In this paper, we propose a maximum margin classifier that deals with uncertainty in data input. More specifically, we reformulate the SVM framework such that each training example can be modeled by a multi-dimensional Gaussian distribution described by its mean vector and its covariance matrix-the latter modeling the uncertainty. We address the classification problem and define a cost function that is the expected value of the classical SVM cost when data samples are drawn from the multi-dimensional Gaussian distributions that form the set of the training examples. Our formulation approximates the classical SVM formulation when the training examples are isotropic Gaussians with variance tending to zero. We arrive at a convex optimization problem, which we solve efficiently in the primal form using a stochastic gradient descent approach. The resulting classifier, which we name SVM with Gaussian Sample Uncertainty (SVM-GSU), is tested on synthetic data and five publicly available and popular datasets; namely, the MNIST, WDBC, DEAP, TV News Channel Commercial Detection, and TRECVID MED datasets. Experimental results verify the effectiveness of the proposed method.

中文翻译：

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用于从不确定数据中学习的线性最大裕度分类器


在本文中，我们提出了一个最大间隔分类器来处理数据输入的不确定性。更具体地说，我们重新构建了 SVM 框架，使得每个训练样例都可以通过其均值向量和协方差矩阵描述的多维高斯分布进行建模，后者对不确定性进行建模。我们解决分类问题并定义一个成本函数，该函数是从形成训练示例集的多维高斯分布中抽取数据样本时经典 SVM 成本的期望值。当训练样本是方差趋于零的各向同性高斯分布时，我们的公式近似于经典的 SVM 公式。我们得到了一个凸优化问题，我们使用随机梯度下降方法以原始形式有效地解决了这个问题。由此产生的分类器，我们将其命名为具有高斯样本不确定性的 SVM (SVM-GSU)，在合成数据和五个公开可用且流行的数据集上进行了测试；即 MNIST、WDBC、DEAP、电视新闻频道商业检测和 TRECVID MED 数据集。实验结果验证了所提方法的有效性。