Decision Theory

APMTH 231 Subject & Catalog Number

Description

ES 201/AM 231 is a course in statistical inference and estimation from a signal processing perspective. The course will emphasize the entire pipeline from writing a model, estimating its parameters and performing inference utilizing real data. The first part of the course will focus on linear and nonlinear probabilistic generative/regression models (e.g., linear, logistic, Poisson regression), and algorithms for optimization (ML/MAP estimation) and Bayesian inference in these models. We will pay particular attention to sparsity-induced regression models, because of their relation to artificial neural networks, the topic of the second part of the course. The second part of the course will introduce students to the nascent and exciting research area of model-based deep learning and sparse auto-encoders. We will see, for instance, how neural-networks with ReLU nonlinearities arise from sparse probabilistic generative models introduced in the first part of the course. This will form the basis for a rigorous recipe we will teach you to build interpretable deep neural networks, from the ground up. More broadly, model-based deep learning and sparse auto-encoders have become popular approaches to reverse-engineer intelligence in both biological and artificial settings: in each case, we are able to train these systems to perform complicated tasks, but our understanding of how they do so remains opaque.

Reverse engineering intelligence—whether in the brain or in artificial neural networks—means using mathematical tools to reveal what information these systems truly represent. By moving beyond performance metrics to probe internal representations, we gain interpretability and transparency, with real-world benefits for the safety, fairness, and trustworthiness of modern AI and brain-machine systems

We will invite an exciting lineup of speakers. We encourage you to pursue a final project that could lead to prototype or production solutions to challenges businesses face around AI adoption due to lack of transparency.

Course Notes

Engineering Sciences 201 is the same as Applied Mathematics 231. Students may not take both for credit. The enrollment cap is for ENG-SCI 201 and APMTH 231 combined.