Abstract Gaussian discriminant analysis is a popular classification model, that in the precise case can produce unreliable predictions in case of high uncertainty (e.g., due to scarce or noisy data). While imprecise probability theory offers a nice theoretical framework to solve such issues, it has not been yet applied to Gaussian discriminant analysis. This work remedies this, by proposing a new Gaussian discriminant analysis based on robust Bayesian analysis and near-ignorance priors. The model delivers cautious predictions, in form of set-valued class, in case of limited or imperfect available information. We present and discuss results of experimentation on real and synthetic datasets, where for this latter we corrupt the test instance to see how our approach reacts to non i.i.d. samples. Experiments show that including an imprecise component in the Gaussian discriminant analysis produces reasonably cautious predictions, and that set-valued predictions correspond to instances for which the precise model performs poorly.

中文翻译：

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不精确的高斯判别分类

摘要 高斯判别分析是一种流行的分类模型，在精确的情况下，在高度不确定的情况下（例如，由于稀缺或嘈杂的数据）会产生不可靠的预测。虽然不精确概率论提供了一个很好的理论框架来解决这些问题，但它尚未应用于高斯判别分析。这项工作通过提出一种基于鲁棒贝叶斯分析和近乎无知先验的新高斯判别分析来解决这个问题。在可用信息有限或不完善的情况下，该模型以集合值类的形式提供谨慎的预测。我们展示并讨论了真实和合成数据集的实验结果，对于后者，我们破坏了测试实例以查看我们的方法如何对非 iid 样本做出反应。