An extension of CatBoost to probabilistic forecasting [91.3755431537592]
  We propose a new framework that predicts the entire conditional distribution of a univariable response variable. CatBoostLSS models all moments of a parametric distribution instead of the conditional mean only. We present both a simulation study and real-world examples that demonstrate the benefits of our approach.
  arXiv  Detail & Related papers  (2020-01-04T15:42:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.