# Discriminative and Generative Learning for Linear Estimation of Random Signals [Lecture Notes]

arXiv: https://arxiv.org/abs/2206.04432 · HTML: https://mlsanity.com/paper/2206.04432/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 12 references that are in the map.
- First posted on arXiv 9 Jun 2022.

## Builds on (most cited first, 5 of 5)

- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization](https://mlsanity.com/paper/2205.02640/) (2022)
- [Learning Convex Optimization Models](https://mlsanity.com/paper/2006.04248/) (2020)
- [Cramer-Rao Bound for Estimation After Model Selection and its Application to Sparse Vector Estimation](https://mlsanity.com/paper/1904.06837/) (2019)

## Built on by (most cited first, 14 of 14)

- [GSP-KalmanNet: Tracking Graph Signals via Neural-Aided Kalman Filtering](https://mlsanity.com/paper/2311.16602/) (2023)
- [SubspaceNet: Deep Learning-Aided Subspace Methods for DoA Estimation](https://mlsanity.com/paper/2306.02271/) (2023)
- [Blind Channel Estimation and Joint Symbol Detection with Data-Driven Factor Graphs](https://mlsanity.com/paper/2401.12627/) (2024)
- [AI-Aided Kalman Filters](https://mlsanity.com/paper/2410.12289/) (2024)
- [Neural Augmented Kalman Filtering with Bollinger Bands for Pairs Trading](https://mlsanity.com/paper/2210.15448/) (2022)
- [Limited Communications Distributed Optimization via Deep Unfolded Distributed ADMM](https://mlsanity.com/paper/2309.14353/) (2023)
- [Near Field Localization via AI-Aided Subspace Methods](https://mlsanity.com/paper/2504.00599/) (2025)
- [OLALa: Online Learned Adaptive Lattice Codes for Heterogeneous Federated Learning](https://mlsanity.com/paper/2506.20297/) (2025)
- [LQGNet: Hybrid Model-Based and Data-Driven Linear Quadratic Stochastic Control](https://mlsanity.com/paper/2210.12803/) (2022)
- [Rapid and Power-Aware Learned Optimization for Modular Receive Beamforming](https://mlsanity.com/paper/2408.00439/) (2024)
- [Optimization of Iterative Blind Detection based on Expectation Maximization and Belief Propagation](https://mlsanity.com/paper/2408.02312/) (2024)
- [Learning Flock: Enhancing Sets of Particles for Multi~Sub-State Particle Filtering with Neural Augmentation](https://mlsanity.com/paper/2408.11348/) (2024)
- [Weighted Bayesian Cramacuteer-Rao Bound for Mixed-Resolution Parameter Estimation](https://mlsanity.com/paper/2508.20761/) (2025)
- [Generative Learning for Ambisonic Upscaling](https://mlsanity.com/paper/2609.23479/) (2026)

## Abstract (arXiv)

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.