  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.

Signal Processing;Machine Learning