Learning a parametric model from a given dataset indeed enables to capture intrinsic dependencies between random variables via a parametric conditional probability distribution and in turn predict the value of a label variable given observed variables. In this paper, we undertake a comparative analysis of generative and discriminative approaches which differ in their construction and the structure of the underlying inference problem. Our objective is to compare the ability of both approaches to leverage information from various sources in an epistemic uncertainty aware inference via the posterior predictive distribution. We assess the role of a prior distribution, explicit in the generative case and implicit in the discriminative case, leading to a discussion about discriminative models suffering from imbalanced dataset. We next examine the double role played by the observed variables in the generative case, and discuss the compatibility of both approaches with semi-supervised learning. We also provide with practical insights and we examine how the modeling choice impacts the sampling from the posterior predictive distribution. With regard to this, we propose a general sampling scheme enabling supervised learning for both approaches, as well as semi-supervised learning when compatible with the considered modeling approach. Throughout this paper, we illustrate our arguments and conclusions using the example of affine regression, and validate our comparative analysis through classification simulations using neural network based models.

翻译：从给定数据集中学习参数化模型确实能够通过参数化条件概率分布捕捉随机变量之间的内在依赖关系，进而基于观测变量预测标签变量的取值。本文对生成式与判别式方法进行了比较分析，这两种方法在其构建方式和底层推理问题的结构上存在差异。我们的目标是比较两种方法在通过后验预测分布进行认知不确定性感知推理时，利用来自不同来源信息的能力。我们评估了先验分布的作用——在生成式方法中显式存在，在判别式方法中隐式存在——并由此讨论了判别式模型在处理不平衡数据集时面临的困境。接着，我们探讨了观测变量在生成式方法中扮演的双重角色，并讨论了两种方法与半监督学习的兼容性。我们还提供了实践见解，研究了建模选择如何影响从后验预测分布中采样的过程。为此，我们提出了一种通用的采样方案，该方案支持两种方法的监督学习，并在与所考虑的建模方法兼容时支持半监督学习。本文通过仿射回归的示例阐释了我们的论点和结论，并基于神经网络的分类模拟验证了我们的比较分析。