Inference tasks in signal processing are often characterized by the availability of reliable statistical modeling with some missing instance-specific parameters. One conventional approach uses data to estimate these missing parameters and then infers based on the estimated model. Alternatively, data can also be leveraged to directly learn the inference mapping end-to-end. These approaches for combining partially-known statistical models and data in inference are related to the notions of generative and discriminative models used in the machine learning literature, typically considered in the context of classifiers. The goal of this lecture note is to introduce the concepts of generative and discriminative learning for inference with a partially-known statistical model. While machine learning systems often lack the interpretability of traditional signal processing methods, we focus on a simple setting where one can interpret and compare the approaches in a tractable manner that is accessible and relevant to signal processing readers. In particular, we exemplify the approaches for the task of Bayesian signal estimation in a jointly Gaussian setting with the mean-squared error (MSE) objective, i.e., a linear estimation setting.

翻译：信号处理中的推理任务通常以存在可靠的统计建模但缺失某些实例特定参数为特征。一种传统方法利用数据估计这些缺失参数，然后基于估计的模型进行推理。另一种方法则是直接利用数据端到端学习推理映射。这些将部分已知统计模型与数据相结合的推理方法，与机器学习文献中通常用于分类器的判别性模型和生成性模型的概念相关。本讲义旨在介绍针对部分已知统计模型的推理中生成性学习与判别性学习的概念。尽管机器学习系统往往缺乏传统信号处理方法所具有的可解释性，我们聚焦于一个简单场景，使得能够以易于信号处理读者理解且相关的方式进行可处理的解释和比较。具体而言，我们在联合高斯设定中以均方误差为目标（即线性估计场景）举例说明这些方法在贝叶斯信号估计任务中的应用。