为SVM预测引入不确定性量化,提升可靠性与可解释性。
Uncertainty Quantification in SVM prediction
- 提出稀疏支持向量分位数回归模型,通过线性规划构建预测区间。
- 在高维数据上实现特征筛选,显著减少冗余特征并提升区间质量。
- 结合置信回归框架,获得有限样本保证的稳定预测集,适合严谨场景。
本文研究SVM预测中的不确定性量化(UQ),尤其针对回归与预测任务。尽管SVM解具有稳定性、稀疏性、最优性和可解释性优势,但现有文献对SVM的不确定性量化研究较少。我们系统综述了现有SVM框架下的预测区间(PI)估计与概率预测方法,并评估其是否满足理想PI模型的关键特性。发现现有模型均未实现稀疏解。为此,提出稀疏支持向量分位数回归(SSVQR)模型,通过求解一对线性规划构建预测区间与概率预测。进一步设计基于SSVQR的特征选择算法,在高维数据下有效剔除大量冗余特征,同时提升预测区间质量。最后,将SVM扩展至置信回归设置,获得具有有限测试集保证的稳定预测集。在人工数据与真实世界基准数据集上的大量实验比较了各类方法特性,验证了所提方法的优势。此外,与现代深度学习模型对比表明,所提SVM方法在概率预测任务中表现相当或更优。
原文摘要 · Abstract (English)
This paper explores Uncertainty Quantification (UQ) in SVM predictions, particularly for regression and forecasting tasks. Unlike the Neural Network, the SVM solutions are typically more stable, sparse, optimal and interpretable. However, there are only few literature which addresses the UQ in SVM prediction. At first, we provide a comprehensive summary of existing Prediction Interval (PI) estimation and probabilistic forecasting methods developed in the SVM framework and evaluate them against the key properties expected from an ideal PI model. We find that none of the existing SVM PI models achieves a sparse solution. To introduce sparsity in SVM model, we propose the Sparse Support Vector Quantile Regression (SSVQR) model, which constructs PIs and probabilistic forecasts by solving a pair of linear programs. Further, we develop a feature selection algorithm for PI estimation using SSVQR that effectively eliminates a significant number of features while improving PI quality in case of high-dimensional dataset. Finally we extend the SVM models in Conformal Regression setting for obtaining more stable prediction set with finite test set guarantees. Extensive experiments on artificial, real-world benchmark datasets compare the different characteristics of both existing and proposed SVM-based PI estimation methods and also highlight the advantages of the feature selection in PI estimation. Furthermore, we compare both, the existing and proposed SVM-based PI estimation models, with modern deep learning models for probabilistic forecasting tasks on benchmark datasets. Furthermore, SVM models show comparable or superior performance to modern complex deep learning models for probabilistic forecasting task in our experiments.
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