A Robust Learning Approach for Regression Models Based on Distributionally Robust Optimization.

IF 4.3 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS
Journal of Machine Learning Research Pub Date : 2018-01-01
Ruidi Chen, Ioannis Ch Paschalidis
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引用次数: 0

Abstract

We present a Distributionally Robust Optimization (DRO) approach to estimate a robustified regression plane in a linear regression setting, when the observed samples are potentially contaminated with adversarially corrupted outliers. Our approach mitigates the impact of outliers by hedging against a family of probability distributions on the observed data, some of which assign very low probabilities to the outliers. The set of distributions under consideration are close to the empirical distribution in the sense of the Wasserstein metric. We show that this DRO formulation can be relaxed to a convex optimization problem which encompasses a class of models. By selecting proper norm spaces for the Wasserstein metric, we are able to recover several commonly used regularized regression models. We provide new insights into the regularization term and give guidance on the selection of the regularization coefficient from the standpoint of a confidence region. We establish two types of performance guarantees for the solution to our formulation under mild conditions. One is related to its out-of-sample behavior (prediction bias), and the other concerns the discrepancy between the estimated and true regression planes (estimation bias). Extensive numerical results demonstrate the superiority of our approach to a host of regression models, in terms of the prediction and estimation accuracies. We also consider the application of our robust learning procedure to outlier detection, and show that our approach achieves a much higher AUC (Area Under the ROC Curve) than M-estimation (Huber, 1964, 1973).

Abstract Image

Abstract Image

Abstract Image

基于分布鲁棒优化的回归模型鲁棒学习方法。
我们提出了一种分布鲁棒优化(DRO)方法来估计线性回归设置中的鲁棒回归平面,当观察到的样本可能受到对抗性异常值的污染时。我们的方法通过对冲观测数据上的一系列概率分布来减轻异常值的影响,其中一些将非常低的概率分配给异常值。所考虑的分布集在瓦瑟斯坦度量的意义上接近经验分布。我们证明这个DRO公式可以松弛为一个包含一类模型的凸优化问题。通过为Wasserstein度量选择适当的范数空间,我们能够恢复几个常用的正则化回归模型。我们对正则化项提供了新的见解,并从置信域的角度对正则化系数的选择提供了指导。在温和的条件下,我们建立了两种类型的性能保证。一个是关于它的样本外行为(预测偏差),另一个是关于估计和真实回归平面之间的差异(估计偏差)。大量的数值结果表明,我们的方法在预测和估计精度方面优于许多回归模型。我们还考虑将鲁棒学习过程应用于离群值检测,并表明我们的方法实现了比m估计高得多的AUC (ROC曲线下的面积)(Huber, 1964,1973)。
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来源期刊
Journal of Machine Learning Research
Journal of Machine Learning Research 工程技术-计算机:人工智能
CiteScore
18.80
自引率
0.00%
发文量
2
审稿时长
3 months
期刊介绍: The Journal of Machine Learning Research (JMLR) provides an international forum for the electronic and paper publication of high-quality scholarly articles in all areas of machine learning. All published papers are freely available online. JMLR has a commitment to rigorous yet rapid reviewing. JMLR seeks previously unpublished papers on machine learning that contain: new principled algorithms with sound empirical validation, and with justification of theoretical, psychological, or biological nature; experimental and/or theoretical studies yielding new insight into the design and behavior of learning in intelligent systems; accounts of applications of existing techniques that shed light on the strengths and weaknesses of the methods; formalization of new learning tasks (e.g., in the context of new applications) and of methods for assessing performance on those tasks; development of new analytical frameworks that advance theoretical studies of practical learning methods; computational models of data from natural learning systems at the behavioral or neural level; or extremely well-written surveys of existing work.
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